Polar code retransmission method based on genetic algorithm optimization

Abstract

The present invention is a polarization code retransmission method based on genetic algorithm optimization, which includes the first step: the pre-retransmission coding part, including parameter definition, copy mapping construction, and retransmission part coding; the second step: genetic algorithm optimization of retransmission puncturing vector, including parameter definition and initialization, population initialization, inheritance and mutation, calculation of individual fitness parameters, population screening, etc.; the codeword used is a concatenated code formed by a cyclic redundancy check (CRC) code and a polarization code. The method of the present invention applies polarization matrix expansion retransmission in the case of decoding failure, applies genetic algorithm to the puncturing sequence of rate matching in retransmission, continuously screens out puncturing sequences with better bit error rate performance in the iterative process, and optimizes the next retransmission sequence based on the puncturing sequence of the previous retransmission, and finally converges to a local optimal solution to obtain performance gain.

Description

Technical Field

[0001] The invention belongs to the technical field of channel coding in wireless communications, and in particular relates to a polarization matrix expansion retransmission method of polarization codes based on genetic algorithm optimization. Background Art

[0002] Polar Code is a type of code that can be proven to have a transmission rate that can reach the channel capacity of a binary input memoryless symmetric channel under the SC decoding method. Polar Code uses channel aggregation and splitting operations to convert N independent physical channels of equal capacity into N new bit channels with different capacities. The position distribution of information bits and frozen bits is determined by analyzing the capacity of these N bit channels or using the Gaussian Approximation (GA).

[0003] Polarizing Matrix Extension Hybrid Automatic Retransmission Request (PME-HARQ) is a retransmission scheme unique to polar codes. After receiving a negative acknowledgment (NACK) at the transmitting end, some information bits are copied and mapped and then encoded and retransmitted, and the received signals are combined and decoded at the receiving end. The retransmission method based on genetic algorithm optimization in the present invention can improve the block error rate (BLER) performance of rate matching puncturing (Puncturing) in the retransmission system. Summary of the invention

[0004] Technical problem: The purpose of the present invention is to provide a polar code retransmission method based on genetic algorithm optimization, and the codeword used is a concatenated code formed by a cyclic redundancy check (CRC) code and a polar code. The method of the present invention applies polarization matrix expansion retransmission in the case of decoding failure, applies genetic algorithm to the puncturing sequence of rate matching in retransmission, continuously selects puncturing sequences with better bit error rate performance in the iterative process, and optimizes the next retransmission sequence based on the puncturing sequence of the previous retransmission, and finally converges to a local optimal solution to obtain performance gain.

[0005] Technical solution: The polar code retransmission method based on genetic algorithm optimization of the present invention comprises the following steps:

[0006] Step 1: Encoding before retransmission. This step includes the following process:

[0007] (1) Parameter definition

[0008] Assume that the length of the initially transmitted polarization code is N, and the number of information bits is K. The channel metric set calculated by the Gaussian approximation method is denoted as where g i , 1≤i≤N represents the Gaussian approximation of the i-th polarization channel; the sequence to be encoded is where u i , 1≤i≤N is the i-th element of the sequence to be encoded; the received sequence after encoding and transmission is where y i ,1≤i≤N is the i-th element of the received sequence;

[0009] Assume that the maximum number of retransmissions is Q, the number of bits per retransmission is E, and the length of the mother code after retransmission is N HARQ , and the code length N of the initially transmitted polar code satisfy the following relationship:

[0010]

[0011] in is the ceiling function;

[0012] The Gaussian approximation method is used to calculate the channel metric parameters after retransmission, which is recorded as where h j ,1≤j≤N HARQ represents the Gaussian approximation of the jth polarization channel; extract the sequence Middle front N HARQ -N elements And form a new sequence denoted as where β l ,1≤l≤N HARQ -N represents the Gaussian approximation of the lth polarization channel in the retransmission part, β l =h l ; Let the number of copy mappings be ω,

