CN114421971A - Dynamic multi-symbol turning decoding method suitable for multi-element LDPC code - Google Patents

Dynamic multi-symbol turning decoding method suitable for multi-element LDPC code Download PDF

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CN114421971A
CN114421971A CN202210064071.2A CN202210064071A CN114421971A CN 114421971 A CN114421971 A CN 114421971A CN 202210064071 A CN202210064071 A CN 202210064071A CN 114421971 A CN114421971 A CN 114421971A
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iteration
sign
decoding
turning
sign bit
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姜明
范东丽
刘蕴箫
包秀文
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Southeast University
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    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
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    • H03M13/1108—Hard decision decoding, e.g. bit flipping, modified or weighted bit flipping

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Abstract

The invention provides a dynamic multi-symbol turning decoding method suitable for a multi-element LDPC code, which presets the maximum number of symbols allowed to be turned simultaneously according to the current iteration times and a turning threshold value, and the actual number of turned symbols cannot exceed the preset value. In the initial stage of iteration, the number of symbols allowed to be turned over is large, the invention can accelerate the convergence rate of decoding and reduce the decoding time delay. Along with the increase of the number of the iterative times of the turning decoding, the number of the symbols allowed to be turned at the same time is gradually reduced, the over-turned sign bit can be effectively corrected, and the turning precision is improved, so that the decoding performance is improved, and the system reliability is improved. The invention sets the number of symbols allowed to be turned over in stages according to the number of iterations. In one iteration, the sign bit with the largest and second largest inversion function values is preferentially inverted, and then the sign bit in which the inversion function value reaches the threshold is detected and inverted from the first sign bit in the coding order until the maximum allowed number of inverted signs is reached or all coded sign bits are traversed.

Description

Dynamic multi-symbol turning decoding method suitable for multi-element LDPC code
Technical Field
The invention relates to an iterative decoding method of a multi-element LDPC code, in particular to a dynamic multi-symbol turning decoding method suitable for the multi-element LDPC code, belonging to the technical field of decoding.
Background
Low Density Parity Check (LDPC) code was originally a linear block code with approaching shannon limit proposed by Gallager in 1962, Davey and Mackay studied a multi-element LDPC code for the first time in 1998, and compared with a binary LDPC code, a multi-element LDPC code with a medium-short code length has a better decoding performance, is more effective in high-order modulation, burst error correction, and the like, and is widely applied in storage, large-scale mobile communication, and other scenarios. The multi-element LDPC decoding algorithm is divided into a hard decision decoding algorithm, a soft decision decoding algorithm and a mixed decision decoding algorithm, wherein a large amount of soft quantity calculation is introduced into the soft decision algorithm, the algorithm complexity is high, the convergence is slow, the decoding complexity of the hard decision algorithm is low, the time delay is small, and the multi-element LDPC decoding algorithm is more suitable for being applied to a communication system requiring fast convergence and low time delay. For a regular multi-element LDPC code, each column (row) has the same number of non-zero elements, where the number of non-zero elements in each column (row) is referred to as the column (row) weight, which makes the implementation of the hard-decision decoding algorithm more efficient.
