CN1859013A - Low density odd-even check code iterative sequencing statistical decoding method - Google Patents

Abstract

This invention relates to an iteration sort statistic decode method for low density odd-even check codes (LDPC), in the process of decoding, a sort statistic decoding method is applied to assist the iteration decode based on the amplitude of the accumulation value of the likelihood ratio output in iteration each time by all variable nodes, namely, the variable nodes output and accumulate the likelihood ratios and the absolute value of the accumulated likelihood ratio is defined as the stability of the current iterated nodes then to sort the columns of the nodes and the check matrixes for ascending order based on the stability and carrying out gauss elimination to the sorted matrixes to generate a matrix combining the system after the gauss eliminatioin and code the sorted two stabilized node information sequences to get a set of code words for selection, if there is no final output for the iteration decode, then the code words for selection with the smallest Euclidean distance are selected and received as the decode output.

Description

Low density odd-even check code iterative sequencing statistical decoding method

Technical field

The present invention is the soft-decision decoding method of low density parity check code, belongs to the decoding technique field of channel error correction coding.

Background technology

In the middle of the interpretation method of LDPC sign indicating number, be that BP decoding has good bit error rate performance based on the iteration soft-decision decoding method of bipartite graph, the irregular LDPC codes for long can reach the performance near shannon limit.But system often adopts the code block of short-and-medium length in the practical application, and the bipartite graph of the LDPC sign indicating number correspondence of finite length no longer has progressive no circle characteristic, and therefore BP decoding and MLD decipher to compare and still have bigger gap in this case.The OSD interpretation method also is a kind of Soft decision decoding that early is applied to linear block codes, is applicable to the short code with certain Algebraic Structure.Usually at the LDPC sign indicating number with certain random configuration more than 100, OSD decoding can't be made high-order and handle, so its error-correcting performance does not far reach the performance of MLD yet for length.Utilize the soft information output of iterative decoding,, can obviously improve the error correcting capability of LDPC sign indicating number with the auxiliary BP decoding of the OSD decoding of lower-order number.Because OSD interpretation method complexity is proportional to N ², the soft information of the output of each iteration is all done OSD decoding handle, increase a lot of time delays can for each iteration, destroy the high-speed coding characteristic of LDPC sign indicating number.If certain iteration in the middle of BP decoding starts OSD decoding, because there is reforming phenomena in the soft information of current iteration output, the performance gain that OSD decoding obtains is very little.Utilize one section initial iterative decoding accumulation likelihood ratio information, can partly overcome reforming phenomena, the amplitude of therefore accumulating likelihood ratio is that more efficiently reliability is weighed information.

Based on the LDPC code iterative sequencing statistical decoding method of accumulation likelihood ratio, be with the iterative decoding output likelihood ratio accumulation of fixed number of times, carry out OSD decoding on this basis and handle.In the process of BP iterative decoding, finish the accumulation and the OSD decoding of likelihood ratio simultaneously and handle, do not increase extra time delay.Based on the fixing decoding of OSD several times of accumulation likelihood ratio, can obviously improve the performance of BP decoding.OSD decoding is handled can expand to single order from zeroth order, second order and three rank, and along with the increase error-correcting performance of exponent number strengthens gradually, the OSD decoding complexity is also by N ²Increase rapidly to N ³Under OSD that system allows decoding amount of calculation restrictive condition, the mixing rank OSD that the different node of reliability made part handle, and are half-way houses preferably between decoding performance and the implementation complexity

Summary of the invention

Technical problem: the purpose of this invention is to provide a kind of low density odd-even check code iterative sequencing statistical decoding method based on the accumulation likelihood ratio, utilize the likelihood ratio cumulative information of iterative decoding output, before iterative decoding finishes the LDPC sign indicating number being made OSD handles, under the condition that does not increase LDPC sign indicating number iterative decoding time delay, finish OSD decoding, improve performance.

