Polar-LDPC coding and decoding method based on genetic algorithm

Abstract

The invention discloses a Polar-LDPC (Low Density Parity Check Code) coding and decoding method based on a genetic algorithm. The method comprises the following steps: S1, obtaining a path vector L by using the genetic algorithm; s2, forming an intermediate channel set; s3, encoding all information bits by using a Polar code, and selecting a part of information bits from the intermediate channel and encoding by using an LDPC code; and S4, carrying out cascaded code BP decoding to obtain a final decoding result. The invention discloses a Polar-LDPC (Low Density Parity Check Code) coding and decoding method based on a genetic algorithm, which adopts an LDPC code as an outer code, constructs an intermediate channel set based on the genetic algorithm, takes a result as a guide, needs less background knowledge, does not need to pay much attention to the process, and can reduce the system calculation complexity, thereby reasonably and efficiently selecting the construction position of the LDPC code, and improving the decoding performance of a polar code. And a parallel BP algorithm is adopted for decoding, decoding delay can be reduced in quantum cryptography distribution and post-processing, and the method is suitable for hardware implementation.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum communication networks and channel coding, and in particular to a Polar-LDPC encoding and decoding method based on a genetic algorithm. Background Art

[0002] Quantum Key Distribution (QKD) is a very important branch of quantum information science. It can realize the secure sharing of keys of spatially separated users, so that both parties of legitimate communication share a set of theoretically unconditionally secure keys. Its security is based on the basic principles of quantum theory (uncertainty principle and no-cloning theorem, etc.). Even if the eavesdropper has infinite computing power, he cannot steal any information.

[0003] Polar codes are the first type of codes that have been theoretically proven to reach the Shannon capacity limit. The introduction of Polar codes has opened up a new direction for channel coding theory for scholars and is currently widely used in channel coding, source coding, and other aspects. After being introduced into the QKD field, Polar codes have achieved significant performance improvements, both in terms of negotiation efficiency and algorithm speed, which are higher than the LDPC-based error negotiation algorithm implemented on the GPU.

[0004] The post-processing algorithm plays a vital role in the key rate and security distance of QKD. Under limited code length, due to the serial algorithm of SC decoding, although good performance can be obtained, the delay is high. Under shorter code length, the performance of bit-by-bit decoding may be affected, especially under high signal-to-noise ratio (SNR). The short code effect will cause the bit error rate performance of bit-by-bit decoding to be poor, which is not as good as some other decoding algorithms. The BP decoding algorithm is an iterative parallel decoding algorithm suitable for low-latency and high-throughput systems. Although its delay is reduced, the decoding performance is insufficient.

[0005] Polar codes can improve decoding performance by cascading other codewords, such as cascading LDPC codes with Polar codes. Without increasing the complexity and decoding delay, LDPC codes can be used to optimize decoding from different aspects. Encoding the bits transmitted in the intermediate channel with LDPC codes in advance can offset performance losses and bring additional gains. However, it is currently impossible to reasonably and efficiently select the intermediate channel for LDPC code encoding, resulting in insufficient decoding performance of the cascade of LDPC codes and Polar codes. Summary of the invention

[0006] In order to solve the problem that an intermediate channel cannot be reasonably and efficiently selected for LDPC code encoding in the current quantum cryptography distribution and post-processing, the present invention provides a Polar-LDPC encoding and decoding method based on a genetic algorithm.

[0007] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0008] A Polar-LDPC encoding and decoding method based on a genetic algorithm comprises the following steps:

[0009] S1: Use the genetic algorithm to iteratively store the individual with the lowest fitness in the path vector L, and obtain the path vector L with the maximum number of iterations;

[0010] S2: Count the number of occurrences of the indexes of all information bits in L, and obtain all the indexes in L whose number of occurrences is not zero, forming a set of intermediate channels;

[0011] S3: Use Polar codes to encode all information bits, select some information bits from the intermediate channel and encode them using LDPC codes, and then send them to the channel for transmission after encoding.

[0012] S4: The channel receiving end receives the concatenated code codeword and performs concatenated code BP decoding to obtain a final decoding result.

[0013] In the above scheme, LDPC code is used as the outer code, and the intermediate channel set is constructed based on the genetic algorithm. It is result-oriented, requires less background knowledge, does not need to pay too much attention to the process, and can reduce the calculation complexity of the system, so as to reasonably and efficiently select the construction position of the LDPC code, improve the polar code decoding performance, and the decoding adopts a parallel BP algorithm, which can reduce the decoding delay and is suitable for hardware implementation.

[0014] Preferably, step S1 specifically includes the following steps:

[0015] S11: Initialize the population P;

[0016] S12: Select the population P from the current population according to the fitness function through the selection operation s ;

[0017] S13: Perform crossover and mutation operations, store the individual with the lowest fitness in the path vector L, and update the current population individual according to the individual with the lowest fitness;

[0018] S14: Repeat steps S12 and S13 until the maximum number of iterations is reached, and obtain the path vector L of the maximum number of iterations.