In the research of the conventional multi-element LDPC decoding algorithm, compared to MP (message-forcing) and MLgD (maximum-likelihood decoding), SFD (Symbol-flipping decoding) algorithm has lower decoding complexity and is easier to be implemented in hardware, and SFD algorithm uses information before Symbol flipping as a flipping criterion, and in order to improve error correction performance, a decoding algorithm introducing information after Symbol flipping into SFD is proposed as sfdp (SFD on prediction) algorithm (see documents s.wang, z.wang, l.j.and q.huang, "Symbol-flipping decoding base on prediction for non-coding LDPC," 2017Optical Fiber communication Conference and exception (OFC),2017, pp.1-3), and the number of times of appearance of symbols after Symbol flipping and sfdp as external prediction information and sfdp (external prediction) of sfdp information, in order to reduce the occurrence of the local cyclic oscillation decoding phenomenon in the decoding process, a D/P-SA-SFDP algorithm containing an automatic adjustment strategy and an N-D/P-SFDP algorithm containing noise as a random penalty term are successively proposed in an inversion standard, in the decoding algorithm, only one sign bit with the maximum or next maximum inversion weight function value is inverted in each iteration process, so that the sign inversion reliability is ensured, but more iteration times are required for decoding, the decoding convergence speed is low, and the decoding delay is low.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a dynamic multi-symbol turning decoding method suitable for a multi-element LDPC code, the whole decoding process is divided into a plurality of stages according to the iteration times, each stage allows turning of different numbers of sign bits, and the dynamic multi-symbol turning decoding of the whole multi-element LDPC code is realized based on the turning principle that firstly turning is performed more and then less, and firstly turning is performed on the sign bit with the maximum and second maximum turning weight function values and then turning is performed on the other sign bits, so that the limit of the maximum iteration times is effectively broken through, the decoding performance is improved under the condition of the limited maximum iteration times, the iteration convergence speed is accelerated, and the decoding time delay is reduced.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a dynamic multi-symbol reverse decoding method suitable for multi-element LDPC code is characterized by that its row and column weights are gamma and rho respectively, and are defined in that q is 2dThe encoding length of finite field GF (q) is N regular multivariate LDPC code C, and the check matrix H of M multiplied by N dimension is [ H [)m,n]M×NWherein h ism,nThe value of the element is recorded as the mth row and the nth column of the check matrix, and q is 2dThe sign elements in the finite field gf (q) have γ and ρ non-zero elements per row/column of the matrix, respectively. Mj＝{i:1≤i≤M,hi,jNot equal to 0 represents a set of syndromes in which the jth sign bit participates, Ni＝{j:1≤j≤N,hi,jNot equal to 0 represents the collection of sign bits participating in the ith check equation, and the decoding method comprises the following steps:
step 1: initialization: initializing all M row check formulas of the multi-element LDPC code into all zero row vector s with dimension of M(1)＝[s1,s2,...,sM](1)＝0MN coded symbols are mapped into Nd bits; the noisy signal transmitted through BPSK modulation and AWGN channel may be denoted as y ═ y in N coded symbols1,y2,...,yN]Wherein a single symbol contains d bits of the received signal yj＝[yj,1,...,yj,d]J ═ 1.., N; obtaining a hard decision symbol sequence with an initial length N by hard decision of bits on a signal y
Figure BDA0003479544650000021
Wherein
Figure BDA0003479544650000022
j 1.. N, for the jth sign bit in the kth iteration
Figure BDA0003479544650000023
Defining variables
Figure BDA0003479544650000024
Setting the step length of the turning threshold as delta and sign turning sign binary vector
Figure BDA0003479544650000031
Wherein the inverted flag bit of the jth sign bit in the kth iteration
Figure BDA0003479544650000032
Indicating that the jth sign bit performed a sign flip operation at the (k-1) th iteration,
Figure BDA0003479544650000033
indicating that the sign bit was not flipped over from the last iteration;
initializing a maximum number of iterations to kTThe whole decoding process is divided into T stages according to the iteration times: 1 to k1The sub-iteration is the 1 st stage, and the maximum allowed overturn w1Symbol, k1+1～k2The sub-iteration is the 2 nd stage, and the maximum allowed overturn w2Symbol … …, kT-1～kTThe sub-iteration is the Tth stage, and the maximum allowed turning wTA symbol, namely the iteration number is divided into T sections { [1, k { ]1],(k1,k2],...,(kT-1,kT]The maximum turnover corresponding to each sectionThe number of symbols is { w1,w2,...,wT}; entering iterative decoding, setting initial iteration times k as 1, initializing symbol reversal flag vector
Figure BDA0003479544650000034
The multiplication and addition operation of matrix elements and decoding symbol elements involved in the decoding process are both according to the operation rule defined by a finite field GF (q);
