CN114095042B - Low-code rate biorthogonal code decoder and decoding method - Google Patents

Abstract

The invention provides a low-bit rate biorthogonal code decoder and a decoding method, wherein the decoder comprises: the two-branch decoder comprises an external information and prior information storage unit, a backward measurement calculation and storage unit and a forward measurement and posterior information calculation unit, wherein the external information and prior information storage unit is used for determining prior information based on the posterior information and the stored external information; the backward measurement calculation and storage unit is used for carrying out backward recursion estimation based on the signal to be decoded and the prior information and outputting a backward measurement value; the forward measurement and posterior information calculation unit is used for carrying out forward recursion estimation based on a signal to be decoded, the prior information and the backward measurement value and outputting a forward measurement value and posterior information; if the forward recursion estimated times reach the preset maximum iteration times, outputting a decoding result; the complexity of the structure and the realization mode of the bi-orthogonal code decoder is reduced, and the bi-orthogonal code decoder is easy to apply in engineering.

Description

Low code rate biorthogonal code decoder and decoding method

technical field

The present invention relates to the technical field of channel coding and decoding, in particular to a low code rate bi-orthogonal code decoder and a decoding method.

Background technique

Channel coding technology ensures the reliability of communication transmission by adding redundant information. As a code set with good autocorrelation and zero cross-correlation, biorthogonal codes are directly used in the transmitter to generate acquisition and synchronization sequences by using the encoder, which can greatly simplify the transmitter structure and reduce the implementation complexity. Biorthogonal-Turbo codes combine the low code rate characteristics of biorthogonal codes and the high coding gain of Turbo codes, and have good applications in low code rate communication scenarios. However, the decoding method of bi-orthogonal-Turbo codes is relatively complicated in engineering technology implementation, and a low-complexity bi-orthogonal-Turbo code decoding method is urgently needed to be applied in engineering implementation.

SUMMARY OF THE INVENTION

Aiming at the problems existing in the prior art, the present invention provides a low code rate bi-orthogonal code decoder and a decoding method.

In a first aspect, the present invention provides a low code rate bi-orthogonal code decoder, comprising:

A two-branch decoder, each branch decoder includes a first unit, a second unit and a third unit, the output of the first unit, and the first input of the second unit and the first unit at the same time. The first input terminal of the three units is connected; the output terminal of the second unit is connected to the second input terminal of the third unit; the first output terminal of the third unit is connected to the first input terminal of the first unit The second output end of the third unit is connected to the second input end of the first unit of the other branch decoder through the interleaving unit;

The first unit is configured to determine the prior information based on the posterior information and the stored extrinsic information;

The second unit is configured to perform reverse recursive estimation based on the signal to be decoded and the prior information, and output a backward metric value;

The third unit is configured to perform forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, and output the forward metric value and a posteriori information; When the number of recursive estimations reaches the preset maximum number of iterations, the decoding result is output;

The first unit is an extrinsic information and a priori information storage unit, the second unit is a backward metric calculation and storage unit, and the third unit is a forward metric and a posteriori information calculation unit.

Optionally, the first unit is configured to determine a priori information based on a posteriori information and stored extrinsic information, including:

initialize the foreign information;

Determine the prior information based on the initial value of the extrinsic information stored in the first unit and the interleaved posterior information;

The interleaved a posteriori information is a result of interleaving the a posteriori information output by the third unit.

Optionally, the second unit is configured to perform reverse recursive estimation based on the signal to be decoded and the prior information, and output a backward metric value, including:

Based on the end state of the branch decoder, initialize the backward metric value at the last moment; when the end state of the branch decoder is zero, the corresponding backward metric value is zero; when the end state of the branch decoder is non-zero , the corresponding backward metric value is the negative maximum value;

Determine the rule based on the branch metric value, and determine the branch metric value at each moment;

Based on the approximation algorithm, and the branch metric values, the corresponding backward metric values are determined by reverse recursion.

Optionally, based on the approximation algorithm and the branch metric value, the corresponding backward metric value is determined by reverse recursion:

Determine the first branch metric value corresponding to the state S when the specific branch decoder of the two branch decoders reaches the state S when the specific symbol decoding result is zero at any time t, and the first backward metric corresponding to time t+1 value;

determining a first metric sum based on the sum of the first branch metric value and the first backward metric value;

It is determined that at any time t, the decoding result of the specific symbol of the specific branch decoder in the two branch decoders is the second branch metric value corresponding to the state S reached at one time, and the second backward metric corresponding to the time t+1 value;

determining a second sum of metrics based on the sum of the second branch metric and the second backward metric;

Based on the approximation algorithm, determine the first metric value sum, and the largest of the second metric value sum and the second metric value sum is the backward metric value at time t;

normalizing the backward metric value;

Based on the initialization value of the backward metric value of the state S at time t+1, the backward recursive update of the backward metric value at all times is reversed;

Wherein, the state S is the state of the branch decoder.

Optionally, the third unit is configured to perform forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, and output the forward metric value and a posteriori information, including:

Based on the initial state of the branch decoder, initialize the forward metric value;

Determine the rule based on the branch metric value, and determine the branch metric value at each moment;

Based on the approximation algorithm and the branch metric value, forward recursion determines the corresponding forward metric value;

A posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the state of the branch decoder and the biorthogonal code matrix.

Optionally, the forward recursion determines the corresponding forward metric value based on the approximate algorithm and the branch metric value, including:

Based on the specific branch decoder in the two-branch decoder, at any time t, the decoding result of the specific symbol reaches the third branch metric value corresponding to state S when the decoding result of the specific symbol is zero, and the third forward metric value at time t-1 ;

determining a third sum of metrics based on the sum of the third branch metric and the third forward metric;

Based on the specific branch decoder in the two-branch decoder at any time t, the decoding result of the specific symbol is that the fourth branch metric value corresponding to the state S is reached at one time, and the fourth forward metric value at time t-1;

determining a fourth sum of metrics based on the sum of the fourth branch metric and the fourth forward metric;

Based on an approximation algorithm, the third metric sum is determined, and the largest of the third metric sum and the fourth metric sum is the forward metric value at time t;

normalizing the forward metric value;

Based on the initialization value of the forward metric value of the state S at time 1, forward recursively update the forward metric value at all times;

Wherein, the state S is the state of the branch decoder.

Optionally, the branch metric value determination rule includes:

Based on the bi-orthogonal code matrix, the signal to be decoded and the prior information, the bi-orthogonal code transformation metric is determined;

Based on the different states of the two branch decoders, corresponding branch metrics are determined.

Optionally, the a posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the branch decoder state and the biorthogonal code matrix, including:

determining a fifth sum of metric values based on the sum of the biorthogonal code transform metric values at time t, the forward metric value at time t, and the backward metric value at time t+1 in the first set;

determining a sixth sum of metric values based on the sum of the biorthogonal code transform metric value at time t, the forward metric value at time t, and the backward metric value at time t+1 in the second set;

Based on an approximation algorithm, determining the maximum value of the sum of the fifth metric values and the maximum value of the sum of the sixth metric values;

Determine the maximum value of the fifth metric value sum, and the difference with the maximum value of the sixth metric value sum is the posterior information of the ith symbol at time t;

The elements of the first set satisfy that when the decoding result of the i-th symbol at time t is zero, the corresponding value in the biorthogonal code matrix is +1, and the elements of the second set satisfy that the i-th symbol at time t is zero. When the decoding result of each symbol is 1, the corresponding value in the biorthogonal code matrix is -1.

Optionally, the third unit is configured to output a decoding result when the number of times of the forward recursive estimation reaches a preset maximum number of iterations, including:

If it is determined that the number of times of the forward recursive estimation reaches the preset maximum number of iterations, the decoding result is output based on the value of the posterior information and the decision function;

The decision function is that when the value of the a posteriori information is greater than or equal to zero, the output decoding result is one; when the value of the a posteriori information is less than zero, the output decoding result is zero.

Optionally, the formula of the decision function is:

为时刻t时第i个符号的后验信息，

为求符号运算，

为时 刻t时第i个符号的译码结果。 in,

is the posterior information of the ith symbol at time t,

For symbolic operations,

is the decoding result of the i-th symbol at time t.

Optionally, the first unit is further configured to update and store extrinsic information based on a posteriori information and a priori information.

Optionally, the interleaving unit is configured to perform interleaving processing on the posterior information, and output the posterior information after interleaving;

Based on the posterior information and the interleaving function, the posterior information after interleaving is determined, and the formula of the interleaving function is:

；

;

为时刻t时第i个符号的后验信息，

为时刻t交织单元对应的交织 地址，

为交织函数。 in,

is the posterior information of the ith symbol at time t,

is the interleaving address corresponding to the interleaving unit at time t,

is the interleaving function.

In a second aspect, the present invention also provides a low code rate bi-orthogonal code decoding method, comprising:

Input the signal to be decoded into the backward metric calculation and storage unit of the two-branch decoder, and the forward metric and a posteriori information calculation unit;

The backward metric calculation and storage unit performs reverse recursive estimation based on the signal to be decoded and the prior information, determines the backward metric value, and outputs it to the forward metric and a posteriori information calculation unit;

The forward metric and a posteriori information calculation unit performs forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, determines the forward metric value and a posteriori information, and outputs The a posteriori information is sent to the external information and a priori information storage unit;

The extrinsic information and a priori information storage unit determines the prior information based on the posterior information and the stored extrinsic information, and outputs it to the backward metric calculation and storage unit and the forward metric and a posteriori information calculation unit; wherein, the The posterior information includes:

Calculate the a posteriori information output by the unit based on the forward metric and posterior information of the branch decoder to which it belongs; or

The interleaved a posteriori information obtained after the a posteriori information output by the forward metric of the other branch decoder and the posterior information calculation unit is processed by the interleaving unit;

The forward metric and a posteriori information calculation unit determines that the number of forward recursive estimations reaches a preset maximum number of iterations, and outputs a decoding result of the signal to be decoded.

Optionally, the extrinsic information and a priori information storage unit determines the prior information based on the posterior information and the stored extrinsic information, including:

initialize the foreign information;

The prior information is determined based on the initial value of the extrinsic information and the interleaved posterior information.

