A Polar-LDPC encoding and decoding method based on genetic algorithm

Abstract

The present invention discloses a Polar-LDPC encoding and decoding method based on a genetic algorithm, comprising the following steps: S1: obtaining a path vector L using a genetic algorithm; S2: forming a set of intermediate channels; S3: encoding all information bits using Polar codes, and selecting some information bits from the intermediate channels and encoding them using LDPC codes; S4: performing concatenated code BP decoding to obtain a final decoding result. The present invention discloses a Polar-LDPC encoding and decoding method based on a genetic algorithm, which uses LDPC codes as outer codes and constructs a set of intermediate channels based on a genetic algorithm. This method is result-oriented, requires little background knowledge, and does not require much attention to the process, thereby reducing the computational complexity of the system. This method allows for the rational and efficient selection of the LDPC code construction position, improving the polar code decoding performance. Furthermore, the decoding method uses a parallel BP algorithm, which can reduce decoding delay in quantum cryptography distribution and post-processing, making it 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), a crucial branch of quantum information science, enables secure key sharing between spatially separated users, allowing both parties in legitimate communication to share a theoretically unconditionally secure set of keys. Its security is based on fundamental principles of quantum theory, such as the uncertainty principle and the no-cloning theorem. Even an eavesdropper with unlimited computing power cannot steal any information.

[0003] Polar codes are the first type of codes theoretically proven to reach the Shannon capacity limit. The introduction of Polar codes has opened up new avenues for channel coding theory and is currently widely used in channel coding and source coding. The introduction of Polar codes into the field of QKD has significantly improved performance, surpassing LDPC-based error negotiation algorithms implemented on GPUs in both negotiation efficiency and algorithm speed.

[0004] Post-processing algorithms play a crucial role in the key rate and security distance of QKD. With limited code lengths, SC decoding, a serial algorithm, can achieve good performance but at a high latency. At shorter code lengths, the performance of bit-by-bit decoding may be affected, especially at high signal-to-noise ratios (SNRs). The short code effect results in poor bit-by-bit decoding error rate performance, inferior to some other decoding algorithms. The BP decoding algorithm is an iterative parallel decoding algorithm suitable for low-latency and high-throughput systems. Although it reduces latency, its 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 decoding complexity or latency, LDPC codes can optimize decoding in various ways. Pre-encoding bits transmitted in the mid-channel with LDPC codes can offset performance losses and provide additional gains. However, currently, it's difficult to rationally and efficiently select mid-channels for LDPC code encoding, resulting in suboptimal decoding performance when cascading LDPC and Polar codes. Summary of the Invention

[0006] In order to solve the problem that the 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 object, 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 the intermediate channel set;

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

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

[0013] In this solution, LDPC codes are used as the outer code, and a set of intermediate channels is constructed based on a genetic algorithm. This result-oriented approach requires minimal background knowledge and process-oriented attention, thus reducing the computational complexity of the system. This allows for the rational and efficient selection of the LDPC code construction location, improving the decoding performance of polar codes. Furthermore, the decoding employs a parallel BP algorithm, which reduces decoding latency 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 channel input information, 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 codeword 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 values ​​of the redundant bits in the LDPC codeword from the channel as input to the LDPC code decoder to obtain the LLR value of the protected information bit;

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

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

[0037] S4.5: The adapter outputs the right polar code codeword information required by the polar code decoder, and combines it with the decoded polar code codeword information 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 leftward and rightward 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. LDPC codes are used as outer codes, and an intermediate channel set is constructed based on the genetic algorithm. This method is result-oriented, requires little background knowledge, and does not require much attention to the process. This method can reduce the computational complexity of the system, thereby rationally and efficiently selecting the construction position of the LDPC code and improving the decoding performance of the polar code. In addition, the decoding method uses a parallel BP algorithm, which can reduce decoding delays in quantum cryptography distribution and post-processing, making it suitable for hardware implementation. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0042] Figure 2 This 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 with reference to the 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 the intermediate channel set;