step 2: calculating a check formula: from s(k)＝z(k)*HTCalculating M check equations, s, for the current iteration(k)，z(k)Respectively representing the syndrome vector and the decoded symbol vector of the kth iteration, HTDenotes the transposition of H, if s(k)＝0MOutputting a current decoded symbol sequence z(k)Decoding is successful; otherwise, if k is less than or equal to kTExecuting a decoding step 3 if k > kTIf the decoding fails, ending the iterative decoding, wherein k represents the current iteration times;
and step 3: calculating a roll-over weight function value: according to the formula
Figure BDA0003479544650000035
Calculating rho external information sums corresponding to the jth sign bit; according to
Figure BDA0003479544650000036
Figure BDA0003479544650000037
Computing the jth sign bit with respect to
Figure BDA0003479544650000038
The value of the roll-over weight function of (1), wherein
Figure BDA0003479544650000039
Is [0,5.0 ]]Floating point numbers within the interval are AND
Figure BDA00034795446500000310
Hamming distance of
Figure BDA00034795446500000311
A positive-valued weighting factor that is a negative correlation,
Figure BDA00034795446500000312
the larger the size of the tube is,
Figure BDA00034795446500000313
the smaller the value is, the specific value is determined by a simulation experiment; calculating to obtain the turning weight function vector of all N sign bits
Figure BDA00034795446500000314
And the corresponding N sign-flip vectors are
Figure BDA00034795446500000315
Wherein
Figure BDA00034795446500000316
And
Figure BDA00034795446500000317
the maximum inversion weight function value and the corresponding sign inversion value of the jth sign bit are respectively, and the global maximum value and the secondary maximum value in the inversion weight function vector are respectively
Figure BDA0003479544650000041
And
Figure BDA0003479544650000042
corresponding sign flip values are respectively
Figure BDA0003479544650000043
And
Figure BDA0003479544650000044
α，β∈[1，N](ii) a Setting the number of current iteration reversed symbols as w to be 0;
and 4, step 4: and (3) turning over the sign bit: firstly, the maximum value of the turning weight function is judged
Figure BDA0003479544650000045
The corresponding sign bit, if
Figure BDA0003479544650000046
And is
Figure BDA0003479544650000047
Then turn over
Figure BDA0003479544650000048
w is w +1, update
Figure BDA0003479544650000049
Secondly, judging the maximum value of the turnover weight function
Figure BDA00034795446500000410
The corresponding sign bit, if
Figure BDA00034795446500000411
And w is less than the number w of symbols allowed to be flipped at most in the kth iteration<wt，k＝kt-1+1,...,ktThen turn over
Figure BDA00034795446500000412
w is w +1, update
Figure BDA00034795446500000413
And finally, sequentially judging sign inversion from the 1 st sign bit of the code word sequence, wherein j is 1
Figure BDA00034795446500000414
w＜wtAnd is
Figure BDA00034795446500000415
Then turn over
Figure BDA00034795446500000416
w is w +1 until the iteration reaches the maximum allowed number of symbols to be flipped wtOr the last sign bit j ═ N is reached, so that a new codeword sequence z is obtained(k+1)Meanwhile, setting the inversion flag bit of the sign bit which is not inverted in the iteration to be 0;
step 5, updating iteration times: and (5) executing a decoding step 2 when the iteration number k is k + 1.
Compared with the prior art, the invention has the following beneficial effects:
the decoding method provided by the invention divides the whole decoding process into a plurality of stages according to the iteration times, each stage allows the reversal of different numbers of sign bits, compared with a decoding algorithm which only allows the reversal of one sign bit per iteration, the decoding convergence speed is accelerated, the decoding time delay is reduced, but simultaneously, the most reliable sign bit, namely the sign bit with the maximum or the second maximum reversal weight function value, is judged to be reversed firstly in each iteration process, and the rest sign bits reaching the reversal threshold are continuously reversed before the number of the symbols which are allowed to be reversed is not reached to the maximum. Under the condition of limited iteration times, the decoding method provided by the invention can not only overturn uncorrectable error sign bits so as to improve the decoding performance, but also successfully decode under less iteration times, reduce the decoding time delay and be beneficial to the utilization of a hardware system requiring low time delay.
The decoding methods provided by the invention are all established on the basis of a symbol flipping decoding algorithm, and have the advantages of fast iterative convergence, low time delay and good error correction performance.
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FIG. 1 is a flowchart illustrating a decoding method according to the present invention.
FIG. 2 is a simulation verification diagram of the present invention: graph of frame error rate for (2,4) - (96,48) -GF (64) -multivariate LDPC codes.
FIG. 3 is a simulation verification diagram of the present invention: graph of average iteration number of (2,4) - (96,48) -GF (64) multivariate LDPC code.
