CN109981112A - A kind of sequencing statistical decoding method of partial cyclic redundancy check auxiliary - Google Patents

Abstract

The invention discloses a kind of sequencing statistical decoding method of partial cyclic redundancy check auxiliary, this method is suitable for the Soft decision decoding that information bit meets low-density checksum (LDPC) code of cyclic redundancy check (CRC).Before decoding, system generator matrix is formed according to the generator polynomial of cyclic redundancy check, and the matrix is divided into two parts, a part is for detecting decoding as a result, another part is used for additional interpretations；It is multiplied the part CRC generator matrix of additional interpretations to obtain joint generator matrix with the generator matrix of low density parity check code；Decoding process mainly uses iterative sequencing statistical to decode (BP-OSD) method, and joint generator matrix is used as the encoder matrix in OSD algorithm.After the completion of decoding, CRC check is done to the information bit of code word, if it is satisfied, the code is as decoding output；Otherwise judgement is decoding failure.This method is biggish while retaining CRC error detection function to enhance the error-correcting performance of LDPC code.

Description

A kind of sequencing statistical decoding method of partial cyclic redundancy check auxiliary

Technical field

The invention belongs to the decoding technique fields of channel error correction coding, more particularly to belong to the decoding skill of channel error correction coding Art field.

Background technique

1. cyclic redundancy check code

Cyclic redundancy check code (Cyclic Redundancy Check, CRC) is a kind of very important error-detecging code, it Not only coding is simple, and probability of miscarriage of justice is very low.CRC is substantially exactly the list entries for being K length, according to certain rules The check code (CRC code) that a length is L is generated, is added to behind original series, the sequence that a new length is K+L is constituted Column are sent.Receiving end is tested by reception sequence according to identical rule, so that it may find whether data transmission malfunctions. This rule, is known as " generator polynomial " in Error control theory.The main function of CRC is for detecting transmission data block In whether have an error code, but there is no the abilities corrected for error code itself.Implementation step is as follows:

If list entries length is K, it is expressed as binary polynomial:

The generator polynomial of cyclic redundancy check is expressed as:

The coding step of transmitting terminal can indicate are as follows:

Step 1: addition L zero in list entries tail portion, corresponding binary polynomial expression is exactly x^La(x)；

Step 2: removing x with generator polynomial g (x)^LA (x) obtains residue p (x), and the corresponding length of the formula is the binary system of L Sequence is CRC；

Step 3: joint x^LA (x) and p (x) obtains code polynomial x^LA (x)+p (x), the corresponding length of the formula are the two of K+L System sequence is to be added to the encoded sequence of CRC.

It receiving end only need to be with identical g (x) except the corresponding binary polynomial of reception sequence in decoding.If residue is Zero, it indicates there is no mistake in data transmission procedure, last L that receive sequence is removed and obtains original input sequence；Otherwise, Indicate data loading error occurring.

2. low density parity check code

2.1 brief introduction

Low-density checksum (LDPC) code is a kind of more special linear block codes, and particularity is its odd even school Test in matrix 1 number be far smaller than 0 number, referred to as sparsity, also referred to as low-density.The check matrix and code word of LDPC code Between meet following relational expression, wherein θ be complete zero column vector:

HC^TMod 2=θ.

The coding of 2.2 low density parity check codes

The cataloged procedure of LDPC code is as follows

Step 1: finding out generator matrix G for convenience, to can easily solve check bit in coding, can lead to Cross algorithm, such as gaussian elimination algorithm, to any one check matrix H can using linear transformation as exemplary verification matrix H ', verify square The columns of battle array H or H ' represents the length of code word, and line number represents the number of parity check bit.Exemplary verification matrix H ' such as following formula institute Show:

H '=[P^T|I]；

Exemplary verification matrix H ' can be divided into two parts, a portion is unit battle array I, another part P^TFor P matrix Transposed matrix.

Step 2: recycling the exemplary verification matrix H ' generator matrix G being shown below can be constructed:

G=[I | P]；

Two parts, a portion can be equally divided into using the typical generator matrix G of exemplary verification matrix H ' construction For a unit matrix I, another part is P matrix.

Step 3: being grouped according to the line number of generator matrix G to source bits U in block encoding, each grouping In include source bits number be generator matrix G line number.Each grouping is multiplied with generator matrix G mould 2 respectively to be encoded Output codons afterwards, each group output codons form output codons sequence according to order of packets.