Optionally, the backward metric calculation and storage unit performs reverse recursive estimation based on the signal to be decoded and the prior information, and determines the backward metric value, including:

Based on the end state of the branch decoder, initialize the backward metric value at the last moment; when the end state of the branch decoder is zero, the corresponding backward metric value is zero; when the end state of the branch decoder is non-zero , the corresponding backward metric value is the negative maximum value;

Determine the rule based on the branch metric value, and determine the branch metric value at each moment;

Based on the approximation algorithm, and the branch metric values, the corresponding backward metric values are determined by reverse recursion.

Optionally, based on the approximation algorithm and the branch metric value, the corresponding backward metric value is determined by reverse recursion, including:

Determine the first branch metric value corresponding to the state S when the specific branch decoder of the two branch decoders reaches the state S when the specific symbol decoding result is zero at any time t, and the first backward metric corresponding to time t+1 value;

determining a first metric sum based on the sum of the first branch metric value and the first backward metric value;

It is determined that at any time t, the decoding result of the specific symbol of the specific branch decoder in the two branch decoders is the second branch metric value corresponding to the state S reached at one time, and the second backward metric corresponding to the time t+1 value;

determining a second sum of metrics based on the sum of the second branch metric and the second backward metric;

Based on the approximation algorithm, determine the first metric value sum, and the largest of the second metric value sum and the second metric value sum is the backward metric value at time t;

normalizing the backward metric value;

Based on the initialization value of the backward metric value at time t+1, the backward recursive update of the backward metric value at all times is reversed;

Wherein, the state S is the state of the branch decoder.

Optionally, the forward metric and a posteriori information calculation unit performs forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, and determines the forward metric value and a posteriori. information, including:

Based on the initial state of the branch decoder, initialize the forward metric value;

Determine the rule based on the branch metric value, and determine the branch metric value at each moment;

Based on the approximation algorithm and the branch metric value, forward recursion determines the corresponding forward metric value;

A posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the state of the branch decoder and the biorthogonal code matrix.

Optionally, the forward recursion determines the corresponding forward metric value based on the approximate algorithm and the branch metric value, including:

Based on the specific branch decoder in the two-branch decoder, at any time t, the decoding result of the specific symbol reaches the third branch metric value corresponding to the state S when the decoding result of the specific symbol is zero, and the third forward direction corresponding to the time t-1 metric;

determining a third sum of metrics based on the sum of the third branch metric and the third forward metric;

Based on the specific branch decoder in the two-branch decoder at any time t, the decoding result of the specific symbol is that the fourth branch metric value corresponding to the state S is reached at one time, and the fourth forward metric value at time t-1;

determining a fourth sum of metrics based on the sum of the fourth branch metric and the fourth forward metric;

Based on an approximation algorithm, the third metric sum is determined, and the largest of the third metric sum and the fourth metric sum is the forward metric value at time t;

normalizing the forward metric value;

Based on the initialization value of the forward metric value of the state S at time 1, forward recursively update the forward metric value at all times;

Wherein, the state S is the state of the branch decoder.

Optionally, the branch metric value determination rule includes:

Based on the bi-orthogonal code matrix, the signal to be decoded and the prior information, the bi-orthogonal code transformation metric is determined;

Based on the different states of the two branch decoders, corresponding branch metrics are determined.

Optionally, the a posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the branch decoder state and the biorthogonal code matrix, including:

determining a fifth sum of metric values based on the sum of the biorthogonal code transform metric values at time t, the forward metric value at time t, and the backward metric value at time t+1 in the first set;

determining a sixth sum of metric values based on the sum of the biorthogonal code transform metric value at time t, the forward metric value at time t, and the backward metric value at time t+1 in the second set;

Based on an approximation algorithm, determining the maximum value of the sum of the fifth metric values and the maximum value of the sum of the sixth metric values;

Determine the maximum value of the fifth metric value sum, and the difference with the maximum value of the sixth metric value sum is the posterior information of the ith symbol at time t;

The elements of the first set satisfy that when the decoding result of the i-th symbol at time t is zero, the corresponding value in the biorthogonal code matrix is +1, and the elements of the second set satisfy that the i-th symbol at time t is zero. When the decoding result of each symbol is 1, the corresponding value in the biorthogonal code matrix is -1.

Optionally, when the forward metric and a posteriori information calculation unit determines that the number of forward recursive estimation reaches a preset maximum number of iterations, it outputs a decoding result of the signal to be decoded, including:

If it is determined that the number of times of the forward recursive estimation reaches the preset maximum number of iterations, the decoding result is output based on the value of the posterior information and the decision function;

The decision function is that when the value of the a posteriori information is greater than or equal to zero, the output decoding result is one; when the value of the a posteriori information is less than zero, the output decoding result is zero.

Optionally, the formula of the decision function is:

为时刻t时第i个符号的后验信息，

为求符号运算，

为时 刻t时第i个符号的译码结果。 in,

is the posterior information of the ith symbol at time t,

For symbolic operations,

is the decoding result of the i-th symbol at time t.

Optionally, the extrinsic information is updated and stored in the extrinsic information and a priori information storage unit based on the posterior information and the prior information.

Optionally, the posterior information output by the forward metric and posterior information calculation unit is processed by the interleaving unit, including:

Based on the posterior information and the interleaving function, the posterior information after interleaving is determined, and the formula of the interleaving function is:

；

;

为时刻t时第i个符号的后验信息，

为时刻t交织单元对应的交织 地址，

为交织函数。 in,

is the posterior information of the ith symbol at time t,

is the interleaving address corresponding to the interleaving unit at time t,

is the interleaving function.

The low code rate bi-orthogonal code decoder and decoding method provided by the present invention, through two branch decoders, simultaneously receive the signal to be decoded, each branch decoder receives the signal to be decoded and another decoder By superimposing the metric values of different codewords to determine the a priori information and a posteriori information, and using reverse recursion and forward recursion to determine the corresponding backward metric value and forward metric value, respectively, When the maximum number of iterations is reached, the decoding result is output. The complexity of the bi-orthogonal code decoder structure and implementation is reduced, and it is easy to be applied in engineering.

Description of drawings

In order to explain the present invention or the technical solutions in the prior art more clearly, the following will briefly introduce the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are the For some embodiments of the invention, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without any creative effort.

1 is a schematic structural diagram of a low code rate bi-orthogonal code decoder provided by the present invention;

FIG. 2 is a schematic flowchart of a method for decoding a low code rate biorthogonal code provided by the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention. , not all examples. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The low code rate bi-orthogonal code decoder and decoding method of the present invention will be described below with reference to FIG. 1 to FIG. 2 .

1 is a schematic structural diagram of a low code rate bi-orthogonal code decoder provided by the present invention; as shown in FIG. 1 , the low code rate bi-orthogonal code decoder includes:

A two-branch decoder, each branch decoder includes a first unit, a second unit and a third unit, the output of the first unit, and the first input of the second unit and the first unit at the same time. The first input terminal of the three units is connected; the output terminal of the second unit is connected to the second input terminal of the third unit; the first output terminal of the third unit is connected to the first input terminal of the first unit The second output end of the third unit is connected to the second input end of the first unit of the other branch through the interleaving unit;

The first unit is an extrinsic information and a priori information storage unit 110 , the second unit is a backward metric calculation and storage unit 120 , and the third unit is a forward metric and a posteriori information calculation unit 130 .

The first unit is configured to determine the prior information based on the posterior information and the stored extrinsic information;

The second unit is configured to perform reverse recursive estimation based on the signal to be decoded and the prior information, and output a backward metric value;

The third unit is configured to perform forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, and output the forward metric value and a posteriori information; When the number of recursive estimations reaches the preset maximum number of iterations, the decoding result is output.

The first unit is an extrinsic information and a priori information storage unit, the second unit is a backward metric calculation and storage unit, and the third unit is a forward metric and a posteriori information calculation unit.

Specifically, the low code rate bi-orthogonal code decoder includes two branch decoders, and each branch decoder mainly includes: an extrinsic information and a priori information storage unit 110 , a backward metric calculation and storage unit 120 And the forward metric and a posteriori information calculation unit 130 further includes an interleaving unit 140. The a posteriori information output by one branch decoder is input into the extrinsic information and a priori information storage unit of another branch decoder after interleaving.

For the extrinsic information and a priori information storage unit 110, the input includes the forward metric of the branch decoder and the posterior information output by the posterior information calculation unit 130, and the forward metric and a posteriori information in another branch decoder The a posteriori information output by the computing unit 130 is subjected to an interleaving unit to generate interleaved a posteriori information. Calculate the prior information. The prior information is used as the first input of the backward metric calculation and storage unit 120 , and is also used as the first input of the forward metric and a posteriori information calculation unit 130 . In addition, operations such as initialization of extrinsic information, updating of extrinsic information, and updating of prior information may also be involved.

The backward metric calculation and storage unit 120 inputs the external information of the branch decoder and the a priori information output by the prior information storage unit 110, and the signal to be decoded; the backward metric value is obtained by calculating, and the backward metric value is used as The second input of the forward metric and a posteriori information calculation unit 130 .

The forward metric and a posteriori information calculation unit 130 inputs the extrinsic information of the branch decoder and the prior information output from the prior information storage unit 110, the backward metric value output from the backward metric calculation and storage unit 120, and the band Decoding signal; calculate the forward metric value and a posteriori information, as the first input of the outer information and a priori information storage unit 110, and simultaneously calculate the forward metric and a posteriori information calculation unit of another branch decoder to obtain The interleaving result of the posterior information of , is used as the second input of the extrinsic information of the branch decoder and the prior information storage unit 110 .

The direction metric calculation and storage unit 120 of the branch decoder receives the signal to be decoded, as well as the a priori information calculated by the above-mentioned extrinsic information and a priori information storage unit 110, and adopts a reverse recursion method to determine the posterior to measure. At the same time, the forward metric and a posteriori information calculation unit 130 of the branch decoder also receives the signal to be decoded, the backward metric value calculated by the backward metric calculation and storage unit 120, the external information and the prior information The priori information calculated by the empirical information storage unit 110 is used to determine the forward metric values at all times and the posterior information by means of forward recursion; The recursive relationship between the forward metric value at a moment and the forward metric value at the current moment, determine the forward metric values from time 1 to time k in turn, and combine the previously determined backward metric values to determine the corresponding posterior information .