[0019] Preferably, step S11 specifically includes: performing channel coding on the polar code by Gaussian approximation to obtain an initial codeword vector M, and initializing the population P using the index of the information bit in M.

[0020] Preferably, the individuals are different channel codes.

[0021] Preferably, the fitness function is the subchannel error probability:

[0022]

[0023] in, is the mean of the log-likelihood ratio (LLR), i is the subchannel number, x is the information of the channel input, and N is the total number of subchannels.

[0024] Preferably, the mean value of LLR is calculated by the following formula:

[0025]

[0026]

[0027]

[0028] Among them, σ 2 is the noise variance of the Gaussian channel, and y is the information received from the channel.

[0029] Preferably, the function φ(x) is defined as

[0030]

[0031] Preferably, in step S4, concatenated code BP decoding is performed based on the factor graph.

[0032] Preferably, step S4 specifically includes the following steps:

[0033] S4.1: The channel receiving end receives the concatenated code word and performs polar code decoding to obtain the LLR values ​​of all information bits;

[0034] S4.2: Select the LLR value of the protected information bit from the LLR values ​​of all information bits, and use it together with the LLR value of the redundant bit in the LDPC code word from the channel as the input of the LDPC code decoder to obtain the LLR value of the protected information bit;

[0035] S4.3: updating the LLR values ​​of all information bits according to the LLR values ​​of the protected information bits;

[0036] S4.4: sending the updated LLR values ​​of all information bits on the left side to the adapter, and completing the adaptation process of the decoded information from left to right in the adapter;

[0037] S4.5: the adapter outputs the information of the right polar code codeword required by the polar code decoder, and combines the decoded information of the polar code codeword from the channel as the input of the next polar code decoder;

[0038] S4.6: Repeat steps S4.1 to S4.5 until the maximum number of iterations is reached, and then perform a hard decision on the sum of the left- and right-transmitted information of the source end to obtain the final decoding result.

[0039] Beneficial technical effects of the present invention:

[0040] The present invention provides a Polar-LDPC encoding and decoding method based on a genetic algorithm. The LDPC code is used as an outer code, and an intermediate channel set is constructed based on a genetic algorithm. The method is result-oriented, requires less background knowledge, does not need to pay too much attention to the process, and can reduce the calculation complexity of the system, so as to reasonably and efficiently select the construction position of the LDPC code, improve the decoding performance of the polarization code, and the decoding adopts a parallel BP algorithm, which can reduce the decoding delay in quantum cryptography distribution and post-processing, and is suitable for hardware implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flowchart of the implementation steps of the technical solution of the present invention;

[0042] Figure 2 is a specific flow chart of step S1 in the present invention;

[0043] Figure 3 Schematic diagram of the factor graph in the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments, but the scope of protection claimed in the present invention is not limited to the following specific embodiments.

[0045] Example 1

[0046] like Figure 1 As shown, a Polar-LDPC encoding and decoding method based on a genetic algorithm includes the following steps:

[0047] S1: Use the genetic algorithm to iteratively store the individual with the lowest fitness in the path vector L, and obtain the path vector L with the maximum number of iterations;

[0048] S2: Count the number of occurrences of the indexes of all information bits in L, and obtain all the indexes in L whose number of occurrences is not zero, forming a set of intermediate channels;

[0049] S3: Use Polar codes to encode all information bits, select some information bits from the intermediate channel and encode them using LDPC codes, and then send them to the channel for transmission after encoding.

[0050] In actual implementation, some information bits that need to be protected by LDPC code are selected from the middle channels, and the channels for transmitting information bits with lower reliability are selected;

[0051] S4: The channel receiving end receives the concatenated code codeword and performs concatenated code BP decoding to obtain a final decoding result.

[0052] In the specific implementation process, LDPC code is used as the outer code, and the intermediate channel set is constructed based on the genetic algorithm. It is result-oriented, requires less background knowledge, and does not need to pay too much attention to the process. It can reduce the calculation complexity of the system, so as to reasonably and efficiently select the construction position of the LDPC code, improve the polar code decoding performance, and the decoding adopts a parallel BP algorithm, which can reduce the decoding delay and is suitable for hardware implementation.

[0053] More specifically, if Figure 2 As shown, step S1 specifically includes the following steps:

[0054] S11: Channel encode the polar code by Gaussian approximation to obtain an initial codeword vector M, and initialize the population P using the index of the information bit in M;

[0055] S12: Select the population P from the current population according to the fitness function through the selection operation s ;

[0056] S13: Perform crossover and mutation operations, store the individual with the lowest fitness in the path vector L, and update the current population individual according to the individual with the lowest fitness;

[0057] S14: Repeat steps S12 and S13 until the maximum number of iterations is reached, and obtain the path vector L of the maximum number of iterations.

[0058] More specifically, individuals are encoded for different channels.