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

[0050] In actual implementation, some information bits that need to be protected by LDPC codes are selected from the intermediate channels, and the channels that transmit information bits with lower reliability are selected;

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

[0052] During the specific implementation process, LDPC code is used as the outer code, and the intermediate channel set is constructed based on the genetic algorithm. This result-oriented method requires little background knowledge and does not require much attention to the process, which can reduce the system's computational complexity. Therefore, the construction position of the LDPC code can be selected reasonably and efficiently, improving the polar code decoding performance. In addition, the decoding adopts a parallel BP algorithm, which can reduce 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 using 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 different channel codes.

[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 channel input information, and N is the total number of subchannels.

[0062] More specifically, the mean of the 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 includes the following steps:

[0071] S4.1: The channel receiving end receives the concatenated codeword 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 values ​​of the redundant bits in the LDPC codeword from the channel as input to the LDPC code decoder (LDPC code decoder output) to obtain the LLR value of the protected information bit;

[0073] S4.3: Update the LLR values ​​of all information bits (output by the polar code decoder) based on the LLR values ​​of the protected information bits (i.e., replace the LLR values ​​of the protected information bits among all information bits output by the polar code decoder with the output values ​​of the LDPC code decoder).

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

[0075] S4.5: The adapter outputs the right polar code codeword information required by the polar code decoder, and combines it with the decoded polar code codeword information 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. Then, a hard decision is performed on the sum of the leftward and rightward transmitted information from the source (including LLR values, channel information, and polar code decoding codewords) to obtain the final decoding result.

[0077] Based on the disclosure and teachings of the above description, those skilled in the art 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 any modifications and variations of the invention should also fall within the scope of protection of the claims of the present invention. In addition, although certain specific terms are used in this description, these terms are for convenience of description only and do not constitute any limitation to the present invention.

Claims

1. A Polar-LDPC encoding and decoding method based on a 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 the intermediate channel set; S3: Use Polar codes to encode all information bits, select some information bits from the intermediate channel and encode them using LDPC codes. After encoding, the encoded bits are sent to the channel for transmission. S4: The channel receiving end receives the concatenated code word and performs concatenated code BP decoding to obtain the final decoding result; Step S1 includes the following steps: S11: Initialize the population P; S12: Select a population from the current population according to the fitness function through selection operation ; The fitness function is the subchannel error probability: ， in, is the mean of the LLR, is the subchannel number, Information input for the channel, is the total number of sub-channels; 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.

2. The Polar-LDPC encoding and decoding method based on a genetic algorithm according to claim 1, characterized in that: Step S11 specifically includes: performing channel coding on the polar code through Gaussian approximation to obtain an initial codeword vector M, and initializing the population P using the index of the information bit in M.

3. The Polar-LDPC encoding and decoding method based on a genetic algorithm according to claim 1, characterized in that: Individuals are different channel codes.

4. The Polar-LDPC encoding and decoding method based on a genetic algorithm according to claim 3, wherein: The mean of LLR is calculated by the following formula; ， in, is the noise variance of the Gaussian channel, and y is the information received from the channel.

5. The Polar-LDPC encoding and decoding method based on genetic algorithm according to claim 4, characterized in that: function Defined as 。 6. The Polar-LDPC encoding and decoding method based on a genetic algorithm according to claim 1, characterized in that: In step S4, concatenated code BP decoding is performed based on the factor graph.

7. 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 codeword 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 values ​​of the redundant bits in the LDPC codeword from the channel as input to the LDPC code decoder to obtain the LLR value of the protected information bit; S4.3: Update the LLR values ​​of all information bits according to the LLR values ​​of the protected information bits; S4.4: Send the updated LLR values ​​of all information bits on the left side to the adapter, and complete the adaptation process of the decoded information from left to right in the adapter; S4.5: The adapter outputs the right polar code codeword information required by the polar code decoder, and combines it with the decoded polar code codeword information 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 leftward and rightward transmitted information of the source end to obtain the final decoding result.

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