Wherein i-th group of U_iThe output codons C being multiplied with generator matrix G_iAre as follows:

C_i=U_iG=[U_i|u_iP]

Wherein: each group of output codons C_iIn include two parts, a portion be this group of source bits U_iIt is generated with typical case It is that unit matrix I in matrix G is multiplied as a result, referred to as system position；Another part U_iP is this group of source bits U_iSquare is generated with typical case P matrix multiple in battle array G as a result, referred to as check bit.

2.3 bipartite graphs indicate

The check matrix of any one low density parity check code can be converted into one corresponding two points (Tanner) Figure, variable node and check-node are the marks that check matrix is converted into after Tanner figure, and variable node corresponds to check matrix Column, check-node correspond to check matrix row.

With check matrix H_4×8For, wherein V and S identifies corresponding variable node and check-node respectively:

The Tanner of conversion schemes as shown in Figure 1, there is 8 variable node v₁, v₂…v₈, 4 check-node s₁, s₂…s₄.With Box identifies check-node, and circle marking variable node connects the check-node and bit that the intersection element of corresponding row and column is 1 Node, such as v₁And s₁、v₁And s₂, will form many circulations in Tanner figure in this way, such as the wherein s of thick line mark₁、v₃、s₃ And v₇。

The iteration Soft decision decoding of 2.4 low density parity check codes

In the interpretation method of LDPC code, the iteration soft-decision decoding method based on bipartite graph, that is, BP decoding has fine Bit error rate performance, by standard and product interpretation method for, the key step of decoding is as follows:

The corresponding bipartite graph variable node of matrix and check-node collection for defining low density parity check code are combined into V={ v_n, N ∈ [1, N] }, S={ s_M,M ∈ [1, M] }；Defined variable node v_nThe check-node set A (n) of participation={ j, h_{J, n}=1 }, wrap Contained in check-node s_mVariable node set B (m)={ i, h_{M, i}=1 }；Define removal verification section in check-node set A (n) Point s_mNode set A (n) m, variable node v is removed in defined variable node set B (m)_nNode set B (m) n, coding Sequence C={ c_n,n∈[1,N]}；

Step 1: initialization: BPSK modulated signal x_n=1-2c_n, n ∈ [1, N] is by zero-mean variances sigma²Gauss white noise Acoustic channel obtains receiving signal sequence Y={ y_n|y_n=x_n+w_n, n ∈ [1, N] }, wherein w_nFor zero-mean variances sigma²White Gaussian Noise signal, initial variable node v_n, n ∈ [1, N] is to check-node s_m, m ∈ [1, M] output informationAnd Sentence to obtain sequence C firmly according to the symbol of signal in Y⁰, while the accumulation likelihood ratio data of initial each variable node And the number of iterations t=1, start iterative decoding；

Step 2: the output of the information of check-node and variable node updates: each check-node s_mBy the change of -1 iteration of kth Measure node output informationThe t times iteration node s is calculated according to the following formula_mTo variable node v_nThe information of output,

Each variable node v_nBy the verification formula output information of participationIt is added, as variable node v_nTo check-node s_mIt will Output,

Step 3: the output of the t times iteration: each variable node v_nBy the check-node s of all participations_m, m ∈ A's (n) OutputIt is added, the variable node as current iteration always exports

Step 4: according to the output information of each variable node of current iterationMake according to the following formula symbol sentence to obtain firmly it is defeated Sequence C out^t,

If the sequence meets all check equations, iterative decoding result will be as final decoding outputTogether When terminate the decoding of the frame, else if current iteration number t is not up to maximum number of iterations, continue iterative decoding, iteration time Number plus one, and jump to second step；

For longer irregular LDPC codes, BP decoding can achieve the performance close to shannon limit.But it is in practical application System through frequently with middle short length code block, and the corresponding bipartite graph of the LDPC code of finite length no longer have it is progressive without circle characteristic, Therefore BP decoding is compared still with maximum-likelihood decoding (MLD) decoding with biggish gap in this case.