Technical scheme: the present invention is a kind of low density odd-even check code iterative sequencing statistical decoding method based on the accumulation likelihood ratio, the characteristics of these association schemes are that likelihood ratio accumulation and OSD decoding are handled and BP decoding is carried out simultaneously, beginning or middle iteration output likelihood ratio are constantly accumulated, obtaining beginning OSD decoding processing on the comparatively stable accumulation likelihood ratio information basis, BP decoding is simultaneously proceeded.Ordering in the OSD interpretation method, the matrix gaussian elimination, Gray code, high-order is handled and Euclidean is broken down into one section continuous iterative decoding in the time apart from processing procedures such as calculating.If reach greatest iteration decoding number of times, the BP interpretation method still can not provide suitable output code word, and what OSD decoding obtained will export as final decoding apart from the candidate codewords of minimum with the information of reception Euclidean.

In the iterative decoding process of low density parity check code, amplitude size according to the likelihood ratio accumulated value of all previous iteration of all variable nodes output, adopt the auxiliary iterative decoding of sequencing statistical decoding method, being each variable node adds up the node likelihood ratio output of all previous iteration, accumulation likelihood ratio absolute value is defined as the node point reliability of current iteration, and the row of node and check matrix are done ascending sort according to the reliability size, the matrix after the row ordering is done gaussian elimination; Owing to linear correlation can occur between the matrix column in the cancellation process, the ascending sort adjustment must try again the row of these linear correlations and corresponding node; In conjunction with system's generator matrix that gaussian elimination obtains, the safe node information sequence behind two minor sorts of front is encoded, obtain one group of candidate codewords; If iterative decoding does not obtain final output, just respectively organized and chosen the candidate codewords and of the conduct decoding output of receiving sequence Euclidean apart from minimum from the front.

The iterative decoding of low density parity check code can be expressed as the step of carrying out in the following order:

The generator matrix G and the check matrix H of definition low density parity check code _{M * N}=[h _{M, n}], corresponding bipartite graph variable node and check-node set are V={v _n, n ∈ [1, N] }, S={s _m, m ∈ [1, M] }; Defined variable node v _nCheck-node set A (n)={ j, the h that participates in _{J, n}=1} is contained in check-node s _mVariable node set B (m)={ i, h _{M, i}=1}; Remove check-node s in the definition check-node set A (n) _mNode set A (n) m, remove variable node v among the defined variable node set B (m) _nNode set B (m) n, coded sequence

C＝{c _n，n∈[1，N]}；

Step (1) initialization: BPSK modulates x _n=1-2c _n, n ∈ [1, N] is through the zero-mean variances sigma ²The white Gaussian noise channel, obtain received signal sequence Y={y _n| y _n=x _n+ w _n, n ∈ [1, N] }, initial variable node v _n, n ∈ [1, N] is to check-node s _m, m ∈ A (n) output information $L_{\mathrm{nm}}^0={2y}_n/{\mathrm{\σ}}^2,$ And declare firmly according to the symbol of signal among the Y and to obtain sequence C ⁰, the accumulation likelihood ratio data of simultaneously initial each variable node $L_n^{\mathrm{sum}}=0,$ And iterations k=1, the beginning iterative decoding;

The information output of step (2) check-node and variable node is upgraded: each check-node s _mVariable node output information L with the k-1 time iteration _{N ' m} ^K-1, calculate iteration node s the k time according to following formula _mTo variable node v _nThe information of output,

$L_{\mathrm{mn}}^k=2a\tanh \underset{n^{\′}\∈B\left(m\right)\backslash n}{\mathrm{\Π}}\tanh (L_{n^{\′}m}^{k-1}/2);$

Each variable node v _nWith the verification formula output information L that participates in _{M ' n} ^kAddition is as variable node v _nTo check-node s _mOutput,

$L_{\mathrm{nm}}^k=\underset{m^{\′}\∈A\left(n\right)\backslash m}{\mathrm{\Σ}}{L}_{m^{\′}n}^k;$