The above processing steps are performed in an iterative manner. The forward metric and a posteriori information calculation unit 130 judges the number of iterations, determines that the preset maximum number of iterations has been reached, and outputs the decoding result. The signal to be decoded is a concatenated code of a turbo code and a biorthogonal code, which is a kind of turbo code. Turbo code was proposed at the International Conference on Communications (ICC) in 1993 as a parallel concatenated convolutional code, which transmits external information through two soft-input-soft-output maximum a posteriori probability decoders to achieve In order to achieve iterative decoding close to the Shannon limit, this long code with pseudo-random properties realized by a pseudo-random interleaver is a "good code" in Shannon's theory.

The low code rate bi-orthogonal code decoder provided by the present invention receives the signal to be decoded simultaneously through two branch decoders, and each branch decoder receives the signal to be decoded and the posterior information of another decoder, By superimposing the metric values of different codewords, the prior information and the posterior information are determined, and the reverse and forward recursion are used to determine the corresponding backward metric value and forward metric value respectively. When the maximum number of iterations is reached , output the decoding result. The complexity of the bi-orthogonal code decoder structure and implementation is reduced, and it is easy to be applied in engineering.

Optionally, the first unit is configured to determine a priori information based on a posteriori information and stored extrinsic information, including:

initialize the foreign information;

Determine the prior information based on the initial value of the extrinsic information stored in the first unit and the interleaved posterior information;

The interleaved a posteriori information is a result of interleaving the a posteriori information output by the third unit.

Specifically, when the low code rate bi-orthogonal decoder works, it needs to initialize the external information first, and the specific formula is:

为外信息，

为时间序号。

为待译码信号的比特长度。上述外 信息

表示一个集合，包括在时刻t所有符号对应的外信息的初始值。 in,

for external information,

is the time sequence number.

is the bit length of the signal to be decoded. The above external information

Represents a set, including the initial value of extrinsic information corresponding to all symbols at time t.

After the initialization of the extrinsic information is completed, it is stored in the extrinsic information and prior information storage unit 110 . Then, the prior information is calculated by the input interleaved posterior information and the stored extrinsic information,

为输入的交织后的后验信息，

为先验信息，

为时间序号。 且该

是另一分支译码器的前向度量及后验信息计算单元130输出的后验信息经过交织 单元进行交织处理后，输入该分支译码器的外信息及先验信息存储单元110。 in,

is the a posteriori information after the input interleaving,

for the prior information,

is the time sequence number. and the

The a posteriori information output by the forward metric and a posteriori information calculation unit 130 of another branch decoder is input to the extrinsic information and a priori information storage unit 110 of the branch decoder after the interleaving unit performs interleaving processing.

Optionally, the second unit is configured to perform reverse recursive estimation based on the signal to be decoded and the prior information, and output a backward metric value, including:

Based on the end state of the branch decoder, initialize the backward metric value at the last moment; when the end state of the branch decoder is zero, the corresponding backward metric value is zero; when the end state of the branch decoder is non-zero , the corresponding backward metric value is the negative maximum value;

Determine the rule based on the branch metric value, and determine the branch metric value at each moment;

Based on the approximation algorithm, and the branch metric values, the corresponding backward metric values are determined by reverse recursion.

Specifically, the backward metric calculation and storage unit 120 receives the signal to be decoded, and the a priori information calculated by the above extrinsic information and a priori information storage unit 110, and uses a reverse recursion method to determine the backward direction at all times. metric.

The backward metric calculation and storage unit 120 first initializes the backward metric value. If the end state of the component decoder is zero, the initialization method is as follows:

为分支译码器的状态序号，

为分量译码器缓存阶数，

为一个预设的最大值，该预设的最大值可以根据译码器采用的码字具体确定。分支译码器 的每个状态序号s对应分支译码器的一个状态S。且分支译码器在每个时刻t可能存在多个 序号，每个序号对应一个状态。上述状态S可能包括多个状态值，这个状态值的范围是[0, 2^m-1]，对应的状态序号s取值也是多个取值，状态序号的取值范围也是[0,2^m-1]。译码的过 程相当于确定待译码的每个符号对应的被译码为正确结果是每个符号被译码为可能性最 大的特定结果。 in,

is the state sequence number of the branch decoder,

is the cache order of the component decoder,

is a preset maximum value, and the preset maximum value can be specifically determined according to the codeword used by the decoder. Each state number s of the branch decoder corresponds to a state S of the branch decoder. And the branch decoder may have multiple sequence numbers at each time t, and each sequence number corresponds to a state. The above state S may include multiple state values. The range of this state value is [0, 2 ^m -1]. The corresponding state serial number s has multiple values, and the value range of the state serial number is also [0, 2 ^m . -1]. The decoding process is equivalent to determining that the decoded correct result corresponding to each symbol to be decoded is a specific result with the highest probability that each symbol is decoded.

If the end state of the component decoder is non-zero, the initialization method is as follows:

After initialization, the branch metric value at each moment is determined according to the branch metric value determination rule.

Specifically, the branch metric determination rule includes:

Based on the bi-orthogonal code matrix, the signal to be decoded and the prior information, the bi-orthogonal code transformation metric is determined;

The formula for calculating the biorthogonal code transformation metric is as follows:

为在时刻t的双正交码变化度量值，

为第

列双正交码矩阵，

为 待译码信号，

为先验信息，

为时间序号，

表示变量

和 变量

之和的内积。 in,

is the biorthogonal code variation metric value at time t,

for the first

column biorthogonal code matrix,

is the signal to be decoded,

for the prior information,

is the time sequence number,

represents a variable

and variable

The inner product of the sum.

是先根据编码器采用的码字，确定对应的码长，在码字库中 找出满足该长度的所有码字，进而确定对应的双正交码矩阵h，其中行数表示码字的长度， 列数表示存在多少个相同码字长度的码字。双正交码矩阵是先验已知的二元矩阵，由+1和- 1构成。 The biorthogonal code matrix

It is to first determine the corresponding code length according to the code words used by the encoder, find all code words that satisfy the length in the code word library, and then determine the corresponding biorthogonal code matrix h, where the number of rows represents the length of the code word, The number of columns indicates how many codewords of the same codeword length exist. A biorthogonal code matrix is a binary matrix known a priori, consisting of +1 and -1.

Based on the different states of the two branch decoders, corresponding branch metrics are determined.

The formula for calculating the branch measure is as follows:

为时刻

状态

时的双正交码变换度量值，

为时刻

状态

时的分支度量值。从状态

转变为状态

，可能存在两种方式，在状态

，某个 或某些符号的译码结果为0达到状态

，即上述某个或者某些符号的译码结果为0的可能性 最大，或者在状态

，某个或某些符号的译码结果为1达到状态

，即上述某个或者某些符 号的译码结果为1的可能性最大；且状态

对应的状态序号为

，状态

对应的状态序号为

。 in,

for the moment

state

The biorthogonal code transform metric value when ,

for the moment

state

The branch metric value at . from the state

transition to state

, there may be two ways, in the state

, the decoding result of one or some symbols is 0 to reach the state

, that is, the decoding result of the above-mentioned one or some symbols is most likely to be 0, or in the state of

, the decoding result of one or some symbols is 1 to reach the state

, that is, the decoding result of one or some of the above symbols is most likely to be 1; and the state

The corresponding state serial number is

,state

The corresponding state serial number is

.

After determining the branch metric value at each moment, an approximation algorithm is used to determine the probability that the decoding result of each symbol at each moment is 0 or 1 when the decoding end state is reached, and the higher probability is determined as the correct symbol at this moment. the decoding result. And based on the initialized value of the backward metric value at the last moment, the recursive relationship between the backward metric value of the previous moment and the backward metric value of the current moment, the backward metric values from time k to time 1 are sequentially determined, This reverse recursion determines the backward metric value. Finally, the backward metric calculation and storage unit 120 outputs it to the forward metric and a posteriori information calculation unit 130 . The value of time k here is the bit length of the signal to be decoded.

Optionally, based on the approximation algorithm and the branch metric value, the corresponding backward metric value is determined by reverse recursion:

Determine the first branch metric value corresponding to the state S when the specific branch decoder of the two branch decoders reaches the first branch metric value corresponding to the state S when the decoding result of the specific symbol is zero at any time t, and the first backward direction corresponding to the time t+1 metric;

determining a first metric sum based on the sum of the first branch metric value and the first backward metric value;

It is determined that at any time t, the decoding result of the specific symbol of the specific branch decoder in the two branch decoders is the second branch metric value corresponding to the state S reached at one time, and the second backward metric value at time t+1 ;

determining a second sum of metrics based on the sum of the second branch metric and the second backward metric;

Based on the approximation algorithm, determine the first metric value sum, and the largest of the second metric value sum and the second metric value sum is the backward metric value at time t;

normalizing the backward metric value;

Based on the initialization value of the backward metric value of the state S at time t+1, the backward recursive update of the backward metric value at all times is reversed;

Wherein, the state S is the state of the branch decoder.

，

，更新后向 度量计算值，具体公式为： Specifically, in the backward metric calculation and storage unit 120, based on

,

, update the calculated value of the backward measure, the specific formula is:

为时间序号。

表示待译码信号中的某个或某些符号在时 刻t被译码为0，使得译码器的状态从

转换到

，同理，

表示待译码信号中的某 个或某些符号在时刻t被译码为1，使得译码器的状态从

转换到

。分支译码器状态

对 应的状态序号为

，分支译码器状态

对应的状态序号为

，分支译码器状态

对应 的状态序号为

。分支译码器的每个状态和对应的状态序号一一对应。且每个时刻t，分支 译码器的状态包括多个，对应的状态序号也有多个。 in,

is the time sequence number.

Indicates that one or some symbols in the signal to be decoded are decoded to 0 at time t, so that the state of the decoder changes from

convert to

, similarly,

Indicates that one or some symbols in the signal to be decoded are decoded as 1 at time t, so that the state of the decoder changes from

convert to

. Branch Decoder Status

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

. Each state of the branch decoder has a one-to-one correspondence with the corresponding state number. And at each time t, there are multiple states of the branch decoder, and there are multiple corresponding state numbers.

The recursive relationship between the backward metric value at the previous moment and the backward metric value at the current moment is determined according to the above formula.