[0013] (2) Constructing a copy mapping

[0014] Get sequence The indices of the K elements with the largest channel metrics in constitute the information bit index set, denoted as Among them A k ,1≤k≤K represents the sequence The index of the kth largest element in the sequence The indices of the largest K elements in form a set, denoted as Among them B k ,1≤k≤K represents the sequence The index of the kth largest element in ,

[0015] The information bit index set of the initial transmitted sequence to be encoded Take the last ω elements and set the reliable bit index of the retransmitted sequence to be encoded Take the first ω elements to form the copy mapping relationship matrix:

[0016]

[0017] The elements in each column of the matrix satisfy a one-to-one correspondence: in Indicates a mapping relationship;

[0018] (3) Retransmission Partial Coding

[0019] The sequence to be encoded in the retransmission part is and initialized to a vector of all 0s, where ν l ,1≤l≤N HARQ -N is the lth element of the retransmitted part of the sequence to be encoded. According to the copy mapping relationship matrix (2), the sequence to be encoded is The value of the ω information bits is copied to the retransmitted coded sequence middle:

[0020]

[0021] Concatenate the two sets of sequences to be encoded into The input mother code length is N HARQ The encoder gets the codeword where x j ,1≤j≤N HARQ is the jth coded bit in the codeword; according to the lower triangular characteristics of the polar code generator matrix, the codeword subsequence of Initial transmission encoding sequence The encoded codeword does not participate in retransmission;

[0022] Step 2: Genetic algorithm optimizes the retransmission puncturing vector. This step includes the following process:

[0023] (1) Parameter definition and initialization

[0024] Let the current number of retransmissions be q, 1≤q≤Q, and initialize q=1; let the current number of iterations of the genetic algorithm be t, 1≤t≤T, where T is the upper limit of the number of iterations, and initialize t=1; let the upper limit of the number of individuals in the population of the genetic algorithm be V, and according to experience, the value of V is generally 5;

[0025] The puncturing vector of the qth retransmission is in Indicates the puncturing of the lth bit in the qth retransmitted codeword. A value of 0 indicates that the bit is a punctured bit and does not participate in transmission. Otherwise, the bit participates in transmission. The puncturing vector satisfies the following relationship:

[0026]

[0027] Where E is the number of bits per retransmission,

[0028] (2) Population initialization

[0029] If q = 1, initialize the population to V binary puncturing vectors of all 0s, denoted by P q =(p q,1 ,...,p q,n ,...,p q,V ), where p q,n , 1≤n≤V represents the nth puncturing vector, and then randomly set E 0s in the above puncturing vector to 1 so that it satisfies equation (4);

[0030] Otherwise, q≠1, first initialize the population to the binary puncturing vector of the previous retransmission, denoted as P q =(p q ,1 ,...,p q,n ,...,p q,V ), so that it satisfies p q,n =p q-1,1 ,1≤n≤V, and then randomly set E 0s in the above puncturing vector to 1 so that it satisfies equation (4);

[0031] (3) Inheritance and variation

[0032] The population participating in the tth iteration is constructed through a two-stage operation;

[0033] Genetic operation: Take any two perforated vectors in the population, perform bitwise AND operation on them, and generate new individuals

[0034]

[0035] Where 1≤n1,n2≤V,n1≠n2, & represents the bitwise AND operation of binary;

[0036] Mutation operation: The number of 0s and 1s in the newly generated individual ξ changes. It is necessary to set qE-∑ξ 0s to 1s. The positions are randomly determined. The mutation characteristics of the genetic algorithm are used to satisfy equation (4).

[0037] Every two sets of vectors in the population generate a new individual, and the newly generated offspring individuals and the original population together constitute ξ q =(ξ q,1 ,...,ξ q,ε ,ξ q,ε+1 ,...,ξ q,ε+V ),in

[0038]

[0039] (4) Calculate the individual fitness parameters

[0040] For the qth retransmission population ξ q All the puncturing vectors in the model channel are used for offline simulation. The model channel selects the additive white Gaussian noise channel or the time-varying fading channel. The transmitter transmits the punctured codeword, which is recorded as The receiving end receives the punctured codeword, which is recorded as where λ l ,1≤l≤N HARQ -N is the lth element, if Then the bit x of the punctured vector l Not transmitted, let λ l = 0; then the received sequence is cascaded into As the received sequence for joint decoding, r j ,1≤j≤N HARQ represents the jth received element, repeat the above process to obtain the bit error rate of each puncturing vector, recorded as the bit error rate vector BLER = (BLER1, ..., BLER ε+V ),