The output of the k time iteration of step (3): each variable node v _nCheck-node s with all participations _m, the output L of m ∈ A (n) _Mn ^kAddition is always exported L as the variable node of current iteration _n ^k, simultaneously according to following formula add up the accumulation likelihood ratio output up to the present of each node, wherein parameter alpha ^k, 0≤α ^k≤ 1 is weight coefficient,

$L_n^{\mathrm{sum}}={\mathrm{\α}}^k\·L_n^{\mathrm{sum}}+L_n^k;$

Step (4) is according to the output information L of each variable node of current iteration _n ^k, make symbol according to following formula and declare firmly and obtain output sequence C _IT ^k,

$\left\{\begin{array}{ccc}{c}_{\mathrm{IT},n}^k=0,& \mathrm{if}& L_n^k>0\\ c_{\mathrm{IT},n}^k=1,& \mathrm{if}& L_n^k\≤0\end{array}\right.;$

If this sequence satisfies all check equations, then the iterative decoding result will be as final decoding output

Stop the decoding of this frame simultaneously, if can not satisfy all check equations and iterations k equals maximum iteration time, then decoding failure stops decoding, current iteration number of times k satisfies else if, mod (k, I)=0, wherein parameter I is the iteration interval of sequencing statistical decoding, then starting sequencing statistical decoding handles, continue iterative decoding simultaneously, jump to step (2), k++.

The sequencing statistical decoding method of low density parity check code is to combine with interative encode method, utilize the reliability information of the likelihood ratio output of each time iteration accumulation in the iterative decoding as each bit, as the sort by of sequencing statistical decoding, sequencing statistical decoding method can be expressed as the step of carrying out in the following order: according to the accumulation likelihood ratio absolute value on each node | L _n ^Sum| order from big to small, node and corresponding check rectangular array are made an ordering π _K1, obtain new sequence node π _K1(V) and check matrix π _K1(H); New check matrix is made gaussian elimination, because the correlation properties between the check matrix column need be made row and be reset π for the second time _K2, obtain new generator matrix G at last _kAnd corresponding with it check matrix π _K2(π _K1And sequence node π (H)) _K2(π _K1(V)); With sequence node π _K2(π _K1(V)) N-M node is according to L before in _n ^SumSymbol make declaring firmly and obtain information sequence, and by corresponding generator matrix G _kCoding obtains code word Do twice rearrangement again and obtain code word $C_{\mathrm{OSD}}^k={\mathrm{\π}}_1^{-1}\left({\mathrm{\π}}_2^{-1}\left({\tilde{C}}_{\mathrm{OSD}}^k\right)\right);$ The code word C that utilizes the decoding of initial receiving sequence Y and sequencing statistical to obtain _OSD ^kCompare the Euclidean distance according to following formula, keep the output that Euclidean is deciphered as sequencing statistical apart from the code word of minimum

$C_{\mathrm{OSD}}=\underset{C_{\mathrm{OSD}}^k}{\arg \min }\underset{n,c_{\mathrm{OSD},n}^k\≠c_n^0}{\mathrm{\Σ}}\left|y_n\right|$

If iterative decoding can not get output correctly, the output of sequencing statistical decoding is C as a result _OSDWill be as the final output of system

Iterative decoding is the interpretation method of a class based on belief propagation; Iterative decoding both can be standard or correction and long-pending interpretation method, also can use the minimum and interpretation method and relevant a series of correction minimums and interpretation method thereof of simplification; These Soft decision decodings based on belief propagation can upgrade the likelihood ratio output of each node by iteration, and weaken the reforming phenomena of iterative decoding output by the accumulation of likelihood ratio; On the basis of certain accumulation likelihood ratio amplitude, sequencing statistical decoding method can with above-mentioned interative encode method parallel processing, if iterative decoding can not provide rational decode results, then being that output is finally deciphered by system with the information of reception Euclidean apart from the result of minimum in the sequencing statistical decoding output.