FIG. 4 is a simulation verification diagram of the present invention: graph of frame error rate for (4,27) - (837,713) -GF (32) -multivariate LDPC codes.
FIG. 5 is a simulation verification diagram of the present invention: graph of average number of iterations of (4,27) - (837,713) -GF (32) -multivariate LDPC codes.
Detailed Description
In order to make the technical solution, objects and advantages of the present invention more clear, the present invention will be further clarified by the following description in conjunction with the accompanying drawings and specific examples, it being understood that these examples are only intended to illustrate the present invention and are not intended to limit the scope of the present invention.
Referring to fig. 1, the present invention provides a decoding method of a multi-element LDPC code, comprising:
let a row weight be γ and ρ, respectively, and be defined as q 2dMultivariate LDPC code C of finite field GF (q) with check matrix H of M multiplied by N dimension [ H ]m,n]M×NWherein h ism,nThe value of the element is recorded as the mth row and the nth column of the check matrix, and q is 2dThe symbol elements in the finite field GF (q) represent the collection of the check formula participated by the jth sign bit as Mj＝{i:1≤i≤M,hi,jNot equal to 0}, and the set of sign bits participating in the ith check formula is marked as Ni＝{j:1≤j≤N,hi,jNot equal to 0 }; transmitted symbol coding sequence c ═ c1,c2,...,cN]Wherein a single symbol contains d bit signals cj＝[cj,1,...,cj,d]，cj∈GF(q)，cj,l∈{0,1}，j＝1,...,N，l＝1,...,d。
In this embodiment, a regular multi-LDPC code C having row and column weights of 4 and 2, a coding length N of 96, and defined in a finite field GF (64) is selected1And a regular multi-element LDPC code C with a row weight of 4 and a column weight of 27, a coding length N of 837 and defined in a finite field GF (32)2Testing the decoding performance of the algorithm with code C1For example, the whole decoding process of the algorithm is detailed:
s1: initialization: general code C1All M-48 row syndromes are initialized to all zero row vectors s(1)＝[s1,s2,...,s48](1)＝048(ii) a The received signal sequence of the symbol coding sequence c after BPSK modulation and AWGN channel transmission is recorded as y ═ y1,y2,...,y96]Wherein y isj＝[yj,1,...,yj,6]J 1.., 96; obtaining a hard decision symbol sequence with an initial length of 96 according to bit hard decision on a received signal y
Figure BDA0003479544650000061
Wherein
Figure BDA0003479544650000062
j＝1,...,96，
Figure BDA0003479544650000063
1, d for the jth sign bit in the kth iteration
Figure BDA0003479544650000064
Defining variables
Figure BDA0003479544650000065
Setting the maximum number of iterations to k T100, the current iteration number k is 1, and the whole decoding process is divided into 3 stages according to the iteration number: 1-6 iterations are the 1 st stage, allowing at most a flip of w1The number of iterations is 7-16, namely 10 symbols, the 2 nd stage, and the maximum allowed overturn w22 symbols, 17-100 iterations are the 3 rd stage, and the maximum allowed overturn w31 symbol, i.e., { [1,6 ]],(6,16],(16,100]The maximum number of the reversed symbols corresponding to the symbols is {10,2,1 }; setting the step length delta of the turning threshold as 1, initializing a sign turning sign vector
Figure BDA0003479544650000066
For hard decision symbol sequence z(1)Carrying out iterative decoding;
s2-1: and (3) calculating a checking formula: from s(k)＝z(k)*HTCalculate 48 syndromes, s, for the current iteration(k)，z(k)Respectively representing the syndrome vector and the decoded symbol vector of the kth iteration, HTRepresents the transpose of H;
s2-2: judging a check formula: if s(k)＝048Outputting the current codeword sequence z(k)Decoding is successful;
s2-3: judging the maximum iteration times: otherwise, if k is less than or equal to 100, executing a decoding step 3, if k is more than 100, failing to decode, and ending iterative decoding, wherein k represents the current iteration times;
s3-1: and (3) calculating a turning weight function value: according to the formula
Figure BDA0003479544650000067
Calculating 2 external information sums corresponding to the jth sign bit; according to
Figure BDA0003479544650000068
Figure BDA0003479544650000069
Computing the jth sign bit with respect to
Figure BDA00034795446500000610
The value of the roll-over weight function of (1), wherein
Figure BDA00034795446500000611
Is and
Figure BDA00034795446500000612
hamming distance of
Figure BDA00034795446500000613