[0041] (5) Population screening

[0042] Filter out the bit error rate vector BLER=(BLER1,...,BLER ε+V ) indices of the V smallest values ​​θ=(θ1,...,θ V ), update the population P q make

[0043] (6) If the number of iterations t<T, set t=t+1 and go to step (3) to continue iterating; otherwise, go to step (7).

[0044] (7) If the number of retransmissions q < Q, then set q = q + 1, t = 1, and proceed to step (2) to optimize the puncturing sequence for the next retransmission; otherwise, the optimization is completed and the first item of the population after Q retransmissions is output, denoted as {p 1,1 ,...,p q,1 ,...,p Q,1}, where p q,1 It represents the local optimal puncturing vector after the qth retransmission optimized by the genetic algorithm, and the whole process is completed.

[0045] The mapping relationship is specifically manifested as follows: in the encoding stage, the to-be-encoded bits corresponding to the left index are used to cover the to-be-encoded bits corresponding to the right index; in the decoding stage, the estimated bits corresponding to the right index are used to cover the estimated bits corresponding to the left index.

[0046] The ω mentioned above needs to satisfy ω≤K and is selected autonomously according to the type of decoder or the channel status.

[0047] The qth retransmission population ξ q All the puncturing vectors in the model channel are used for offline simulation. The model channel can be an additive white Gaussian noise channel or a time-varying fading channel.

[0048] The mutation operation described above is as follows: the number of 0s and 1s in the newly generated individual ξ changes, and qE-∑ξ 0s need to be set to 1s.

[0049] Beneficial effect: The polarization code retransmission method based on genetic algorithm optimization of the present invention can optimize the polarization matrix expansion retransmission scheme. The optimization process is mainly aimed at the retransmission rate matching puncturing scheme. First, a population of puncturing vectors is constructed, and then the inheritance and mutation process of the genetic algorithm is applied to generate a new child population from the parent population. The new vector population is screened out according to the bit error rate BLER obtained by simulation, and the result is finally output by continuous iteration. The present invention also designs an optimization process for multiple retransmission puncturing, that is, the puncturing vector of the next retransmission is optimized based on the local optimal solution of the previous retransmission puncturing, so as to ensure the continuity and effectiveness of the system. The present invention obtains a large performance gain under a time-varying fading channel, and the method converges quickly. As an offline search and optimization, it does not bring additional complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a polar code retransmission method based on genetic algorithm optimization according to the present invention;

[0051] Figure 2 It is a schematic diagram of retransmission copy mapping in a specific implementation manner of the present invention. DETAILED DESCRIPTION

[0052] The polar code decoding method based on dynamic copy mapping of the present invention has a code length N=4, a number of information bits K=3, and a code length N after retransmission. HARQ =8, and the cyclic redundancy check code length r=2. The construction method of the polar code in this example is Gaussian approximation, the construction signal-to-noise ratio is 1.5 dB, and the generating polynomial of the cyclic redundancy check code is g(x)=x 2 +1.

[0053] like Figure 1 As shown, the following steps are included:

[0054] Step 1: Encoding before retransmission. This step includes the following process:

[0055] (1) Parameter definition

[0056] Assume that the length of the initially transmitted polarization code is N = 4, and the number of information bits is K = 3; the channel metric set calculated by the Gaussian approximation method is denoted as The sequence to be encoded is The received sequence after encoding and transmission is Assume that the maximum number of retransmissions is Q = 4, the number of bits in each retransmission is E = 1, and the length of the mother code after retransmission is N HARQ =8;

[0057] The Gaussian approximation method is used to calculate the channel metric parameters after retransmission, which is recorded as Remove sequence The first 4 elements in the sequence form a new sequence, denoted as β l =h l ; Assume that the number of copy mappings is ω=1, which can be selected autonomously according to the type of decoder or channel status.