The computational methods of accumulation likelihood ratio are: along with parameter alpha ^kDifference choose scheme, following several different way of realization can be arranged; α at first ^kIf do not change with iterations k, then the process of likelihood ratio accumulation is similar to the IIR Filtering Processing of each iteration output likelihood ratio being done a single order; Secondly if parameter alpha ^kBe always 1 or 0, accumulation is equivalent to each time exported addition completely or only choose current likelihood ratio and is output as the reliability sort by; Last if α ^kOnly the iterations in some fixed intervals is to be zero, all the other the time satisfy α ^k∈ (0,1], then the process of this accumulation is equivalent between these iteration interval the fix FIR Filtering Processing of exponent number of likelihood ratio to output.

Sequencing statistical decoding method can reach the output result who provides sequencing statistical decoding when maximum iteration time finishes in the iterative decoding failure since the k time iteration and interative encode method parallel processing; The scheme of iterative decoding and sequencing statistical decoding algorithm Parallel Implementation can be improved the decoding performance of low density parity check code under the situation that does not increase the low density odd-even check code iterative decoding delay like this; Sequencing statistical decoding method also can serially concatenated in the rear end of iterative decoding process, the likelihood ratio information that such processing mode can the most effective utilization accumulation obtains better bit error rate performance.

Sequencing statistical decoding is according to the sequence node π after sorting _K2(π _K1(V)) do and declare coding firmly; Definition is zeroth order sequencing statistical decoding order-0 according to the scheme of declaring sequential coding firmly directly, and the sequencing statistical decoding treatment process that preceding N-M information bit symbol is traveled through upset i bit sign is defined as order-i; Can carry out the high-order upset to the lower node of part reliability and handle, do and mix rank sequencing statistical decoding processing H_order (e ₁, e ₂E _r), e wherein _iFor doing the interstitial content that order-i handles.

Beneficial effect: beneficial effect of the present invention is mainly reflected in the following aspects:

1) under the situation that the BP iterative decoding can't rationally be exported, because OSD decoding processing is auxiliary, a large amount of iteration can not the error correction mistake can obtain correct decode results.

2) reforming phenomena of nodal information has partly been eliminated in the accumulation of likelihood ratio, and decoding is handled and carried to OSD

3) supplied reliability criterion more accurately.

4) parallel processing of BP and OSD decoding does not increase system's decoding delay, has guaranteed the high speed characteristics of original iterative decoding.

5) adjustment of parameter alpha can further improve the validity of likelihood ratio accumulation, improves OSD decoding handling property.

Description of drawings

Fig. 1 is a LDPC sign indicating number bipartite graph connection diagram.Wherein, Fig. 1 a is the connection diagram of check-node and variable node, and Fig. 1 b is the check-node connection diagram of certain variable node and its participation, and Fig. 1 c is the variable node connection diagram that certain check-node comprises with it.

Fig. 2 is the iterative sequencing statistical BP-OSD interpretation method flow chart of LDPC sign indicating number.

Fig. 3 is the process chart of OSD interpretation method.

Fig. 4 is at 5/6 code check (576,480) the LDPC sign indicating number of stipulating in the 802.16e agreement, the sequential relationship of OSD decoding decomposition computation and iterative decoding.

Fig. 5 is the frame error rate performance curve of (576,480) LDPC sign indicating number under BP decoding and BP-OSD decoding.

Below be all explanation of symbols:

OSD: sequencing statistical decoding method;

BP: belief propagation decoding algorithm;

Total code block length of N:LDPC sign indicating number;

The information bit length of K:LDPC sign indicating number;

The line number of M:LDPC code check matrix;

The maximum iteration time of W:BP decoding;

The code check of R:LDPC sign indicating number;

The piecemeal LDPC sign indicating number matrix of z:802.16e agreement regulation, sub-piece dimension;

F:LDPC sign indicating number decoding system clock frequency;

λ: the data throughput rate of ldpc code decoder.

v _n: n variable node;

s _m: m check-node;

A (n): variable node v _nThe check-node set that participates in;

B (m): variable node s _mThe variable node set that comprises;