Determining code C by simulation experiment1Simulation parameter [ theta ]0,θ1,θ2,θ3,θ4,θ5,θ6]The value is [3.0,0.5,0.3,0.3,0.3,0.3, 0.3%]；
S3-2: determining a flipping weight function vector and a corresponding sign flipping vector: maximum flipping weight function value of jth sign bit
Figure BDA0003479544650000071
Corresponding to a symbol rollover value of
Figure BDA0003479544650000072
Finally, the turning weight function vector of all 96 sign bits is obtained
Figure BDA0003479544650000073
And itCorresponding sign flip vector
Figure BDA0003479544650000074
Wherein the global maximum and the sub-maximum in the vector of the inverse weight function are respectively
Figure BDA0003479544650000075
Corresponding sign flip values are respectively
Figure BDA0003479544650000076
S3-3: updating the number of the reversed symbols: setting the number of current iteration flip symbols as w to be 0;
s4-1: and turning over the sign bit meeting the turning condition: first, it is judged
Figure BDA0003479544650000077
The corresponding sign bit, if
Figure BDA0003479544650000078
And is
Figure BDA0003479544650000079
Then turn over
Figure BDA00034795446500000710
w is w +1, update
Figure BDA00034795446500000711
Second, the judgment
Figure BDA00034795446500000712
The corresponding sign bit, if
Figure BDA00034795446500000713
And w is less than the number w of symbols allowed to be flipped at most in the kth iteration<wt，k＝kt-1+1,...,ktThen turn over
Figure BDA00034795446500000714
w is w +1, update
Figure BDA00034795446500000715
And finally, sequentially judging the sign inversion from the 1 st sign bit of the sign sequence, wherein j is 1, a, 96, j is not equal to alpha and beta, and if the sign inversion is judged to be not equal to alpha and beta, the sign inversion is carried out
Figure BDA00034795446500000716
Figure BDA00034795446500000717
w<wtAnd is
Figure BDA00034795446500000718
Then turn over
Figure BDA00034795446500000719
w is w +1 until the iteration reaches the maximum allowed number of symbols to be flipped wtOr the last sign bit j is reached 96;
s4-2: updating the turning zone bit: setting the inversion flag bit of the non-inverted sign bit of the iteration to 0; obtaining a new codeword sequence z(k+1)；
S5: updating the iteration times: the iteration number k is k +1, and the process returns to the decoding step S2-1.
The decoding method provided by the invention divides the whole decoding process into a plurality of stages according to the iteration number, each stage allows different numbers of sign bits to be inverted, as described in S1, code C1In the whole iterative decoding process, the number of iterations is divided into 3 stages, each stage allows 10,2 and 1 sign bits to be inverted at most, and after the first decoding stage is finished, symbols which are over-inverted or have an error sign number which is not inverted can be inverted through the last two stages; meanwhile, each iteration process ensures that the two sign bits with the maximum or second maximum inversion weight function values are judged and inverted firstly, just as described in S4-1, so that the whole decoding process has higher decoding convergence speed and low decoding time delay, and can ensure that the wrong sign bits are inverted as correctly as possible, thereby improving the decoding performance.
FIGS. 2 and 3 show the D-SFDP algorithm and the present invention, respectivelyCode C under the algorithm (dynamic multi-symbols SFDP, DM-D-SFDP)1The Frame Error Rate (FER) and The Average iteration Number (The Average Number of Iterations) of The Frame Error Rate (FER) are plotted in a lower graph with different SNR, as can be seen from FIG. 2, The Frame Error Rate (FER) is 2 × 104In the process, the signal-to-noise ratio required by the D-SFDP algorithm is about 6dB, the signal-to-noise ratio required by the decoding algorithm provided by the invention is about 5.5dB, and the gain of 0.5dB is realized, and as can be seen from the graph in FIG. 3, the average iteration number of the decoding algorithm provided by the invention is 1/3 to 1/2 of the D-SFDP decoding algorithm in the range of the tested signal-to-noise ratio, so that the dynamic multi-symbol decoding method suitable for the multi-element LDPC code provided by the invention has better performance. FIGS. 4 and 5 show code C2At the maximum iteration number of 100, according to { [1,10 ]],(10,35],(35,100]The graph of the frame error rate and the average iteration times under different signal-to-noise ratios under the parameter setting that the maximum number of the turned symbols is {15,2,1}, and delta is 1 shows the same code C1Consistent decoding effect.