[0058] (2) Constructing a copy mapping

[0059] Get sequence The indices of the three elements with the largest channel metrics in constitute the information bit index set, denoted as Get sequence The indices of the three largest elements in form a set, denoted as

[0060] The information bit index set of the initial transmission sequence to be encoded Take the last element and set the reliable bit index of the retransmitted sequence to be encoded Take the first element to form a matrix

[0061] (3) Retransmission Partial Coding

[0062] The sequence to be encoded in the retransmission part is And initialized to all 0 vectors. According to the copy mapping relationship, the sequence to be encoded The value of the information bit with the lowest reliability is copied to the retransmitted coded sequence The information bit with higher reliability is: ν1=u2. Then the two sets of sequences to be encoded are concatenated as Send it to the encoder with a mother code length of 8 to get the codeword, recorded as According to the lower triangular characteristics of the polar code generator matrix, the codeword The subsequence of This sequence is the initial transmission encoding sequence The encoded codeword does not participate in retransmission.

[0063] Step 2: Genetic algorithm optimizes the retransmission puncturing vector. This step includes the following process:

[0064] (1) Parameter definition and initialization.

[0065] Let the current number of retransmissions be q, 1≤q≤Q, and let q=1; let the current number of iterations of the genetic algorithm be t, 1≤t≤T, where T is the upper limit of the number of iterations, and let t=1; let the upper limit of the number of individuals in the population of the genetic algorithm be V=3;

[0066] Assume the puncturing vector of the qth retransmission is in 1≤l≤N HARQ -N represents the puncturing of the lth bit in the qth retransmission codeword. A value of 0 indicates that the bit is a punctured bit and does not participate in transmission. Otherwise, the bit participates in transmission. The puncturing vector satisfies the following relationship:

[0067]

[0068] Where E=1.

[0069] (2) Population initialization.

[0070] If q=1, initialize the population to V binary puncturing vectors of all 0s, and then randomly set E 0s in the above puncturing vectors to 1s:

[0071]

[0072] Otherwise, q≠1, first initialize the population to the binary puncturing vector of the previous retransmission, and then randomly set E zeros in the above puncturing vector to 1, taking q=2 as an example:

[0073]

[0074] (3) Inheritance and variation

[0075] Construct the population that participates in the tth iteration of the genetic algorithm. Take any two perforated vectors in the population, perform a bitwise AND operation on them, and set qE-∑ξ0s to 1 (the positions are randomly determined) to generate new individuals. Take q=2 as an example:

[0076] ξ 2,1 =p 2,1 &p 2,2 =(0,0,0,1)→(0,1,0,1)

[0077] ξ 2,2 =p 2,1 &p 2,3 =(0,0,0,1)→(1,0,0,1)

[0078] ξ 2,3 =p 2,2 &p 2,3=(0,0,1,1)→(0,0,1,1)

[0079] Every two sets of vectors in the population can generate a new individual. The newly generated offspring individuals and the original population together constitute a new population, denoted as ξ 2 =(ξ 2,1 ,ξ 2,2 ,ξ 2,3 ,p 2,1 ,p 2,2 ,p 2,3 ).

[0080] (4) Calculate the individual fitness parameters

[0081] For the qth retransmission population ξ q All puncturing vectors in the model channel are used for offline simulation (the model channel selects the time-varying fading channel). The codeword transmitted by the transmitter after puncturing is recorded as The receiving end receives the punctured codeword, which is recorded as if Then it means bit x l Not transmitted, let λ l = 0. Cascade the received signal into Repeat the above simulation process to obtain the bit error rate of each puncturing vector

[0082] BLER=(BLER1,...,BLER6)=(0.01,0.015,0.012,0.014,0.011,0.017)

[0083] (5) Population screening

[0084] Filter out the indexes of the V minimum values ​​in the bit error rate vector BLER, denoted as θ = (θ1, θ2, θ3) = (1, 3, 5);

[0085] Update population P q ,make

[0086] (6) If the number of iterations t<T, set t=t+1 and go to step (3) to continue iterating; otherwise, go to step (7).