The 2.5 LDPC code iterative sequencing statistical decoding methods based on accumulation likelihood ratio

Sequencing statistical decoding (OSD) method is also a kind of relatively early Soft decision decoding for being applied to linear block codes, is applicable in In the short code with certain Algebraic Structure.For length usually 100 or more the LDPC code with certain random configuration, OSD Decoding can not make high-order processing, therefore the performance of maximum-likelihood decoding (MLD) is also far not achieved in its error-correcting performance.It is translated using iteration The Soft Inform ation output of code can significantly improve the error correcting capability of LDPC code with the OSD decoding auxiliary BP decoding of lower order.By N is proportional in OSD interpretation method complexity², OSD decoding processing is all done to the output Soft Inform ation of each iteration, can be changed to each In generation, increases many time delays, destroys the high-speed coding characteristic of LDPC code.If certain iteration starting OSD among BP decoding is translated Code, since the Soft Inform ation of current iteration output is there are reforming phenomena, performance gain very little that OSD is decoded.Using initial One section of iterative decoding accumulates likelihood ratio information, can part overcome reforming phenomena, therefore the amplitude for accumulating likelihood ratio is more Effective reliability scaling information.

Specific step is as follows for the OSD method for assisting BP to decode:

Step 1: the variable node of current iteration, which always exports, is in the t times output of iterative decodingAccording to the following formula Add up the accumulation likelihood ratio output of each node up to the present, and wherein parameter alpha, 0≤α≤1 are weighting coefficient:

With the different Choices of parameter alpha, there are several types of different ways of realization: if α first is not with iteration time Number t changes and changes, then the process of likelihood ratio accumulation is similar to the IIR for doing a single order to each iteration output likelihood ratio and filters Processing；If secondly parameter alpha is always 1 or 0, accumulation is equivalent to the complete addition of each output or only selection is current seemingly It is so reliability sort by than output；If it is zero that last α is only in the number of iterations of certain fixed intervals, remaining when meet α ∈ (0,1], then the process of the accumulation, which is equivalent between these iteration intervals, fixes the FIR of order to the likelihood ratio of output Filtering processing；

Step 2: the likelihood ratio obtained using iterative decoding is exported as the reliability information of each bitAs The sort by of sequencing statistical decoding, according to reliability information absolute valueSequence from big to small, to node and generation Matrix respective column makes a sequence π₁, obtain new sequence node π₁(V) and generator matrix π₁(G)；

Step 3: making gaussian elimination to new generator matrix, due to the correlation properties between generator matrix column, need to column Make second of rearrangement π₂, finally obtain new generator matrixAnd sequence node

Step 4: by sequence node π₂(π₁(V)) in preceding a node of N-K-L ' according toSymbol make hard decision:

Obtain information sequenceIt does the traversal that order is s to a information bit symbol of preceding N-K-L ' again to overturn, i.e. selection institute Possible 0~s bit combination, altogether Kind does bit Overturning, obtains P_sA information sequenceRespectively with corresponding generator matrixMultiplication obtains code wordIt does to reset twice again and obtains all P_sA code word:

Step 5: rightSequence C is sentenced using initial reception sequence Y and its firmly⁰Compare Euclidean away from guarantor The output for staying Euclidean to decode away from the smallest code word as sequencing statistical

Final decoding output

It is to export the iterative decoding of fixed number of times based on the LDPC code iterative sequencing statistical decoding method of accumulation likelihood ratio Likelihood ratio accumulation, carries out OSD decoding processing on this basis.During BP iterative decoding, it is completed at the same time the tired of likelihood ratio Long-pending and OSD decoding processing, does not increase additional time delay.Based on the decoding of OSD several times that accumulation likelihood ratio is fixed, can obviously change The performance of kind BP decoding.

OSD decoding processing single order, second order and three ranks can be expanded to from zeroth order, with order increase error-correcting performance gradually Enhancing, OSD decoding complexity is also with the rising of factorial rank.In the case where the OSD that system is allowed decodes calculation amount restrictive condition, to reliable The mixing rank OSD processing that different nodes makees part is spent, is a preferable compromise side between decoding performance and implementation complexity Case.

Summary of the invention

Technical problem: the object of the present invention is to provide a kind of sequencing statistical decoding sides of partial cyclic redundancy check auxiliary Method meets cyclic redundancy check characteristic using LDPC code information bit, makees OSD decoding to LDPC code after iterative decoding, Middle Gray code matrix is the part generator matrix of cyclic redundancy check and the confederate matrix of LDPC system generator matrix, is not being increased Under conditions of system entirety decoding delay, completing performance, more preferably OSD is decoded.