In summary, the decoding method for the multi-element LDPC code provided by the present invention can realize dynamic inversion of multiple sign bits in the iterative process, and ensure that two sign bits having the maximum and second maximum inversion weight function values can be preferentially inverted, the number of symbols which are allowed to be inverted at most at the later stage of the decoding stage is reduced to 2 or 1, and the remaining erroneous sign bits can be accurately inverted, so that the decoding performance can be improved on the basis of increasing the decoding convergence speed. Compared with the existing symbol reversal decoding algorithm, the dynamic multi-symbol reversal decoding method applicable to the multi-element LDPC codes, provided by the invention, not only can obtain better decoding performance, but also can accelerate decoding convergence and reduce decoding time delay, and is suitable for being used in a hardware system with higher time delay requirement.
The above is the preferred embodiment of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (5)

1. A dynamic multi-symbol flipping decoding method suitable for a multi-element LDPC code is characterized by comprising the following steps:
step S1: initializing a row check formula, a coding symbol and a maximum iteration number of the multi-element LDPC code, setting a turning threshold step length and initializing a symbol turning sign vector;
step S2: calculating a check formula, and performing check formula judgment and maximum iteration number judgment;
step S3: calculating a turning weight function value, determining a turning weight function vector and a corresponding sign turning vector, and updating the number of turning signs;
step S4: turning over the sign bit meeting the turning-over condition and updating the turning-over flag bit;
step S5: the number of iterations is updated, and the process returns to the decoding step S2.
2. The method of claim 1, wherein the row weight and column weight are γ and ρ, respectively, and are defined as q-2dThe encoding length of finite field GF (q) is N regular multivariate LDPC code C, and the check matrix H of M multiplied by N dimension is [ H [)m，n]M×NWherein h ism，nThe value of the element is recorded as the mth row and the nth column of the check matrix, and q is 2dSymbol elements in a finite field GF (q), wherein each row/column of the matrix is provided with gamma and rho nonzero elements respectively; mj＝{i：1≤i≤M，hi，jNot equal to 0 represents a set of syndromes in which the jth sign bit participates, Ni＝{j：1≤j≤N，hi，jNot equal to 0, represents a set of sign bits participating in the ith check equation, and step S1 specifically includes:
initializing all M row check formulas of the multi-element LDPC code into all zero row vector s with dimension of M(1)＝[s1，s2，...，sM](1)＝0MN coded symbols are mapped into Nd bits; the noisy signal transmitted through BPSK modulation and AWGN channel may be denoted as y ═ y in N coded symbols1，y2，...，yN]Wherein a single symbol contains d bits of the received signal yj＝[yj，1，...，yj，d]J ═ 1.., N; obtaining a hard decision symbol sequence with an initial length N by hard decision of bits on a signal y
Figure FDA0003479544640000011
Wherein
Figure FDA0003479544640000012
j 1.. N, for the jth sign bit in the kth iteration
Figure FDA0003479544640000013
Defining variables
Figure FDA0003479544640000014
Setting the step length of the turning threshold as delta and sign turning sign binary vector
Figure FDA0003479544640000015
Wherein the inverted flag bit of the jth sign bit in the kth iteration
Figure FDA0003479544640000016
Indicating that the jth sign bit performed a sign flip operation at the (k-1) th iteration,
Figure FDA0003479544640000021
indicating that the sign bit was not flipped over from the last iteration;
initializing a maximum number of iterations to kTThe whole decoding process is divided into T stages according to the iteration times: 1 to k1The sub-iteration is the 1 st stage, and the maximum allowed overturn w1Symbol, k1+1～k2The sub-iteration is the 2 nd stage, and the maximum allowed overturn w2Symbol … …, kT-1～kTThe sub-iteration is the Tth stage, and the maximum allowed turning wTA symbol, namely the iteration number is divided into T sections { [1, k { ]1]，(k1，k2]，...，(kT-1，kT]The maximum turnover corresponding to each sectionThe number of symbols is { w1，w2，...，wT}; entering iterative decoding, setting initial iteration times k as 1, initializing symbol reversal flag vector
Figure FDA0003479544640000022
The multiplication and addition operations of the matrix elements and the decoding symbol elements involved in the decoding process are according to the operation rule defined by the finite field GF (q).