L _Nm ^k: the k time iteration variable node v _nTo check-node s _mThe likelihood ratio information of transmitting;

L _Mn ^k: the k time iteration check-node s _mTo variable node v _nThe likelihood ratio information of transmitting;

L _n ^k: the k time iteration variable node v _nThe likelihood ratio information of output;

L _n ^Sum: variable node v _nThe all previous repeatedly likelihood ratio information accumulation of big output;

C ^K0: K ₀Inferior iteration is declared sequence firmly according to what the accumulation likelihood ratio obtained;

C _OSD ^K0: k ₀Output is handled in the OSD decoding of inferior iteration;

C _OSD: the final processing output of OSD decoding;

The final output of BP-OSD decoding;

G ^K0: k ₀Inferior iteration OSD handles the system's generator matrix that obtains;

Order-1: single order OSD deciphers processing;

H_order (e ₁, e ₂): mix second order OSD decoding, e ₁, e ₂It is individual to be respectively 1 rank, 2 rank processing nodes.

Embodiment

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

Fig. 1 (a) is a LDPC sign indicating number bipartite graph structure chart, i.e. the connection diagram of check-node and variable node, and variable node and check-node are designated as v and s respectively.(b) be variable node v _nBe connected signal with the check-node of its participation, and the likelihood ratio information of transmitting between node.(c) be check-node s _mBe connected signal with the variable node that it comprises, and the likelihood ratio information of transmitting between node.

Fig. 2 is the flow process of BP-OSD decoding.Pass through k in advance ₀Inferior iterative processing is with preceding k ₀The likelihood ratio input OSD decoding of inferior iteration accumulation.When iterative decoding continued to carry out, node continued to export the likelihood ratio accumulation, with k ₀Accumulated value start OSD decoding.If when the 0th OSD processing finished, the BP iterations was k ₁, proceed to k ₁The likelihood ratio accumulated value of inferior iteration is carried out OSD decoding.BP-OSD decoding reaches up to maximum iteration time by this step executed in parallel, can't finish iterative decoding, then with OSD decoding output.

The accumulation likelihood ratio that Fig. 3 will import is at first determined different reliability segmentations with each thresholding, again ordering is done in these segmentations.Node after segmentation and the ordering according to reliability order from low to high, is made gaussian elimination to different segmentations and is handled, and obtains system's generator matrix of correspondence up to the matrix of new sort.Utilize sequence and generator matrix after sorting, make coding and European square and calculate, keep the corresponding code word of European square minimum.

Fig. 4 is the sequential chart at the concrete case study on implementation of BP iterative decoding of 5/6 code check (576,480) the LDPC sign indicating number of 802.16e agreement regulation and OSD decoding parallel computation, and wherein OSD is order-1 and handles.

Fig. 5 is under the awgn channel, length overall 576, message length 480, the irregular LDPC codes of 5/6 code check, 100 iteration BP methods, frame error rate under 100 iteration BP-OSD interpretation methods and bit error rate performance relatively, wherein the OSD algorithm is according to last concrete upset exponent number, provide order-1 and H_order (400,50) respectively and mix 2 rank performance curves.The likelihood ratio output of preceding 10 iteration is accumulated in parameter alpha=1 of likelihood ratio accumulation, begins OSD decoding on this basis and handles.The decoding performance of the parallel decoding scheme that we provide when the OSD of order-1 handles improved nearly 0.3dB than original BP interpretation method.As can be seen from the figure, the BP-OSD interpretation method of mixing 2 rank has obtained surpassing the performance gain of 0.4dB than direct BP iterative decoding.