Technical solution:

A kind of sequencing statistical decoding method of partial cyclic redundancy check auxiliary, it is characterised in that: specific to include following step It is rapid:

Define the system generator matrix G of low density parity check code_LDPCWith system check matrix H_LDPC, corresponding bipartite graph The collection of variable node is combined into V={ v_n,n∈[1,N]}；Information sequence m={ m_k, k ∈ [1, K] }, including K-L information bits With L cyclic redundancy check positions, the generator polynomial of L cyclic redundancy check isCoded sequence C ={ c_n, n ∈ [1, N] }, and meet C=mG_LDPC；

Step 1, it initializes: the generator polynomial of L cyclic redundancy check is expressed as to the generator matrix shape of (K-L) × K Formula:

Gaussian elimination based on linear transformation is carried out to generator matrix, preceding A=K-L column are converted into unit matrix, can be obtained The system form of cyclic redundancy check generator matrix:

G'_CRC=[I_A×A|P_A×L]；

Corresponding system form check matrix are as follows:

Use the part generator matrix of L ' (0≤L '≤L) position cyclic redundancy check are as follows:

Wherein, A '=K-L ', by G '_CRCIt is expressed as Column vector groups { g₁,g₂,g₃,…,g_K-1,g_K, then P_A×L' it is G '_CRCAfterwards The matrix of L ' column composition, i.e. P_A×L'={ g_K-L′+1,g_K-L′+2,…,g_K-1,g_K}；Then partial cyclic redundancy check and low-density parity The A ' of check code × N combines generator matrix are as follows:

G=G "_CRC×G_LDPC；

BPSK modulated signal x_n=1-2c_n, n ∈ [1, N] is by zero-mean variances sigma²Gaussian white noise channel, connect Receive signal sequence Y={ y_n|y_n=x_n+w_n, n ∈ [1, N] }, wherein w_nFor zero-mean variances sigma²White Gaussian noise signal, it is corresponding Sentence sequence firmly and be denoted as

Step 2, docking receive signal sequence Y use the iterative decoding method based on belief propagation, as standard or it is modified and Product interpretation method or the minimum and interpretation method of simplification；The number of iterations is denoted as t, and the likelihood ratio of each each variable node of iteration is defeated It is outThe accumulation likelihood ratio output to add up according to the following formula up to the presentWherein accumulation likelihood ratio is initially complete zero, ginseng Number α, 0≤α≤1 are preset weighting coefficient,

Make symbol according to the following formula to the output information of each variable node of current iteration to sentence to obtain output sequence C firmly^t:

If K bit meets cyclic redundancy check before the sequence meets all check equations and the sequence, it may be assumed that

Wherein, θ is full null vector；Then iterative decoding result will be as final decoding outputTerminating simultaneously should The decoding of frame；Else if current iteration number t is not up to maximum number of iterations t_max, then continue iterative decoding, and update accumulative Likelihood ratio output, the number of iterations add one, t++, repeat step 2；

Step 3, if iterative decoding is reaching maximum number of iterations t_maxIt is not able to satisfy all check equations still afterwards, utilizes The likelihood ratio output of each secondary iteration accumulation in iterative decodingAs the reliability information of each bit, according on each node Accumulation likelihood ratio absolute valueSequence from big to small makes one to node and above-mentioned joint generator matrix respective column A sequence π₁, obtain new sequence node π₁(V) and generator matrix π₁(G)；Gaussian elimination is made to new generator matrix, due to life At the correlation properties between rectangular array, need to make column second of rearrangement π₂, finally obtain new generator matrix:

And corresponding sequence node π₂(π₁(V))；By sequence node π₂(π₁(V)) preceding a node of N-K-L ' in According toSymbol make hard decision:

Obtain information sequenceIt does the traversal that order is s to a information bit symbol of preceding N-K-L ' again to overturn, i.e. selection institute Possible 0~s bit combination, altogether Kind does bit Overturning, obtains P_sA information sequenceRespectively with corresponding generator matrixMultiplication obtains code wordIt does to reset twice again and obtains all P_sA code word:

It is rightSequence C is sentenced using initial reception sequence Y and its firmly⁰Compare Euclidean away from reservation Euclidean The output decoded away from the smallest code word as sequencing statistical

To K bit before the output sequence, i.e. information bit m_OSDDo CRC check, it may be assumed that

H'_CRCm_OsDMod 2=θ；

If above formula meets, final decoding outputIt is such as unsatisfactory for, superior exports one and is unable to complete decoding Mistake in judgment.