[0087] (7) If the number of retransmissions q < Q, then set q = q + 1, t = 1, and proceed to step (1) to optimize the puncturing sequence for the next retransmission; otherwise, the optimization is completed and the first item of the population after Q retransmissions is output, denoted as {p 1,1 ,...,p q,1 ,...,p Q,1}, where p q,1 It represents the local optimal puncturing vector after the qth retransmission optimized by the genetic algorithm, and the whole process is completed.

[0088] The specific embodiments described herein are merely examples of the present invention. Those skilled in the relevant technical field may modify and supplement the specific embodiments described and further optimize the parameter values. Without departing from the principles of the present invention, these improvements are also considered to be within the protection scope of the present invention.

Claims

1. A polar code retransmission method based on genetic algorithm optimization, characterized in that The method comprises the following steps: Step 1: Encoding before retransmission. This step includes the following process: (1) Parameter definition Assume that the length of the initially transmitted polarization code is N, and the number of information bits is K. The channel metric set calculated by the Gaussian approximation method is denoted as where g i , 1≤i≤N represents the Gaussian approximation of the i-th polarization channel; the sequence to be encoded is where u i , 1≤i≤N is the i-th element of the sequence to be encoded; the received sequence after encoding and transmission is where y i ,1≤i≤N is the i-th element of the received sequence; Assume that the maximum number of retransmissions is Q, the number of bits per retransmission is E, and the length of the mother code after retransmission is N HARQ , and the code length N of the initially transmitted polar code satisfy the following relationship: in is the ceiling function; The Gaussian approximation method is used to calculate the channel metric parameters after retransmission, which is recorded as where h j ,1≤j≤N HARQ represents the Gaussian approximation of the jth polarization channel; extract the sequence Middle front N HARQ -N elements And form a new sequence denoted as where β l ,1≤l≤N HARQ -N represents the Gaussian approximation of the lth polarization channel in the retransmission part, β l =h l ; Let the number of copy mappings be ω, (2) Constructing a copy mapping Get sequence The indices of the K elements with the largest channel metrics in constitute the information bit index set, denoted as Among them A k ,1≤k≤K represents the sequence The index of the kth largest element in the sequence The indices of the largest K elements in form a set, denoted as Among them B k ,1≤k≤K represents the sequence The index of the kth largest element in , The information bit index set of the initial transmitted sequence to be encoded Take the last ω elements and set the reliable bit index of the retransmitted sequence to be encoded Take the first ω elements to form the copy mapping relationship matrix: The elements in each column of the matrix satisfy a one-to-one correspondence: Where a represents the mapping relationship; (3) Retransmission Partial Coding The sequence to be encoded in the retransmission part is and initialized to a vector of all 0s, where ν l ,1≤l≤N HARQ -N is the lth element of the retransmitted part of the sequence to be encoded. According to the copy mapping relationship matrix (2), the sequence to be encoded is The value of the ω information bits is copied to the retransmitted coded sequence middle: Concatenate the two sets of sequences to be encoded into The input mother code length is N HARQ The encoder gets the codeword where x j ,1≤j≤N HARQ is the jth coded bit in the codeword; according to the lower triangular characteristics of the polar code generator matrix, the codeword subsequence of Initial transmission encoding sequence The encoded codeword does not participate in retransmission; Step 2: Genetic algorithm optimizes the retransmission puncturing vector. This step includes the following process: (1) Parameter definition and initialization Let the current number of retransmissions be q, 1≤q≤Q, and initialize q=1; let the current number of iterations of the genetic algorithm be t, 1≤t≤T, where T is the upper limit of the number of iterations, and initialize t=1; let the upper limit of the number of individuals in the population of the genetic algorithm be V, and according to experience, the value of V is generally 5; The puncturing vector of the qth retransmission is in Indicates the puncturing of the lth bit in the qth retransmitted codeword. A value of 0 