The present invention is in the iterative decoding process of low density parity check code, amplitude size according to the likelihood ratio accumulated value of all previous iteration of all variable nodes output, adopt the auxiliary iterative decoding of sequencing statistical decoding method, being each variable node adds up the node likelihood ratio output of all previous iteration, accumulation likelihood ratio absolute value is defined as the node point reliability of current iteration, and the row of node and check matrix are done ascending sort according to the reliability size, the matrix after the row ordering is done gaussian elimination; Owing to linear correlation can occur between the matrix column in the cancellation process, the ascending sort adjustment must try again the row of these linear correlations and corresponding node; In conjunction with system's generator matrix that gaussian elimination obtains, the safe node information sequence behind two minor sorts of front is encoded, obtain one group of candidate codewords; If iterative decoding does not obtain final output, just respectively organized and chosen the candidate codewords and of the conduct decoding output of receiving sequence Euclidean apart from minimum from the front.

LDPC code iterative sequencing statistical decoding method based on the accumulation likelihood ratio can be expressed as in the following order the step of carrying out, wherein the BP iterative decoding with standard with long-pending interpretation method be example:

The generator matrix G and the check matrix H of definition low density parity check code _{M * N}=[h _{M, n}], corresponding bipartite graph variable node and check-node set are V={v _n, n ∈ [1, N] }, S={s _m, m ∈ [1, M] }; Defined variable node v _nCheck-node set A (n)={ j, the h that participates in _{J, n}=1} is contained in check-node s _mVariable node set B (m)={ i, h _{M, i}=1}; Remove check-node s in the definition check-node set A (n) _mNode set A (n) m, remove variable node v among the defined variable node set B (m) _nNode set B (m) n, coded sequence

C＝{c _n，n∈[1，N]}；

(1) initialization: BPSK modulates x _n=1-2c _n, n ∈ [1, N] is through the zero-mean variances sigma ²The white Gaussian noise channel, obtain received signal sequence Y={y _n| y _n=x _n+ w _n, n ∈ [1, N] }, initial variable node v _n, n ∈ [1, N] is to check-node s _m, m ∈ A (n) output information $L_{\mathrm{nm}}^0={2y}_n/{\mathrm{\σ}}^2,$ And declare firmly according to the symbol of signal among the Y and to obtain sequence C ⁰, the accumulation likelihood ratio data of simultaneously initial each variable node $L_n^{\mathrm{sum}}=0,$ And iterations k=1, the beginning iterative decoding;

(2) output of the information of check-node and variable node is upgraded: each check-node s _mVariable node output information L with the k-1 time iteration _{N ' m} ^K-1, calculate iteration node s the k time according to following formula _mTo variable node v _nThe information of output,

$L_{\mathrm{mn}}^k=2a\tanh \underset{n^{\′}\∈B\left(m\right)\backslash n}{\mathrm{\Π}}\tanh (L_{n^{\′}m}^{k-1}/2);$

Each variable node v _nWith the verification formula output information L that participates in _{M ' n} ^kAddition is as variable node v _nTo check-node s _mOutput,

$L_{\mathrm{nm}}^k=\underset{m^{\′}\∈A\left(n\right)\backslash m}{\mathrm{\Σ}}{L}_{m^{\′}n}^k;$

The output of (3) the k time iteration: each variable node v _nCheck-node s with all participations _m, the output L of m ∈ A (n) _Mn ^kAddition is always exported L as the variable node of current iteration _n ^k, simultaneously according to following formula add up the accumulation likelihood ratio output up to the present of each node, wherein parameter alpha ^k, 0≤α ^k≤ 1 is weight coefficient,

$L_n^{\mathrm{sum}}={\mathrm{\α}}^k\·L_n^{\mathrm{sum}}+L_n^k;$

(4) according to the output information L of each variable node of current iteration _n ^k, do symbol according to following formula and declare firmly and obtain output sequence C _IT ^k,

$\left\{\begin{array}{ccc}{c}_{\mathrm{IT},n}^k=0,& \mathrm{if}& L_n^k>0\\ c_{\mathrm{IT},n}^k=1,& \mathrm{if}& L_n^k\≤0\end{array}\right..$

If this sequence satisfies all check equations, then the iterative decoding result will be as final decoding output