The utility model has the advantages that the beneficial effects are mainly reflected as follows the following aspects:

1) cyclic redundancy check is divided into two parts function, and a part remains the function of superior system feedback error detection Can, another part assists OSD error correction, further improves the performance of decoding.

2) cyclic redundancy check auxiliary is assured that with the generator matrix of combining of LDPC in initial phase, and common OSD decoding, which is compared, will not bring additional delay and computation complexity.

3) in the case where BP iterative decoding is unable to get correct output, available original is decoded with CRC auxiliary low order OSD The performance for carrying out high-order OSD avoids high-order OSD bring computational complexity, and ensure that decoding performance.

Detailed description of the invention

Fig. 1 (a) is the connection schematic diagram of check-node and variable node；

Fig. 1 (b) is the check-node connection schematic diagram that some variable node is participated in it；

Fig. 1 (c) be some check-node with it includes variable node connection schematic diagram；

Fig. 2 is the Iterative statistical sequence interpretation method flow chart of cyclic redundancy check auxiliary；

Fig. 3 is the process flow diagram of OSD interpretation method；

Fig. 4 is 2/3 code rate (360,240) LDPC code of the BG_2 class basic matrix construction defined for 5G, part CRC auxiliary BP-OSD decode frame error rate and False Rate curve under awgn channel；

Fig. 5 is BP-OSD decoding of (180,120) LDPC code in the part CRC BP-OSD decoding and different rank assisted Under frame error rate and False Rate curve.

All explanation of symbols:

CRC: cyclic redundancy check；

OSD: sequencing statistical decoding method；

BP: BP decoding algorithm；

Total code block length of N:LDPC code；

The information bit length of K:LDPC code；

The maximum number of iterations of W:BP decoding；

The code rate of R:LDPC code；

L:CRC total length；

L ': the part CRC length of additional interpretations；

The order of s:OSD；

v_n: n-th of variable node；

s_m: m-th of check-node；

The code word that Gray code obtains；

The code word reset twice after Gray code；

By two minor sorts and complete the joint generator matrix of gaussian elimination；

G: the joint generator matrix that part CRC generator matrix and LDPC generator matrix are constituted；

V: variable node set.

Specific embodiment

The present invention is further illustrated below in conjunction with attached drawing:

The object of the present invention is to provide a kind of partial cyclic redundancy check auxiliary sequencing statistical decoding method, this method Feature is the low density parity check code for meeting cyclic redundancy check for an information bit, according to the generation of cyclic redundancy check Multinomial forms system generator matrix, and the matrix is divided into two parts, and a part is for detecting decoding as a result, another part is used In additional interpretations；The part CRC generator matrix of additional interpretations is multiplied with the generator matrix of low density parity check code and is joined Close generator matrix；In iterative decoding process, according to the amplitude of the likelihood ratio accumulated value of all previous iteration output of all variable nodes Size definition node reliability does descending sort by column of the reliability size to node and above-mentioned joint generator matrix, arranges column Matrix after sequence does gaussian elimination；In conjunction with the association system generator matrix that gaussian elimination obtains, the safe node after sequence is believed Breath sequence is encoded, and one group of candidate codewords is obtained；It is just each from being previously obtained if iterative decoding does not obtain final output Sequence Euclidean is chosen and received in group candidate codewords away from the smallest code；CRC check is done to the information bit of this yard, if it is satisfied, should Code is as decoding output；Otherwise judgement is decoding failure.The biggish LDPC code that enhances retain CRC error detection function while Error-correcting performance.

Fig. 1 (a) is a LDPC code bipartite graph structure chart, the i.e. connection schematic diagram of check-node and variable node, variable Node and check-node are denoted as v and s respectively.Fig. 1 (b) is variable node v_nThe check-node connection signal participated in it, and The likelihood ratio information transmitted between node.Fig. 1 (c) is check-node s_mWith it includes variable node connection signal and node Between the likelihood ratio information transmitted.

Fig. 2 is the BP-OSD interpretation method flow chart of part CRC auxiliary.Previously according to the generator matrix and CRC of LDPC code Generator polynomial calculate joint generator matrix, and initialize coded sequence；After BP decoding iteration each time, likelihood ratio is done Add up and store, determine current results sentence firmly sequence whether and meanwhile meet check matrix and CRC, export knot if satisfaction Otherwise fruit continues iteration until the number of iterations reaches preset maximum value；Cumulative likelihood ratio is executed into OSD decoding, Middle Gray code matrix selects the joint generator matrix precalculated, finally using OSD decoding output as output result.