为一个组合，确定这个组合中的最大值，并用

中的每 个值减去这个最大值对其进行归一化处理，具体公式为：

Then, there may be multiple symbols in the signal to be decoded at the same time, which can make the state corresponding to the decoder satisfy the above formula, that is, the determined

For a combination, determine the maximum value in this combination, and use

Each value in is normalized by subtracting this maximum value by the formula:

。 Reverse recursion in turn, update the backward metric to

.

，

，

至后向度量计算及存储单元 120。 output and store

,

,

to the backward metric calculation and storage unit 120 .

Optionally, the third unit is configured to perform forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, and output the forward metric value and a posteriori information, including:

Based on the initial state of the branch decoder, initialize the forward metric value;

Determine the rule based on the branch metric value, and determine the branch metric value at each moment;

Based on the approximation algorithm and the branch metric value, forward recursion determines the corresponding forward metric value;

A posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the state of the branch decoder and the biorthogonal code matrix.

Specifically, while the backward metric calculation and storage unit 120 determines the corresponding backward metric value according to the to-be-decoded signal, the to-be-decoded signal is also input to the forward metric and a posteriori information calculation unit 130, in which the approximation is also used. Algorithm, forward recursion to determine the corresponding forward metric value and a posteriori information.

The forward metric value is initialized in the forward metric and a posteriori information calculation unit 130, and the initialization method is as follows:

为分支译码器的状态序号，

为分量译码器缓存阶数，

为一个预设的最大值，是一个在合理位宽内的达到的最大值，具体可根据编码的码长确定。

为

时刻状态

的前向度量值，状态

对应的状态序号为

。分支译码器的每个状态 序号对应分支译码器的一个状态。 in,

is the state sequence number of the branch decoder,

is the cache order of the component decoder,

is a preset maximum value, which is a maximum value reached within a reasonable bit width, which can be specifically determined according to the encoded code length.

for

state of the moment

The forward measure of , the state

The corresponding state serial number is

. Each state number of the branch decoder corresponds to a state of the branch decoder.

After initialization, the branch metric value at each moment is determined according to the branch metric value determination rule.

The specific method for determining the branch metric value at each moment is the same as that in the backward metric calculation and storage unit 120, which is not repeated here.

After determining the branch metric value at each moment, an approximation algorithm is used to determine the probability that the decoding result of each symbol at each moment is 0 or 1 when the decoding end state is reached, and the higher probability is determined as the correct symbol at this moment. the decoding result. And based on the initialized value of the forward metric value at time 1, the recursive relationship between the forward metric value at the previous time and the forward metric value at the current time, determine the forward metric from time 1 to time k+1 in turn. value, so that forward recursion determines the forward metric value. The value of time k here is the bit length of the signal to be decoded.

After the forward metric value is determined, the a posteriori information is determined according to the approximation algorithm, the state of the branch decoder and the preset rule determined by the biorthogonal code matrix.

Optionally, the forward recursion determines the corresponding forward metric value based on the approximate algorithm and the branch metric value, including:

Based on the specific branch decoder in the two-branch decoder, at any time t, the decoding result of the specific symbol reaches the third branch metric value corresponding to state S when the decoding result of the specific symbol is zero, and the third forward metric corresponding to the time t-1 value;

determining a third sum of metrics based on the sum of the third branch metric and the third forward metric;

Based on the specific branch decoder in the two-branch decoder at any time t, the decoding result of the specific symbol is that the fourth branch metric value corresponding to the state S is reached at one time, and the fourth forward metric value at time t-1;

determining a fourth sum of metrics based on the sum of the fourth branch metric and the fourth forward metric;

Based on an approximation algorithm, the third metric sum is determined, and the largest of the third metric sum and the fourth metric sum is the forward metric value at time t;

normalizing the forward metric value;

Based on the initialization value of the forward metric value of the state S at time 1, forward recursively update the forward metric value at all times;

Wherein, the state S is the state of the branch decoder.

Specifically, in the forward metric and a posteriori information calculation unit 130, based on

，

，更新 前向度量计算值， For example, assuming the initial value of the backward metric value at the last moment, and then according to

,

, update the calculated value of the forward metric,

为时间序号。

表示待译码信号中的某个或者某些符 号在时刻t被译码为0，使得译码器的状态从

转换到

，同理，

表示待译码信号 中的某个或者某些符号在时刻t被译码为1，使得译码器的状态从

转换到

，其中，u代 表任意一个符号。分支译码器状态

对应的状态序号为

，分支译码器状态

对应的状态 序号为

，分支译码器状态

对应的状态序号为

。分支译码器的每个状态和对应的 状态序号一一对应。 in,

is the time sequence number.

Indicates that one or some symbols in the signal to be decoded are decoded to 0 at time t, so that the state of the decoder changes from

convert to

, similarly,

Indicates that one or some symbols in the signal to be decoded are decoded as 1 at time t, so that the state of the decoder changes from

convert to

, where u represents any symbol. Branch Decoder Status

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

. Each state of the branch decoder has a one-to-one correspondence with the corresponding state number.

The recursive relationship between the forward metric value at the previous moment and the forward metric value at the current moment is determined according to the above formula.

为一个组合，确定这个组合中的最大值，并用

中的每个值减去这个最大值对其进行归一化处理，具体公式为：

；其中，

为归一化处理后的前向度量值。 Then, there may be multiple symbols in the signal to be decoded at the same time, which can make the state corresponding to the decoder satisfy the above formula, that is, the determined forward metric value

For a combination, determine the maximum value in this combination, and use

Each value in is normalized by subtracting this maximum value by the formula:

;in,

is the normalized forward metric value.

。 Forward recursion in turn, update the forward metric to

.

至前向度量及后验信息计算 单元130。 output and store

to the forward metric and a posteriori information calculation unit 130 .

After the forward metric value is determined, the forward metric and a posteriori information calculation unit 130 determines the posterior information again according to the approximation algorithm.

Optionally, a posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the branch decoder state and the biorthogonal code matrix, including:

determining a fifth sum of metric values based on the sum of the biorthogonal code transform metric values at time t, the forward metric value at time t, and the backward metric value at time t+1 in the first set;

determining a sixth sum of metric values based on the sum of the biorthogonal code transform metric value at time t, the forward metric value at time t, and the backward metric value at time t+1 in the second set;

Based on an approximation algorithm, determining the maximum value of the sum of the fifth metric values and the maximum value of the sum of the sixth metric values;

Determine the maximum value of the fifth metric value sum, and the difference with the maximum value of the sixth metric value sum is the posterior information of the ith symbol at time t;

The elements of the first set satisfy that when the decoding result of the i-th symbol at time t is zero, the corresponding value in the biorthogonal code matrix is +1, and the elements of the second set satisfy that the i-th symbol at time t is zero. When the decoding result of each symbol is 1, the corresponding value in the biorthogonal code matrix is -1.

Specifically, the forward metric and a posteriori information calculation unit 130 calculates the posterior information according to the following formula:

表示满足

的状态且

对应的前向度量值，后向度 量值以及双正交码变换度量值的集合，

表示满足

的状态且

对应 的前向度量值，后向度量值以及双正交码变换度量值的集合，

为时刻

第

个符号的 后验信息。

表示待译码信号中的某个或者某些符号在时刻t被译码为0，使得译码 器的状态从

转换到

，且在双正交码矩阵中对应位

的值为+1，同理，

表 示待译码信号中的某个或者某些符号在时刻t被译码为1，使得译码器的状态从

转换到

，且在双正交矩阵码矩阵中对应位

的值为-1，

表示双正交码矩阵的第j列的第 i个符号对应的码字，其中，u代表任意一个符号。分支译码器状态

对应的状态序号为

，分 支译码器状态

对应的状态序号为

，分支译码器状态

对应的状态序号为

。分 支译码器的每个状态和对应的状态序号一一对应。 in,

express satisfaction

state and

Corresponding forward metric value, backward metric value and set of biorthogonal code transform metric value,

express satisfaction

state and

Corresponding forward metric value, backward metric value and set of biorthogonal code transform metric value,

for the moment

the first

a posteriori information of the symbols.

Indicates that one or some symbols in the signal to be decoded are decoded to 0 at time t, so that the state of the decoder changes from

convert to

, and the corresponding bits in the biorthogonal code matrix

The value of is +1, in the same way,

Indicates that one or some symbols in the signal to be decoded are decoded as 1 at time t, so that the state of the decoder changes from

convert to

, and the corresponding bits in the biorthogonal matrix code matrix

is -1,

Indicates the codeword corresponding to the i-th symbol in the j-th column of the biorthogonal code matrix, where u represents any symbol. Branch Decoder Status

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

. Each state of the branch decoder has a one-to-one correspondence with the corresponding state number.

The calculated posterior information is output to the extrinsic information storage unit and the interleaving unit 110 .

Optionally, the third unit is configured to output a decoding result when the number of times of the forward recursive estimation reaches a preset maximum number of iterations, including:

If it is determined that the number of times of the forward recursive estimation reaches the preset maximum number of iterations, the decoding result is output based on the value of the posterior information and the decision function;

The decision function is that when the value of the a posteriori information is greater than or equal to zero, the output decoding result is one; when the value of the a posteriori information is less than zero, the output decoding result is zero.

Specifically, the forward metric and a posteriori information calculation unit 130 determines whether the number of iterations of the branch decoder reaches a preset maximum number of iterations, and if it reaches the preset maximum number of iterations, according to the value of the posterior information and the decision function , and output the decoding result. That is, it is determined that the number of iterations of the branch decoder is greater than or equal to the preset threshold, and the decoding result is output. The preset threshold value may be determined according to the analysis of the previous statistical results or an initial value may be artificially set, and adjusted in the subsequent calculation process to find the most suitable value of the preset threshold value. The low code rate bi-orthogonal code decoder provided by the present invention is composed of two branch decoders. After the loop iteration reaches a certain number of times, the results of the two branch decoders tend to converge. Both the forward metric and a posteriori information calculation unit of the decoder can determine whether the number of iterations reaches a preset threshold, and output the decoding result.

The formula corresponding to the decision function is:

为时刻t时第i个符号的后验信息，

为求符号运算，

为时 刻t时第i个符号的译码结果。 in,

is the posterior information of the ith symbol at time t,

For symbolic operations,

is the decoding result of the i-th symbol at time t.

Optionally, the first unit is further configured to update and store extrinsic information based on a posteriori information and a priori information.