3. The method according to claim 2, wherein the step S2 specifically includes: from s(k)＝z(k)*HTCalculating M check equations, s, for the current iteration(k)，z(k)Respectively representing the syndrome vector and the decoded symbol vector of the kth iteration, HTDenotes the transposition of H, if s(k)＝0MOutputting a current decoded symbol sequence z(k)Decoding is successful; otherwise, if k is less than or equal to kTExecuting a decoding step 3 if k > kTAnd ending the iterative decoding, wherein the decoding fails, and k represents the current iteration times.
4. The method according to claim 2, wherein the step S3 specifically includes: according to the formula
Figure FDA0003479544640000023
Computing the rho extrinsic information sums for the jth sign bit, where Ni＝{j：1≤j≤N，hi，jNot equal to 0 represents the set of sign bits participating in the ith check; according to
Figure FDA0003479544640000024
Figure FDA0003479544640000025
Computing the jth sign bit with respect to
Figure FDA0003479544640000026
The value of the roll-over weight function of (1), wherein
Figure FDA0003479544640000027
Figure FDA0003479544640000028
Value is (0, 5.0)]Interval is, is
Figure FDA0003479544640000029
Hamming distance of
Figure FDA00034795446400000210
A positive-valued weighting factor that is a negative correlation,
Figure FDA00034795446400000211
the larger the size of the tube is,
Figure FDA00034795446400000212
the smaller the specific value optimization is, the more the specific value optimization is determined by simulation experiments, Mj＝{i：1≤i≤M，hi，jNot equal to 0 represents the set of syndromes participated in by the jth sign bit; calculating to obtain the turning weight function vector of all N sign bits
Figure FDA00034795446400000213
And the corresponding N sign-flip vectors are
Figure FDA00034795446400000214
Wherein
Figure FDA00034795446400000215
And
Figure FDA0003479544640000031
the maximum inversion weight function value and the corresponding sign inversion value of the jth sign bit respectively, and the global maximum value in the inversion weight function vector is
Figure FDA0003479544640000032
A sub-maximum of
Figure FDA0003479544640000033
Corresponding sign flip values are respectively
Figure FDA0003479544640000034
And
Figure FDA0003479544640000035
α，β∈[1，N](ii) a The number of inverted symbols of the current iteration is set to w ═ 0.
5. The method according to claim 4, wherein the step S4 specifically includes: firstly, the maximum value of the turning weight function is judged
Figure FDA0003479544640000036
The corresponding decoded sign bit, if
Figure FDA0003479544640000037
And is
Figure FDA0003479544640000038
Then turn over
Figure FDA0003479544640000039
w is w +1, update
Figure FDA00034795446400000310
Secondly, judging the maximum value of the turnover weight function
Figure FDA00034795446400000311
The corresponding sign bit, if
Figure FDA00034795446400000312
Figure FDA00034795446400000313
And w is less than the number w < w of symbols allowed to be inverted at most in the kth iterationt，k＝kt-1+1，...，ktThen turn over
Figure FDA00034795446400000314
w is w +1, update
Figure FDA00034795446400000315
And finally, sequentially judging sign inversion from the 1 st sign bit of the code word sequence, wherein j is 1
Figure FDA00034795446400000316
w＜wtAnd is
Figure FDA00034795446400000317
Then turn over
Figure FDA00034795446400000318
w is w +1 until the iteration reaches the maximum allowed number of symbols to be flipped wtOr the last sign bit j ═ N is reached, so that a new codeword sequence z is obtained(k+1)And simultaneously setting the inversion flag bit of the non-inverted sign bit of the iteration to be 0.
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