Fig. 3 sorts accumulation likelihood ratio, that is, reliability of input according to sequence from high to low, to save storage and operation Amount, can only sort to index；Gaussian elimination is done from left to right to the joint generator matrix after sequence, if there is linear phase The column and corresponding node value are put into matrix finally, remaining columns sequentially move forward one by the column (i.e. complete zero column) of pass, final new sort Joint generator matrix obtain corresponding system generator matrix.Using the sequence and generator matrix after sequence, make coding and European Square calculates, and retains the smallest corresponding code word of European square.

Fig. 4 is 2/3 code rate (360,240) LDPC code of the BG_2 class basic matrix construction defined for 5G, part CRC auxiliary BP-OSD decode frame error rate performance curve under awgn channel and corresponding CRC judges curve by accident.As seen from the figure, it is selecting When with 16 CRC additional interpretations, performance is better than common single order BP-OSD algorithm about 0.08dB, is better than common BP algorithm about 0.2dB； Meanwhile remaining 8 CRC can make judgement to the correctness of decoding, and feed back to higher level, omission factor controls within 1%.

Fig. 5 is the mistake frame of the BP-OSD algorithm of the part CRC auxiliary of 2/3 code rate (180,120) LDPC code under awgn channel Rate performance curve.By comparing in figure it is found that under K=120 length, 16 CRC assist the performance of 1 rank BP-OSD decoding and common 2 rank BP-OSD decoding is suitable, but the former decoding efficiency is much higher than the latter, such as at 2.5dB, and 16 CRC assist 1 rank BP-OSD Decoding rate is about 5.6ms/ frame, and common 2 rank BP-OSD decoding rate is about 55ms/ frame, and efficiency improves nearly ten times.

2/3 code rate (360,240) and 2/3 code rate of the present invention for the construction of BG_2 class basic matrix defined in 5G agreement The sequencing statistical decoding of (180,120) LDPC code implementation section CRC auxiliary, by taking 2/3 code rate (360,240) LDPC code as an example, respectively Item code word and decoding parameter setting are as follows:

N=360, K=240, R=2/3, W=100, L=24；

G (D)=D²⁴+D²³+D¹⁸+D¹⁷+D¹⁴+Dⁿ+D¹⁰

+D⁷+D⁶+D⁵+D⁴+D³+D+1；

According to the definition of cyclic code, the generator polynomial of CRC is converted into size and is 216 × 240 generator matrix, and led to It crosses gaussian elimination and turns to system generator matrix.By taking L '=16 as an example, 16 CRC generator matrixes are by one 224 × 224 unit Battle array, complete zero gust of 8 × 8,216 × 8 matrix P composition, wherein matrix P is made of last 8 column of above system generator matrix.

16 CRC generator matrixes are multiplied with the LDPC system generator matrix that size is 240 × 360, obtain one CRC-LDPC confederate matrix, the matrix will act as the Gray code matrix of OSD method.

System modulates to obtain using biphase phase shift keying BPSK sends sequence, passes by additive white Gaussian noise awgn channel Defeated, receiving end demodulates to obtain logarithm naturally than the reliable degree series of expression.

To sequence is received using standard and long-pending iteration (BP) decoding, determined by LDPC check matrix, CRC check matrix Decode whether correct, such as correct directly output；Otherwise OSD decoding is carried out.

The method of OSD decoding is as it was noted above, distinguish the only replacement in Gray code matrix.OSD decoding output result still needs to By CRC check, the verification digit really acted at this time only has 24-16=8, verifies error detecing capability than under complete CRC-24 Drop, but still can reach 1% False Rate below, such as Fig. 4, in 5 shown in dotted line.If the result is able to satisfy CRC check, export Decode result；Otherwise decoding failure, the operation such as superior request retransmission are exported.

While main innovation point of the invention is to retain information bit CRC error detecing capability, promotion error-correcting performance is utilized；It adopts Mode does not utilize CRC error detecing capability auxiliary judgement code selection, is multiplied with part CRC matrix with generator matrix and generates connection Close generator matrix, the Gray code matrix in replacement OSD decoding；Judging from the experimental results, in the condition for not increasing system complexity Under improve decoding performance.