Specifically, the extrinsic information and prior information storage unit 110 can not only store extrinsic information and prior information, but also update the stored extrinsic information according to the posterior information and prior information. The specific formula is:

为先验信息，

为时刻t时第i个符号的后验信息，

为存储的 外信息，

为更新后的外信息，

为时间序号。并且先验信息

，存储的外 信息

以及更新后的外信息

均表示一个集合，对应不同的i值，均有集合中的一个 值与其对应。同样，先验信息

也表示一个集合，对应不同的i值，均有集合中的一个值与 其对应。其中，i表示第i个符号。 in,

for the prior information,

is the posterior information of the ith symbol at time t,

For stored foreign information,

For updated external information,

is the time sequence number. and prior information

, the stored foreign information

and updated external information

Both represent a set, corresponding to different i values, and each has a value in the set corresponding to it. Likewise, prior information

It also represents a set, corresponding to different i values, there is a value in the set corresponding to it. where i represents the ith symbol.

Optionally, the interleaving unit is configured to perform interleaving processing on the posterior information, and output the posterior information after interleaving;

Based on the posterior information and the interleaving function, the posterior information after interleaving is determined, and the formula of the interleaving function is:

；

;

为时刻t时第i个符号的后验信息，

为时刻t交织单元对应的交织 地址，

为交织函数。具体的，

为时刻t交织单元对应的交织地址表示一个集合，包括 在时刻t所有符号的交织单元对应的交织地址。具体含义为：将信号

按照交织地址

的顺序重新排列。 in,

is the posterior information of the ith symbol at time t,

is the interleaving address corresponding to the interleaving unit at time t,

is the interleaving function. specific,

The interleaving addresses corresponding to the interleaving units at time t represent a set, including the interleaving addresses corresponding to the interleaving units of all symbols at time t. The specific meaning is: the signal

By interleaved address

rearranged in order.

The low code rate bi-orthogonal code decoder provided by the present invention receives the signal to be decoded simultaneously through two branch decoders, and each branch decoder receives the signal to be decoded and the posterior information of another decoder, By superimposing the metric values of different codewords, the prior information and the posterior information are determined, and the reverse and forward recursion are used to determine the corresponding backward metric value and forward metric value respectively. When the maximum number of iterations is reached , output the decoding result. The complexity of the bi-orthogonal code decoder structure and implementation is reduced, and it is easy to be applied in engineering.

FIG. 2 is a schematic flowchart of a method for decoding a low code rate bi-orthogonal code provided by the present invention. As shown in FIG. 2 , the method includes:

Step 201: Input the signal to be decoded into the backward metric calculation and storage unit and the forward metric and a posteriori information calculation unit of the two-branch decoder.

Step 202, the backward metric calculation and storage unit performs reverse recursive estimation based on the signal to be decoded and the prior information, determines the backward metric value, and outputs it to the forward metric and a posteriori information calculation unit;

Step 203: The forward metric and a posteriori information calculation unit performs forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, and determines the forward metric value and a posteriori information , and output the a posteriori information to the external information and a priori information storage unit;

Step 204, the external information and a priori information storage unit determines the a priori information based on the a posteriori information and the stored external information, and outputs to the backward metric calculation and storage unit and the forward metric and a posteriori information calculation unit; The posterior information includes:

Calculate the a posteriori information output by the unit based on the forward metric and posterior information of the branch decoder to which it belongs; or

The interleaved a posteriori information obtained after the a posteriori information output by the forward metric of the other branch decoder and the posterior information calculation unit is processed by the interleaving unit;

Step 205: When the forward metric and a posteriori information calculation unit determines that the number of forward recursive estimations reaches a preset maximum number of iterations, the decoding result of the signal to be decoded is output.

Specifically, specifically, the low code rate biorthogonal code decoding method provided by the embodiment of the present invention is implemented based on the above-mentioned decoder. The low bit rate bi-orthogonal code decoding method is inputting the to-be-decoded signal to the backward metric calculation and storage unit and the forward metric and a posteriori information calculation unit of the two-branch decoder.

The extrinsic information and a priori information storage unit determines the prior information based on the posterior information and the stored extrinsic information, and outputs it to the backward metric calculation and storage unit and the forward metric and a posteriori information calculation unit; wherein, the The posterior information includes:

Calculate the a posteriori information output by the unit based on the forward metric and posterior information of the branch decoder to which it belongs; or

The a posteriori information after the interleaving after the a posteriori information output by the forward metric of the other branch decoder and the posterior information calculation unit is processed by the interleaving unit;

Determine the prior information based on the initialized extrinsic information, and the result of the interleaving unit processing the posterior information output by the forward metric and the posterior information computing unit;

The above-mentioned prior information is respectively input into the backward metric calculation and storage unit, and the forward metric and a posteriori information calculation unit.

The direction metric calculation and storage unit uses reverse recursive estimation on the signal to be decoded and the a priori information to determine the backward metric value. For example, by presetting the initial value of the backward measurement value at the last moment, and combining the relationship between the backward measurement value at the previous moment and the backward measurement value at the current moment, the backward measurement value at all times can be determined and output to the forward measurement and A posteriori information calculation unit.

The forward metric and a posteriori information calculation unit performs forward recursive estimation on the signal to be decoded, the above-mentioned prior information, and the backward metric value output to the metric calculation and storage unit, and determines the forward metric value and Posterior information. For example, by presetting the initial value of the forward metric value at time 1, and combining the relationship between the forward metric value at the next time and the backward metric value at the current time, the forward metric values at all times can be determined, and the posterior value can be output. Information to external information and a priori information storage unit.

When the forward metric and a posteriori information calculation unit determines that the number of iterations of the forward recursive estimation in the above steps reaches the maximum value, it outputs a decoding result determined based on the posteriori information.

The method for decoding a low bit rate bi-orthogonal code provided by the present invention uses two branch decoders to simultaneously receive the signal to be decoded, and each branch decoder receives the signal to be decoded and the a posteriori information of another decoder. , by superimposing the metric values of different codewords to determine a priori information and a posteriori information, and using reverse recursion and forward recursion to determine the corresponding backward metric value and forward metric value, respectively, when the maximum iteration is reached When the number of times, the decoding result is output. The complexity of the bi-orthogonal code decoder structure and implementation is reduced, and it is easy to be applied in engineering.

Optionally, the extrinsic information and a priori information storage unit determines the prior information based on the posterior information and the stored extrinsic information, including:

initialize the foreign information;

The prior information is determined based on the initial value of the extrinsic information and the interleaved posterior information.

Optionally, the backward metric calculation and storage unit performs reverse recursive estimation based on the signal to be decoded and the prior information, and determines the backward metric value, including:

Based on the end state of the branch decoder, initialize the backward metric value at the last moment; when the end state of the branch decoder is zero, the corresponding backward metric value is zero; when the end state of the branch decoder is non-zero , the corresponding backward metric value is the negative maximum value;

Determine the rule based on the branch metric value, and determine the branch metric value at each moment;

Based on the approximation algorithm, and the branch metric values, the corresponding backward metric values are determined by reverse recursion.

Optionally, based on the approximation algorithm and the branch metric value, the corresponding backward metric value is determined by reverse recursion, including:

Determine the first branch metric value corresponding to the state S when the specific branch decoder of the two branch decoders reaches the state S when the specific symbol decoding result is zero at any time t, and the first backward metric corresponding to time t+1 value;

determining a first metric sum based on the sum of the first branch metric value and the first backward metric value;

It is determined that at any time t, the decoding result of the specific symbol of the specific branch decoder in the two branch decoders is the second branch metric value corresponding to the state S reached at one time, and the second backward metric corresponding to the time t+1 value;

determining a second sum of metrics based on the sum of the second branch metric and the second backward metric;

Based on the approximation algorithm, determine the first metric value sum, and the largest of the second metric value sum and the second metric value sum is the backward metric value at time t;

normalizing the backward metric value;

Based on the initialization value of the backward metric value at time t+1, the backward recursive update of the backward metric value at all times is reversed;

Wherein, the state S is the state of the branch decoder.

Optionally, the forward metric and a posteriori information calculation unit performs forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, and determines the forward metric value and a posteriori. information, including:

Based on the initial state of the branch decoder, initialize the forward metric value;

Determine the rule based on the branch metric value, and determine the branch metric value at each moment;

Based on the approximation algorithm and the branch metric value, forward recursion determines the corresponding forward metric value;

A posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the state of the branch decoder and the biorthogonal code matrix.

Optionally, the forward recursion determines the corresponding forward metric value based on the approximate algorithm and the branch metric value, including:

Based on the specific branch decoder in the two-branch decoder, at any time t, the decoding result of the specific symbol reaches the third branch metric value corresponding to the state S when the decoding result of the specific symbol is zero, and the third forward direction corresponding to the time t-1 metric;

determining a third sum of metrics based on the sum of the third branch metric and the third forward metric;

Based on the specific branch decoder in the two-branch decoder at any time t, the decoding result of the specific symbol is that the fourth branch metric value corresponding to the state S is reached at one time, and the fourth forward metric value at time t-1;

determining a fourth sum of metrics based on the sum of the fourth branch metric and the fourth forward metric;

Based on an approximation algorithm, the third metric sum is determined, and the largest of the third metric sum and the fourth metric sum is the forward metric value at time t;

normalizing the forward metric value;

Based on the initialization value of the forward metric value of the state S at time 1, forward recursively update the forward metric value at all times;

Wherein, the state S is the state of the branch decoder.

Optionally, the branch metric value determination rule includes:

Based on the bi-orthogonal code matrix, the signal to be decoded and the prior information, the bi-orthogonal code transformation metric is determined;

Based on the different states of the two branch decoders, corresponding branch metrics are determined.

Optionally, the a posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the branch decoder state and the biorthogonal code matrix, including:

determining a fifth sum of metric values based on the sum of the biorthogonal code transform metric values at time t, the forward metric value at time t, and the backward metric value at time t+1 in the first set;

determining a sixth sum of metric values based on the sum of the biorthogonal code transform metric value at time t, the forward metric value at time t, and the backward metric value at time t+1 in the second set;

Based on an approximation algorithm, determining the maximum value of the sum of the fifth metric values and the maximum value of the sum of the sixth metric values;

Determine the maximum value of the fifth metric value sum, and the difference with the maximum value of the sixth metric value sum is the posterior information of the ith symbol at time t;

The elements of the first set satisfy that when the decoding result of the i-th symbol at time t is zero, the corresponding value in the biorthogonal code matrix is +1, and the elements of the second set satisfy that the i-th symbol at time t is zero. When the decoding result of each symbol is 1, the corresponding value in the biorthogonal code matrix is -1.