Stop the decoding of this frame simultaneously, if can not satisfy all check equations and iterations k equals maximum iteration time, then decoding failure stops decoding and jumping to step (6), current iteration number of times k satisfies else if, mod (k, I)=0, wherein parameter I is the iteration interval of sequencing statistical decoding, then the decoding of setting up procedure (5) sequencing statistical is handled, continue iterative decoding simultaneously, jump to step (2), k++;

(5) according to the accumulation likelihood ratio absolute value on each node | L _n ^Sum| order from big to small, node and corresponding check rectangular array are made an ordering π _K1, obtain new sequence node π _K1(V) and check matrix π _K1(H); New check matrix is made gaussian elimination, because the correlation properties between the check matrix column need be made row and be reset π for the second time _K2, obtain new generator matrix G at last _kAnd corresponding with it check matrix π _K2(π _K1And sequence node π (H)) _K2(π _K1(V)); With sequence node π _K2(π _K1(V)) N-M node is according to L before in _n ^SumSymbol make declaring firmly and obtain information sequence, and by corresponding generator matrix G _kCoding obtains code word

Do twice rearrangement again and obtain code word $C_{\mathrm{OSD}}^k={\mathrm{\π}}_1^{-1}\left({\mathrm{\π}}_2^{-1}\left({\tilde{C}}_{\mathrm{OSD}}^k\right)\right);$ The code word C that utilizes the decoding of initial reception information Y and sequencing statistical to obtain _OSD ^kCompare the Euclidean distance according to following formula, keep the output that Euclidean is deciphered as sequencing statistical apart from the code word of minimum

$C_{\mathrm{OSD}}=\underset{C_{\mathrm{OSD}}^k}{\arg \min }\underset{n,c_{\mathrm{OSD},n}^k\≠c_n^0}{\mathrm{\Σ}}\left|y_n\right|$

(6) if iterative decoding can not get output correctly, the output of sequencing statistical decoding is C as a result _OSDWill be as the final output of system

If iterative decoding has correct output, the output that sequencing statistical is deciphered at this moment is C as a result _OSDThe Euclidean distance and the BP iterative decoding Euclidean that obtains code word apart from comparing, select Euclidean apart from little final output as system.

The cumulative process of likelihood ratio can have the different forms of expression along with the value of parameter alpha changes.Different according to code length and hardware resource consumption amount, the OSD interpretation method can be carried out in the process of iterative decoding and once arrive repeatedly.After the gaussian elimination process of OSD decode procedure each time, the information bit node of Different Reliability can be made partially mixed high-order and handle under the restrictive condition of overall amount of calculation.Repeatedly OSD decoding and mix high-order and handle and will obtain more candidate codewords apart from size, is only stored the code word of Euclidean apart from minimum according to the Euclidean of the candidate codewords and the information of reception.

Main innovate point of the present invention is the middle iteration output information of BP decoding is added up, with the likelihood ratio information basis that decoding is handled as OSD of accumulation; OSD decoding is handled in a period of time that is broken down into repeatedly iterative decoding and the iterative decoding parallel processing; According to the difference of ordering back information node reliability, adopt the mixing high-order to handle to part of nodes; Along with the processing of iterative decoding, the value of flexible Control Parameter α.

The present invention is directed to 5/6 code check (576,480) the LDPC sign indicating number stipulated in the 802.16e agreement, to implement the concrete scheme that BP-OSD decoding handles as follows, wherein BP decoding employing standard with long-pending interpretation method:

1, every code word and decoding parameter setting are as follows:

N＝576，K＝480，M＝96，z＝24，R＝5/6，W＝100，f＝100MHz，

The BP iterative decoding can determine that according to z=24 final decoding rate is roughly λ=10Mbps.The required clock of whole system iterative decoding is W2z=4800 clock.

2, in the time of iterations k=10, utilized the tentatively likelihood ratio data of accumulation, start OSD decoding and handle.By simulation study, we set 7 likelihood ratio threshold values from small to large, and progressively the accumulation likelihood ratio sequence with each node is divided into 8 sections.Set a segmentation computing unit and comprise 7 comparators and corresponding threshold value, need 3 clock to handle a segmentation.Be provided with the segmentation ordering of 24 segmentation computing unit parallel processing sequences, different nodes is made pipeline and is handled, and needs 2+576/24=26 clock altogether.