[0059] More specifically, the fitness function is the subchannel error probability:

[0060]

[0061] in, is the mean of the log-likelihood ratio (LLR), i is the subchannel number, x is the information of the channel input, and N is the total number of subchannels.

[0062] More specifically, the mean value of LLR is calculated by the following formula:

[0063]

[0064]

[0065]

[0066] Among them, σ 2 is the noise variance of the Gaussian channel, and y is the information received from the channel.

[0067] More specifically, the function φ(x) is defined as

[0068]

[0069] More specifically, if Figure 3 As shown, in step S4, concatenated code BP decoding is performed based on the factor graph.

[0070] More specifically, step S4 specifically includes the following steps:

[0071] S4.1: The channel receiving end receives the concatenated code word and performs polar code decoding to obtain the LLR values ​​of all information bits;

[0072] S4.2: Select the LLR value of the protected information bit from the LLR values ​​of all information bits, and use it together with the LLR value of the redundant bit in the LDPC code word from the channel as the input of the LDPC code decoder (LDPC code decoder output) to obtain the LLR value of the protected information bit;

[0073] S4.3: updating the LLR values ​​of all information bits (output by the polar code decoder) according to the LLR value of the protected information bit (i.e., replacing the LLR value of the protected information bit in all information bits output by the polar code decoder with the output value of the LDPC code decoder);

[0074] S4.4: sending the updated LLR values ​​of all information bits on the left side to the adapter, and completing the adaptation process of the decoded information from left to right in the adapter;

[0075] S4.5: the adapter outputs the information of the right polar code codeword required by the polar code decoder, and combines the decoded information of the polar code codeword from the channel as the input of the next polar code decoder;

[0076] S4.6: Repeat steps S4.1 to S4.5 until the maximum number of iterations is reached, and then perform hard decision on the sum of the left- and right-hand transmission information of the source end (including LLR value, channel information, and polarization code decoding codeword) to obtain the final decoding result.

[0077] According to the disclosure and teaching of the above description, those skilled in the art to which the present invention belongs may also make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments disclosed and described above, and some modifications and changes to the invention should also fall within the scope of protection of the claims of the present invention. In addition, although some specific terms are used in this specification, these terms are only for the convenience of description and do not constitute any limitation to the present invention.

Claims

1. A Polar-LDPC encoding and decoding method based on genetic algorithm, characterized in that: The following steps are involved: S1: Use the genetic algorithm to iteratively store the individual with the lowest fitness in the path vector L, and obtain the path vector L with the maximum number of iterations; S2: Count the number of occurrences of the indexes of all information bits in L, and obtain all the indexes in L whose number of occurrences is not zero, forming a set of intermediate channels; S3: Use Polar codes to encode all information bits, select some information bits from the intermediate channel and encode them using LDPC codes, and then send them to the channel for transmission after encoding. S4: The channel receiving end receives the concatenated code codeword and performs concatenated code BP decoding to obtain a final decoding result.

2. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11: Initialize the population P; S12: Select the population P from the current population according to the fitness function through the selection operation S ; S13: Perform crossover and mutation operations, store the individual with the lowest fitness in the path vector L, and update the current population individual according to the individual with the lowest fitness; S14: Repeat steps S12 and S13 until the maximum number of iterations is reached, and obtain the path vector L of the maximum number of iterations.

3. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 2, characterized in that: Step S11 specifically includes: channel coding the polar code by Gaussian approximation to obtain an initial codeword vector M, and initializing the population P by using the index of the information bit in M.

4. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 2, characterized in that: Individuals are coded for different channels.

5. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 2, characterized in that: The fitness function is the subchannel error probability: in, is the mean of LLR, i is the subchannel number, x is the information of channel input, and N is the total number of subchannels.

6. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 5, characterized in that: The mean value of LLR is calculated by the following formula: Among them, σ 2 is the noise variance of the Gaussian channel, and y is the information received from the channel.

7. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 6, characterized in that: The function φ(x) is defined as 8. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 1, characterized in that: In step S4, concatenated code BP decoding is performed based on the factor graph.

9. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 1, characterized in that: Step S4 specifically includes the following steps: S4.1: The channel receiving end receives the concatenated code word and performs polar code decoding to obtain the LLR values ​​of all information bits; S4.2: Select the LLR value of the protected information bit from the LLR values ​​of all information bits, and use it together with the LLR value of the redundant bit in the LDPC code word from the channel as the input of the LDPC code decoder to obtain the LLR value of the protected information bit; S4.3: updating the LLR values ​​of all information bits according to the LLR values ​​of the protected information bits; S4.4: sending the updated LLR values ​​of all information bits on the left side to the adapter, and completing the adaptation process of the decoded information from left to right in the adapter; S4.5: the adapter outputs the information of the right polar code codeword required by the polar code decoder, and combines the decoded information of the polar code codeword from the channel as the input of the next polar code decoder; S4.6: Repeat steps S4.1 to S4.5 until the maximum number of iterations is reached, and then perform a hard decision on the sum of the left- and right-transmitted information of the source end to obtain the final decoding result.

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