Optionally, when the forward metric and a posteriori information calculation unit determines that the number of forward recursive estimation reaches a preset maximum number of iterations, it outputs a decoding result of the signal to be decoded, including:

If it is determined that the number of times of the forward recursive estimation reaches the preset maximum number of iterations, the decoding result is output based on the value of the posterior information and the decision function;

The decision function is that when the value of the a posteriori information is greater than or equal to zero, the output decoding result is one; when the value of the a posteriori information is less than zero, the output decoding result is zero.

Optionally, the formula of the decision function is:

为时刻t时第i个符号的后验信息，

为求符号运算，

为时 刻t时第i个符号的译码结果。 in,

is the posterior information of the ith symbol at time t,

For symbolic operations,

is the decoding result of the i-th symbol at time t.

Optionally, the extrinsic information is updated and stored in the extrinsic information and a priori information storage unit based on the posterior information and the prior information.

Optionally, the posterior information output by the forward metric and posterior information calculation unit is processed by the interleaving unit, including:

Based on the posterior information and the interleaving function, the posterior information after interleaving is determined, and the formula of the interleaving function is:

；

;

为时刻t时第i个符号的后验信息，

为时刻t交织单元对应的交织 地址，

为交织函数。具体的，

为时刻t交织单元对应的交织地址表示一个集合，包括 在时刻t所有符号的交织单元对应的交织地址。 in,

is the posterior information of the ith symbol at time t,

is the interleaving address corresponding to the interleaving unit at time t,

is the interleaving function. specific,

The interleaving addresses corresponding to the interleaving units at time t represent a set, including the interleaving addresses corresponding to the interleaving units of all symbols at time t.

Described below with specific embodiments:

The low code rate biorthogonal code decoding method provided by the present invention includes the following steps:

Step 1: Initialize the external information storage unit, and set the stored information to zero. A posteriori information output by another decoder is received, and a priori information is calculated.

Initialize the external information storage unit, set the information to zero,

为外信息，

为时间序号。

为待译码信号的比特长度。上述外 信息

表示一个集合，包括在时刻t所有符号对应的外信息的初始值。 in,

for external information,

is the time sequence number.

is the bit length of the signal to be decoded. The above external information

Represents a set, including the initial value of extrinsic information corresponding to all symbols at time t.

The prior information is calculated by inputting the interleaved posterior information and the stored extrinsic information,

为输入的交织后的后验信息，

为先验信息，

为时间序 号。 in,

is the a posteriori information after the input interleaving,

for the prior information,

is the time sequence number.

Step 2: The backward metric calculation unit reads the a priori information output by the external information storage unit, calculates the backward metric value by using the channel information and the prior information, and stores it in the backward metric storage unit.

The backward metric value is initialized first in the backward metric calculation unit. If the component decoder end state is zero, the initialization method is as follows:

为分支译码器的状态序号，

为分支译码器缓存阶数，

为预设的最大值，是一个在合理位宽内的达到的最大值。具体可根据编码的码长确定，分支 译码器的每个状态序号

对应分支译码器的状态

。 in,

is the state sequence number of the branch decoder,

is the cache order for the branch decoder,

is the preset maximum value, which is an attainable maximum value within a reasonable bit width. Specifically, it can be determined according to the code length of the encoding, and the sequence number of each state of the branch decoder

The state of the corresponding branch decoder

.

If the end state of the component decoder is non-zero, the initialization method is as follows:

Calculate the biorthogonal code transform metric,

为在时刻t的双正交码变化度量值，

为第

列双正交码矩阵，

为 待译码信号，

为先验信息，

为时间序号，

表示变量

和 变量

之和的内积。in,

is the biorthogonal code variation metric value at time t,

for the first

column biorthogonal code matrix,

is the signal to be decoded,

for the prior information,

is the time sequence number,

represents a variable

and variable

The inner product of the sum.

The formula for calculating branch metrics is:

为时刻

状态

时的双正交码变换度量值，

为时刻

状态

时的分支度量值。从状态

转变为状态

，可能存在两种方式，在状态

，某个 或某些符号的译码结果为0达到状态

，或者在状态

，某个或某些符号的译码结果为1达 到状态

，即上述某个或者某些符号的译码结果为1的可能性最大；且状态

对应的状态序 号为

，状态

对应的状态序号为

。 in,

for the moment

state

The biorthogonal code transform metric value when ,

for the moment

state

The branch metric value at . from the state

transition to state

, there may be two ways, in the state

, the decoding result of one or some symbols is 0 to reach the state

, or in the state

, the decoding result of one or some symbols is 1 to reach the state

, that is, the decoding result of one or some of the above symbols is most likely to be 1; and the state

The corresponding state serial number is

,state

The corresponding state serial number is

.

，

，更新后向度量计算值， for

,

, update the calculated value of the backward measure,

为后向度量值时间序号。

表示待译码信号中的某个或某 些符号在时刻t被译码为0，使得译码器的状态从

转换到

，同理，

表示待译码 信号中的某个或某些符号在时刻t被译码为1，使得译码器的状态从

转换到

。分支译 码器状态

对应的状态序号为

，分支译码器状态

对应的状态序号为

，分支译码器 状态

对应的状态序号为

。分支译码器的每个状态和对应的状态序号一一对应。且每 个时刻t，分支译码器的状态包括多个，对应的状态序号也有多个。 in,

is the time sequence number of the backward measure.

Indicates that one or some symbols in the signal to be decoded are decoded to 0 at time t, so that the state of the decoder changes from

convert to

, similarly,

Indicates that one or some symbols in the signal to be decoded are decoded as 1 at time t, so that the state of the decoder changes from

convert to

. Branch Decoder Status

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

. Each state of the branch decoder has a one-to-one correspondence with the corresponding state number. And at each time t, there are multiple states of the branch decoder, and there are multiple corresponding state numbers.

，其中，

为更新后的后向度量值。 Normalize the backward measurement value, the specific formula is:

,in,

is the updated backward measure.

。 Reverse recursion in turn, update the backward metric to

.

至后向度量计算及存储单元。 output and store

To the backward metric calculation and storage unit.

Step 3: The forward metric and extrinsic information calculation unit reads the data of the prior information storage unit and the backward metric storage unit, and calculates the forward metric value, a posteriori information and symbol through the channel information, the prior information, and the backward metric value As a result of the decision, a posteriori information is output to the interleaving unit.

The forward metric and external information calculation unit is initialized first. The forward metric initialization method is as follows:

为分支译码器的状态序号，

为分量译码器缓存阶数，

为一个预设的最大值，是一个在合理位宽内的达到的最大值，具体可根据编码的码长确定。

为

时刻状态

的前向度量值，状态

对应的状态序号为

。分支译码器的每个状态 序号对应分支译码器的一个状态。in,

is the state sequence number of the branch decoder,

is the cache order of the component decoder,

is a preset maximum value, which is a maximum value reached within a reasonable bit width, which can be specifically determined according to the encoded code length.

for

state of the moment

The forward measure of , the state

The corresponding state serial number is

. Each state number of the branch decoder corresponds to a state of the branch decoder.

Compute the biorthogonal code transform metric:

为在时刻t的双正交码变化度量值，

为第

列双正交码矩阵，

为 待译码信号，

为先验信息，

为时间序号，

表示变量

和 变量

之和的内积。 in,

is the biorthogonal code variation metric value at time t,

for the first

column biorthogonal code matrix,

is the signal to be decoded,

for the prior information,

is the time sequence number,

represents a variable

and variable

The inner product of the sum.

The formula for calculating branch metrics is:

为时刻

状态

时的双正交码变换度量值，

为时刻

状态

时的分支度量值。从状态

转变为状态

，可能存在两种方式，在状态

，某个 或某些符号的译码结果为0达到状态

，即上述某个或者某些符号的译码结果为0的可能性 最大，或者在状态

，某个或某些符号的译码结果为1达到状态

，即上述某个或者某些符 号的译码结果为1的可能性最大；且状态

对应的状态序号为

，状态

对应的状态序号为

。 in,

for the moment

state

The biorthogonal code transform metric value when ,

for the moment

state

The branch metric value at . from the state

transition to state

, there may be two ways, in the state

, the decoding result of one or some symbols is 0 to reach the state

, that is, the decoding result of the above-mentioned one or some symbols is most likely to be 0, or in the state of

, the decoding result of one or some symbols is 1 to reach the state

, that is, the decoding result of one or some of the above symbols is most likely to be 1; and the state

The corresponding state serial number is

,state

The corresponding state serial number is

.

，

，更新前向度量计算值， for

,

, update the calculated value of the forward metric,

为时间序号。

表示待译码信号中的某个或者某些符 号在时刻t被译码为0，使得译码器的状态从

转换到

，同理，

表示待译码信号 中的某个或者某些符号在时刻t被译码为1，使得译码器的状态从

转换到

，其中，u代 表任意一个符号。分支译码器状态

对应的状态序号为

，分支译码器状态

对应的状态 序号为

，分支译码器状态

对应的状态序号为

。分支译码器的每个状态和对应的 状态序号一一对应。 in,

is the time sequence number.

Indicates that one or some symbols in the signal to be decoded are decoded to 0 at time t, so that the state of the decoder changes from

convert to

, similarly,

Indicates that one or some symbols in the signal to be decoded are decoded as 1 at time t, so that the state of the decoder changes from

convert to

, where u represents any symbol. Branch Decoder Status

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

. Each state of the branch decoder has a one-to-one correspondence with the corresponding state number.

； The calculated value of the forward metric is normalized, and the specific formula is:

;

。 Forward recursion in turn, update the forward metric to

.

至前向度量及后验信息计算 单元130。 output and store

to the forward metric and a posteriori information calculation unit 130 .

After the forward metric value is determined, the forward metric and a posteriori information calculation unit determines the posterior information again according to the approximation algorithm.