indicates that the bit is a punctured bit and does not participate in transmission. Otherwise, the bit participates in transmission. The puncturing vector satisfies the following relationship: Where E is the number of bits per retransmission, (2) Population initialization If q = 1, initialize the population to V binary puncturing vectors of all 0s, denoted by P q =(p q,1 ,...,p q,n ,...,p q,V ), where p q,n , 1≤n≤V represents the nth puncturing vector, and then randomly set E 0s in the above puncturing vector to 1 so that it satisfies equation (4); Otherwise, q≠1, first initialize the population to the binary puncturing vector of the previous retransmission, denoted as P q =(p q,1 ,...,p q ,n ,...,p q,V ), so that it satisfies p q,n =p q-1,1 ,1≤n≤V, and then randomly set E 0s in the above puncturing vector to 1 so that it satisfies equation (4); (3) Inheritance and variation The population participating in the tth iteration is constructed through a two-stage operation; Genetic operation: Take any two perforated vectors in the population, perform bitwise AND operation on them, and generate new individuals Where 1≤n1,n2≤V,n1≠n2, & represents the bitwise AND operation of binary; Mutation operation: The number of 0s and 1s in the newly generated individual ξ changes. It is necessary to set qE-∑ξ 0s to 1s. The positions are randomly determined. The mutation characteristics of the genetic algorithm are used to satisfy equation (4). Every two sets of vectors in the population generate a new individual, and the newly generated offspring individuals and the original population together constitute ξ q =(ξ q,1 ,...,ξ q,ε ,ξ q,ε+1 ,...,ξ q,ε+V ),in (4) Calculate the individual fitness parameters For the qth retransmission population ξ q All the puncturing vectors in the model channel are used for offline simulation. The model channel selects the additive white Gaussian noise channel or the time-varying fading channel. The transmitter transmits the punctured codeword, which is recorded as The receiving end receives the punctured codeword, which is recorded as where λ l ,1≤l≤N HARQ -N is the lth element, if Then the bit x of the punctured vector l Not transmitted, let λ l = 0; then the received sequence is cascaded into As the received sequence for joint decoding, r j ,1≤j≤N HARQ represents the jth receiving element, repeat the above simulation process to obtain the bit error rate of each puncturing vector, recorded as the bit error rate vector BLER = (BLER1, ..., BLER ε+V ), (5) Population screening Filter out the bit error rate vector BLER=(BLER1,...,BLER ε+V ) indices of the V smallest values ​​θ=(θ1,...,θ V ), update the population P q make (6) If the number of iterations t < T, set t = t + 1 and proceed to step (3) to continue iterating; otherwise, proceed to step (7). (7) If the number of retransmissions q < Q, then set q = q + 1, t = 1, and proceed to step (2) to optimize the puncturing sequence for the next retransmission; otherwise, the optimization is completed and the first item of the population after Q retransmission optimization is output, denoted as {p 1,1 ,...,p q,1 ,...,p Q,1 }, where p q,1 It represents the local optimal puncturing vector after the qth retransmission optimized by the genetic algorithm, and the whole process is completed.

2. The polar code retransmission method based on genetic algorithm optimization according to claim 1, characterized in that: The mapping relationship is specifically manifested as follows: in the encoding stage, the to-be-encoded bits corresponding to the left index are used to cover the to-be-encoded bits corresponding to the right index; in the decoding stage, the estimated bits corresponding to the right index are used to cover the estimated bits corresponding to the left index.

3. The polar code retransmission method based on genetic algorithm optimization according to claim 1, characterized in that: The ω mentioned above needs to satisfy ω≤K and is selected autonomously according to the type of decoder or the channel status.

4. The polar code retransmission method based on genetic algorithm optimization according to claim 1, characterized in that: The qth retransmission population ξ q All the puncturing vectors in the model channel are used for offline simulation. The model channel can be an additive white Gaussian noise channel or a time-varying fading channel.

5. The polar code retransmission method based on genetic algorithm optimization according to claim 1, characterized in that: The mutation operation described above is as follows: the number of 0s and 1s in the newly generated individual ξ changes, and qE-Σξ 0s need to be set to 1s.

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