Claims (1)

1. a kind of sequencing statistical decoding method of partial cyclic redundancy check auxiliary, it is characterised in that: specifically include the following steps:

Define the system generator matrix G of low density parity check code_LDPCWith system check matrix H_LDPC, corresponding bipartite graph variable The collection of node is combined into V={ v_n,n∈[1,N]}；Information sequence m={ m_k, k ∈ [1, K] }, including K-L information bits and L The generator polynomial of cyclic redundancy check position, L cyclic redundancy check isCoded sequence C={ c_n,n ∈ [1, N] }, and meet C=mG_LDPC；

Step 1, it initializes: the generator polynomial of L cyclic redundancy check is expressed as to the generator matrix form of (K-L) × K:

Gaussian elimination based on linear transformation is carried out to generator matrix, preceding A=K-L column are converted into unit matrix, can be recycled The system form of redundancy check generator matrix:

G′_CRC=[I_A×A|P_A×L]；

Corresponding system form check matrix are as follows:

Use the part generator matrix of L ' (0≤L '≤L) position cyclic redundancy check are as follows:

Wherein, A '=K-L ', by G '_CRCIt is expressed as Column vector groups { g₁,g₂,g₃,…,g_K-1,g_K, then P_A×L′It is G '_CRCL ' column group afterwards At matrix, i.e. P_A×L′={ g_K-L′+1,g_K-L′+2,…,g_K-1,g_K}；Then partial cyclic redundancy check and low density parity check code A ' × N combine generator matrix are as follows:

G=G "_CRC×G_LDPC；

BPSK modulated signal x_n=1-2c_n, n ∈ [1, N] is by zero-mean variances sigma²Gaussian white noise channel, obtain receive letter Number sequence Y={ y_n|y_n=x_n+w_n, n ∈ [1, N] }, wherein w_nFor zero-mean variances sigma²White Gaussian noise signal, it is corresponding hard Sentence sequence to be denoted as

Step 2, docking receives signal sequence Y and uses the iterative decoding method based on belief propagation, as standard or modified and product are translated Code method or the minimum and interpretation method of simplification；The number of iterations is denoted as t, and the likelihood ratio output of each each variable node of iteration isThe accumulation likelihood ratio output to add up according to the following formula up to the presentWherein accumulation likelihood ratio is initially complete zero, parameter alpha, 0≤α≤1 is preset weighting coefficient,

Make symbol according to the following formula to the output information of each variable node of current iteration to sentence to obtain output sequence C firmly^t:

If K bit meets cyclic redundancy check before the sequence meets all check equations and the sequence, it may be assumed that

Wherein, θ is full null vector；Then iterative decoding result will be as final decoding outputThe frame is terminated simultaneously Decoding；Else if current iteration number t is not up to maximum number of iterations t_max, then continue iterative decoding, and update accumulative likelihood Than output, the number of iterations adds one, t++, repeats step 2；

Step 3, if iterative decoding is reaching maximum number of iterations t_maxIt is not able to satisfy all check equations still afterwards, utilizes iteration The likelihood ratio output of each secondary iteration accumulation in decodingAs the reliability information of each bit, according to tired on each node Product likelihood ratio absolute valueSequence from big to small makes a row to node and above-mentioned joint generator matrix respective column Sequence π₁, obtain new sequence node π₁(V) and generator matrix π₁(G)；Gaussian elimination is made to new generator matrix, due to generating square Correlation properties between array need to make column second of rearrangement π₂, finally obtain new generator matrix:

And corresponding sequence node π₂(π₁(V))；By sequence node π₂(π₁(V)) in preceding a node of N-K-L ' according toSymbol make hard decision:

Obtain information sequenceAgain to a information bit symbol of preceding N-K-L ' do order be s traversal overturn, that is, choose it is all can 0~s bit combination of energy, altogether Kind is done bit and is turned over Turn, obtains P_sA information sequenceRespectively with corresponding generator matrixMultiplication obtains code wordIt does to reset twice again and obtains all P_sA code word:

It is rightSequence C is sentenced using initial reception sequence Y and its firmly⁰Compare Euclidean away from reservation Euclidean is away from most The output that small code word is decoded as sequencing statistical

To K bit before the output sequence, i.e. information bit m_OSDDo CRC check, it may be assumed that

H′_CRCm_OSDMod 2=θ；

If above formula meets, final decoding outputIt is such as unsatisfactory for, superior exports one and is unable to complete sentencing for decoding Certainly mistake.