The formula for calculating the posterior information is:

表示满足

的状态且

对应的前向度量值，后向度 量值以及双正交码变换度量值的集合，

表示满足

的状态且

对应 的前向度量值，后向度量值以及双正交码变换度量值的集合，

为时刻

第

个符号的 后验信息。

表示待译码信号中的某个或者某些符号在时刻t被译码为0，使得译码 器的状态从

转换到

，且在双正交码矩阵中对应位

的值为+1，同理，

表 示待译码信号中的某个或者某些符号在时刻t被译码为1，使得译码器的状态从

转换到

，且在双正交矩阵码矩阵中对应位

的值为-1，

表示双正交码矩阵的第j列的第 i个符号对应的码字，其中，u代表任意一个符号。分支译码器状态

对应的状态序号为

，分 支译码器状态

对应的状态序号为

，分支译码器状态

对应的状态序号为

。分 支译码器的每个状态和对应的状态序号一一对应。 in,

express satisfaction

state and

Corresponding forward metric value, backward metric value and set of biorthogonal code transform metric value,

express satisfaction

state and

Corresponding forward metric value, backward metric value and set of biorthogonal code transform metric value,

for the moment

the first

a posteriori information of the symbols.

Indicates that one or some symbols in the signal to be decoded are decoded to 0 at time t, so that the state of the decoder changes from

convert to

, and the corresponding bits in the biorthogonal code matrix

The value of is +1, in the same way,

Indicates that one or some symbols in the signal to be decoded are decoded as 1 at time t, so that the state of the decoder changes from

convert to

, and the corresponding bits in the biorthogonal matrix code matrix

is -1,

Indicates the codeword corresponding to the i-th symbol in the j-th column of the biorthogonal code matrix, where u represents any symbol. Branch Decoder Status

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

, the branch decoder state

The corresponding state serial number is

. Each state of the branch decoder has a one-to-one correspondence with the corresponding state number.

The calculated posterior information is output to the extrinsic information storage unit and the interleaving unit.

According to the decision function, the decoding result is determined. The formula of the decision function is:

为时刻t时第i个符号的后验信息，

为求符号运算，

为时 刻t时第i个符号的译码结果。 in,

is the posterior information of the ith symbol at time t,

For symbolic operations,

is the decoding result of the i-th symbol at time t.

Step 4: A posteriori information and a priori information are input into the external information storage unit, and the external information is updated.

The posterior information and prior information are input into the external information storage unit, and the external information is updated and stored. The specific formula is:

为先验信息，

为时刻t时第i个符号的后验信息，

为存储的 外信息，

为更新后的外信息，

为时间序号。并且先验信息

，存储的外 信息

以及更新后的外信息

均表示一个集合，对应不同的i值，均有集合中的一个 值与其对应。同样，先验信息

也表示一个集合，对应不同的i值，均有集合中的一个值与 其对应。其中，i表示第i个符号。 in,

for the prior information,

is the posterior information of the ith symbol at time t,

For stored foreign information,

For updated external information,

is the time sequence number. and prior information

, the stored foreign information

and updated external information

Both represent a set, corresponding to different i values, and each has a value in the set corresponding to it. Likewise, prior information

It also represents a set, corresponding to different i values, there is a value in the set corresponding to it. where i represents the ith symbol.

Update out-of-storage information.

Step 5: After the a posteriori information passes through the interleaving unit, the interleaving a posteriori information is output and input to the extrinsic information storage unit of another decoder.

The posterior information output by the forward metric and posterior information calculation unit enters the interleaving unit, and the interleaving unit interleaves the posterior information and outputs it to the external information storage unit. The formula of the corresponding interleaving function is:

；

;

为时刻t时第i个符号的后验信息，

为时刻t交织单元对应的交织 地址，

为交织函数。具体的，

为时刻t交织单元对应的交织地址表示一个集合，包括 在时刻t所有符号的交织单元对应的交织地址。 in,

is the posterior information of the ith symbol at time t,

is the interleaving address corresponding to the interleaving unit at time t,

is the interleaving function. specific,

The interleaving addresses corresponding to the interleaving units at time t represent a set, including the interleaving addresses corresponding to the interleaving units of all symbols at time t.

Repeat steps 2 to 5 until the number of iterations reaches the maximum number of iterations, and then go to step 6.

Step 6: After reaching the maximum number of iterations, the forward metric and a posteriori information calculation unit outputs the decoding result of the signal to be decoded.

The method for decoding a low bit rate bi-orthogonal code provided by the present invention uses two branch decoders to simultaneously receive the signal to be decoded, and each branch decoder receives the signal to be decoded and the a posteriori information of another decoder. , by superimposing the metric values of different codewords to determine a priori information and a posteriori information, and using reverse recursion and forward recursion to determine the corresponding backward metric value and forward metric value, respectively, when the maximum iteration is reached When the number of times, the decoding result is output. The complexity of the bi-orthogonal code decoder structure and implementation is reduced, and it is easy to be applied in engineering.

The methods and apparatuses provided by the embodiments of the present invention are based on the same inventive concept. Since the methods and apparatuses have similar principles for solving problems, the implementations of the apparatuses and the methods can be referred to each other, and repeated descriptions will not be repeated.

The device embodiments described above are only illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in One place, or it can be distributed over multiple network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution in this embodiment. Those of ordinary skill in the art can understand and implement it without creative effort.

From the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and certainly can also be implemented by hardware. Based on this understanding, the above-mentioned technical solutions can be embodied in the form of software products in essence or the parts that make contributions to the prior art, and the computer software products can be stored in computer-readable storage media, such as ROM/RAM, magnetic A disc, an optical disc, etc., includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to perform the methods described in various embodiments or some parts of the embodiments.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand: it can still be Modifications are made to the technical solutions described in the foregoing embodiments, or some technical features thereof are equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (24)

1. a low code rate bi-orthogonal code decoder, is characterized in that, comprises: A two-branch decoder, each branch decoder includes a first unit, a second unit and a third unit, the output end of the first unit, simultaneously and the first input end of the second unit and the first unit The first input terminal of the three units is connected; the output terminal of the second unit is connected to the second input terminal of the third unit; the first output terminal of the third unit is connected to the first input terminal of the first unit The second output end of the third unit is connected to the second input end of the first unit of the other branch decoder through the interleaving unit; The first unit is configured to determine the prior information based on the posterior information and the stored extrinsic information; The second unit is configured to perform reverse recursive estimation based on the signal to be decoded and the prior information, and output a backward metric value; The third unit is configured to perform forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, and output the forward metric value and a posteriori information; When the number of recursive estimations reaches the preset maximum number of iterations, the decoding result is output; The first unit is an extrinsic information and a priori information storage unit, the second unit is a backward metric calculation and storage unit, and the third unit is a forward metric and a posteriori information calculation unit. 2. The low code rate biorthogonal code decoder according to claim 1, wherein the first unit is configured to determine a priori information based on a posteriori information and stored extrinsic information, comprising: initialize the foreign information; Determine the prior information based on the initial value of the extrinsic information stored in the first unit and the interleaved posterior information; The interleaved a posteriori information is a result of interleaving the a posteriori information output by the third unit. 3. The low code rate bi-orthogonal code decoder according to claim 1, wherein the second unit is configured to perform reverse recursive estimation based on the signal to be decoded and the prior information, Output backward metrics, including: Based on the end state of the branch decoder, initialize the backward metric value at the last moment; when the end state of the branch decoder is zero, the corresponding backward metric value is zero; when the end state of the branch decoder is non-zero , the corresponding backward metric value is the negative maximum value; Determine the rule based on the branch metric value, and determine the branch metric value at each moment; Based on the approximation algorithm, and the branch metric values, the corresponding backward metric values are determined by reverse recursion. 4. The low code rate bi-orthogonal code decoder according to claim 3, wherein, based on the approximation algorithm and the branch metric value, the corresponding backward metric value is determined by reverse recursion: Determine the first branch metric value corresponding to the state S when the specific branch decoder of the two branch decoders reaches the first branch metric value corresponding to the state S when the decoding result of the specific symbol is zero at any time t, and the first backward direction corresponding to the time t+1 metric; determining a first metric sum based on the sum of the first branch metric value and the first backward metric value; It is determined that at any time t, the decoding result of the specific symbol of the specific branch decoder in the two branch decoders is the second branch metric value corresponding to the state S reached at one time, and the second backward metric corresponding to the time t+1 value; determining a second sum of metrics based on the sum of the second branch metric and the second backward metric; Based on the approximation algorithm, determine the first metric value sum, and the largest of the second metric value sum and the second metric value sum is the backward metric value at time t; normalizing the backward metric value; Based on the initialization value of the backward metric value of the state S at time t+1, the backward recursive update of the backward metric value at all times is reversed; Wherein, the state S is the state of the branch decoder. 5 . The low code rate bi-orthogonal code decoder according to claim 1 , wherein the third unit is configured to be based on the signal to be decoded, the prior information, and the backward metric value. 6 . , perform forward recursive estimation, and output forward metrics and posterior information, including: Based on the initial state of the branch decoder, initialize the forward metric value; Determine the rule based on the branch metric value, and determine the branch metric value at each moment; Based on the approximation algorithm and the branch metric value, forward recursion determines the corresponding forward metric value; A posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the state of the branch decoder and the biorthogonal code matrix. 6. The low code rate bi-orthogonal code decoder according to claim 5, wherein, based on the approximation algorithm and the branch metric value, forward recursion determines the corresponding forward metric value, comprising: : Based on the specific branch decoder in the two-branch decoder, at any time t, the decoding result of the specific symbol reaches the third branch metric value corresponding to state S when the decoding result of the specific symbol is zero, and the third forward metric corresponding to the time t-1 value; determining a third sum of metrics based on the sum of the third branch metric and the third forward metric; Based on the specific branch decoder in the two-branch decoder at any time t, the decoding result of the specific symbol is that the fourth branch metric value corresponding to the state S is reached at one time, and the fourth forward metric value at time t-1; determining a fourth sum of metrics based on the sum of the fourth branch metric and the fourth forward metric; Based on an approximation algorithm, the third metric sum is determined, and the largest of the third metric sum and the fourth metric sum is the forward metric value at time t; normalizing the forward metric value; Based on the initialization value of the forward metric value of the state S at time 1, forward recursively update the forward metric value at all times; Wherein, the state S is the state of the branch decoder. 7. The low code rate biorthogonal code decoder according to any one of claims 3 or 5, wherein the branch metric value determination rule comprises: Based on the bi-orthogonal code matrix, the signal to be decoded and the prior information, the bi-orthogonal code transformation metric is determined; Based on the different states of the two branch decoders, corresponding branch metrics are determined. 8. The low code rate biorthogonal code decoder according to claim 5, wherein the a posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is based on a branch decoder The state and the biorthogonal code matrix are determined, including: determining a fifth sum of metric values based on the sum of the biorthogonal code transform metric values at time t, the forward metric value at time t, and the backward metric value at time t+1 in the first set; determining a sixth sum of metric values based on the sum of the biorthogonal code transform metric value at time t, the forward metric value at time t, and the backward metric value at time t+1 in the second set; Based on an approximation algorithm, determining the maximum value of the sum of the fifth metric values and the maximum value of the sum of the sixth metric values; Determine the maximum value of the fifth metric value sum, and the difference with the maximum value of the sixth metric value sum is the posterior information of the ith symbol at time t; The elements of the first set satisfy that when the decoding result of the i-th symbol at time t is zero, the corresponding value in the biorthogonal code matrix is +1, and the elements of the second set satisfy that the i-th symbol at time t is zero. When the decoding result of each symbol is 1, the corresponding value in the biorthogonal code matrix is -1. 9 . The low code rate bi-orthogonal code decoder according to claim 1 , wherein the third unit is configured to be used when the number of times of the forward recursive estimation reaches a preset maximum number of iterations. 10 . Next, output the decoding results, including: If it is determined that the number of times of the forward recursive estimation reaches the preset maximum number of iterations, the decoding result is output based on the value of the posterior information and the decision function; The decision function is that when the value of the a posteriori information is greater than or equal to zero, the output decoding result is one; when the value of the a posteriori information is less than zero, the output decoding result is zero. 10. The low code rate bi-orthogonal code decoder according to claim 9, wherein the formula of the decision function is:

in,

is the posterior information of the ith symbol at time t,

For symbolic operations,

is the decoding result of the i-th symbol at time t. 11 . The low code rate biorthogonal code decoder according to claim 1 , wherein the first unit is further configured to update and store extrinsic information based on a posteriori information and a priori information. 12 . 12. The low code rate bi-orthogonal code decoder according to claim 1, wherein the interleaving unit is configured to perform interleaving processing on the posterior information, and output the posterior information after interleaving; Based on the posterior information and the interleaving function, the posterior information after interleaving is determined, and the formula of the interleaving function is:

; in,

is the posterior information of the ith symbol at time t,

is the interleaving address corresponding to the interleaving unit at time t,

is the interleaving function. 13. A method for low code rate biorthogonal code decoding, comprising: Input the signal to be decoded into the backward metric calculation and storage unit of the two-branch decoder, and the forward metric and a posteriori information calculation unit; The backward metric calculation and storage unit performs reverse recursive estimation based on the signal to be decoded and the prior information, determines the backward metric value, and outputs it to the forward metric and a posteriori information calculation unit; The forward metric and a posteriori information calculation unit performs forward recursive estimation based on the signal to be decoded, the prior information, and the backward metric value, determines the forward metric value and a posteriori information, and outputs The a posteriori information is sent to the external information and a priori information storage unit; The extrinsic information and a priori information storage unit determines the prior information based on the posterior information and the stored extrinsic information, and outputs it to the backward metric calculation and storage unit and the forward metric and a posteriori information calculation unit; wherein, the The posterior information includes: Calculate the a posteriori information output by the unit based on the forward metric and posterior information of the branch decoder to which it belongs; or The forward metric of the other branch decoder and the posterior information output by the posterior information calculation unit, the posterior information after interleaving obtained after being processed by the interleaving unit; The forward metric and a posteriori information calculation unit determines that the number of forward recursive estimations reaches a preset maximum number of iterations, and outputs a decoding result of the signal to be decoded. 14. The method for decoding a low code rate biorthogonal code according to claim 13, wherein the extrinsic information and a priori information storage unit determines the prior information based on the posterior information and the stored extrinsic information, include: initialize the foreign information; The prior information is determined based on the initial value of the extrinsic information and the interleaved posterior information. 15. The method for decoding a low code rate biorthogonal code according to claim 13, wherein the backward metric calculation and storage unit performs backward recursive estimation based on the signal to be decoded and a priori information , which determines the backward metrics, including: Based on the end state of the branch decoder, the backward metric value at the last moment is initialized; when the end state of the branch decoder is zero, the corresponding backward metric value is zero; when the end state of the branch decoder is non-zero , the corresponding backward metric value is the negative maximum value; Determine the rule based on the branch metric value, and determine the branch metric value at each moment; Based on the approximation algorithm, and the branch metric values, the corresponding backward metric values are determined by reverse recursion. 16. The method for decoding a low bit rate biorthogonal code according to claim 15, wherein the corresponding backward metric value is determined by reverse recursion based on the approximation algorithm and the branch metric value, include: Determine the first branch metric value corresponding to the state S when the specific branch decoder of the two branch decoders reaches the state S when the specific symbol decoding result is zero at any time t, and the first backward metric corresponding to time t+1 value; determining a first metric sum based on the sum of the first branch metric value and the first backward metric value; It is determined that at any time t, the specific symbol decoding result of the specific branch decoder in the two branch decoders reaches the second branch metric value corresponding to the state S at one time, and the second backward metric value corresponding to the time t+1 ; determining a second sum of metrics based on the sum of the second branch metric and the second backward metric; Based on the approximation algorithm, determine the first metric value sum, and the largest of the second metric value sum and the second metric value sum is the backward metric value at time t; normalizing the backward metric value; Based on the initialization value of the backward metric value at time t+1, the backward recursive update of the backward metric value at all times is reversed; Wherein, the state S is the state of the branch decoder. 17 . The method for decoding a low bit rate biorthogonal code according to claim 13 , wherein the forward metric and a posteriori information calculation unit is based on the signal to be decoded, the prior information and the Backward metric value, perform forward recursive estimation, determine forward metric value and posterior information, including: Based on the initial state of the branch decoder, initialize the forward metric value; Determine the rule based on the branch metric value, and determine the branch metric value at each moment; Based on the approximation algorithm and the branch metric value, forward recursion determines the corresponding forward metric value; A posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is determined based on the state of the branch decoder and the biorthogonal code matrix. 18. The method for decoding a low code rate biorthogonal code according to claim 17, wherein the corresponding forward metric value is determined by forward recursion based on the approximation algorithm and the branch metric value, include: Based on the specific branch decoder in the two-branch decoder, at any time t, the decoding result of the specific symbol reaches the third branch metric value corresponding to the state S when the decoding result of the specific symbol is zero, and the third forward direction corresponding to the time t-1 metric; determining a third sum of metrics based on the sum of the third branch metric and the third forward metric; Based on the specific branch decoder in the two-branch decoder at any time t, the decoding result of the specific symbol is that the fourth branch metric value corresponding to the state S is reached at one time, and the fourth forward metric value at time t-1; determining a fourth sum of metrics based on the sum of the fourth branch metric and the fourth forward metric; Based on an approximation algorithm, the third metric sum is determined, and the largest of the third metric sum and the fourth metric sum is the forward metric value at time t; normalizing the forward metric value; Based on the initialization value of the forward metric value of the state S at time 1, forward recursively update the forward metric value at all times; Wherein, the state S is the state of the branch decoder. 19. The method for decoding a low bit rate biorthogonal code according to any one of claims 15 or 17, wherein the branch metric value determination rule comprises: Based on the bi-orthogonal code matrix, the signal to be decoded and the prior information, the bi-orthogonal code transformation metric is determined; Based on the different states of the two branch decoders, the corresponding branch metrics are determined. 20. The method for decoding a low bit rate biorthogonal code according to claim 17, wherein the a posteriori information is determined based on an approximation algorithm and a preset rule; the preset rule is based on branch decoding determined by the state of the device and the biorthogonal code matrix, including: determining a fifth sum of metric values based on the sum of the biorthogonal code transform metric values at time t, the forward metric value at time t, and the backward metric value at time t+1 in the first set; determining a sixth sum of metric values based on the sum of the biorthogonal code transform metric values at time t, the forward metric value at time t, and the backward metric value at time t+1 in the second set; Based on an approximation algorithm, determining the maximum value of the sum of the fifth metric values and the maximum value of the sum of the sixth metric values; Determine the maximum value of the fifth metric value sum, and the difference with the maximum value of the sixth metric value sum is the posterior information of the ith symbol at time t; The elements of the first set satisfy that when the decoding result of the i-th symbol at time t is zero, the corresponding value in the biorthogonal code matrix is +1, and the elements of the second set satisfy that the i-th symbol at time t is zero. When the decoding result of each symbol is 1, the corresponding value in the biorthogonal code matrix is -1. 21. The method for low bit rate biorthogonal code decoding according to claim 13, wherein the forward metric and a posteriori information calculation unit determines that the number of times of forward recursive estimation reaches a preset maximum iteration When the number of times, output the decoding result of the signal to be decoded, including: If it is determined that the number of times of the forward recursive estimation reaches a preset maximum number of iterations, the decoding result is output based on the value of the posterior information and the decision function; The decision function is that when the value of the a posteriori information is greater than or equal to zero, the output decoding result is one; when the value of the a posteriori information is less than zero, the output decoding result is zero. 22. The method for low code rate biorthogonal code decoding according to claim 21, wherein the formula of the decision function is:

in,

is the posterior information of the ith symbol at time t,

For symbolic operations,

is the decoding result of the i-th symbol at time t. 23. The method for decoding a low code rate biorthogonal code according to claim 13, wherein the extrinsic information is updated and stored in the extrinsic information and a priori information storage unit based on a posteriori information and a priori information. storage. 24. The method for decoding a low code rate biorthogonal code according to claim 13, wherein the a posteriori information output by the forward metric and a posteriori information calculation unit is processed by an interleaving unit, comprising: Based on the posterior information and the interleaving function, the posterior information after interleaving is determined, and the formula of the interleaving function is:

; in,

is the posterior information of the ith symbol at time t,

is the interleaving address corresponding to the interleaving unit at time t,

is the interleaving function.

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