3, finish after the segmentation, according to reliability order from small to large, exchange sort is made in each sequence segmentation, different segmentations can be made pipeline and handle.Complete each section of uniform distribution, every section block length 576/8=72 considers the error of thresholding, supposes that here the longest one section is 100.We to each segment, adopt the method for exchange sort earlier simultaneously to 4 sections of back and line ordering, promptly constantly minimum value are moved backward.This borough chief has a comparator, totally 99 between per two of 100 the sequence.Comparator is divided into two groups, presses the clock alternation for two groups.In a Clock, comparator is imported two numbers, big number is put back to the register on the left side after finishing relatively, the little register of putting back to the right, and finishing a minor sort needs 99+98=197 clock.

4, after segmentation ordering work finishes substantially, at 96 row that are emitted on the check bit position, we classify one group as with two and begin gaussian elimination, earlier matrix are become a following triangle battle array.To each group, sought 1 at first before this, after finding again 1 top cancellation.After matrix being become a lower triangular matrix, again by going 1 cancellation of triangle down.According to our statistics, finishing system's battle array cancellation process average needs 3200 clock.

5, recode and can quicken by improving the hardware degree of parallelism, suppose that with 8 bits, a byte is a unit, we once can read two row of H matrix, simultaneously two row are encoded.To each row, we are divided into three grades and encode, and the first order is divided into 60 sections, and every section 8 bit obtains 60 bits; The second level is divided into 8 sections, and every section 8 bit obtains 8 bits; 8 bit XORs of afterbody obtain corresponding code word bits.

If Pipeline, having compiled 0 rank OSD code word needs 96/2+4=54 clock.

6, in coding, we will carry out the calculating of Euclidean distance, and the Euclidean of 0 rank and 1 exponent word is stored each Euclidean distance apart from calculating together with 481 registers.Wherein, the calculating of information bit part Euclidean distance is carried out after can sorting the last time and finishing, and calculates while the check digit part is encoded.When coding and Euclidean apart from calculate all finish after, will export the code word from all OSD and select corresponding Euclidean one apart from minimum.

Here the searching of minimum value, we adopt the classification manner of comparison, find out minimum one from 4 numbers at every turn, to the searching of the minimum value of 481 numbers, adopt this mode, need 6 clock.If BP decoding has output, we also will with the Euclidean of BP decoding output code word apart from comparing, select Euclidean apart from the code word of minimum as final decoding output, that can reduce BP decoding so effectively can not the error correction mistake.Certainly, the calculating of the code word of BP output here Euclidean distance is calculated in advance.If the code word of last output is a high-order OSD code word, owing to the high-order code word is not left before us, also to once encode again, need 54 clock.Coding, Euclidean are about 114 clock apart from calculating and export the total clock number of final result like this.

Claims (7)

1. low density odd-even check code iterative sequencing statistical decoding method, it is characterized in that: in the iterative decoding process of low density parity check code, amplitude size according to the likelihood ratio accumulated value of all previous iteration of all variable nodes output, adopt the auxiliary iterative decoding of sequencing statistical decoding method, being each variable node adds up the node likelihood ratio output of all previous iteration, accumulation likelihood ratio absolute value is defined as the node point reliability of current iteration, and the row of node and check matrix are done ascending sort according to the reliability size, the matrix after the row ordering is done gaussian elimination; Owing to linear correlation can occur between the matrix column in the cancellation process, the ascending sort adjustment must try again the row of these linear correlations and corresponding node; In conjunction with system's generator matrix that gaussian elimination obtains, the safe node information sequence behind two minor sorts of front is encoded, obtain one group of candidate codewords; If iterative decoding does not obtain final output, just respectively organized and chosen the candidate codewords and of the conduct decoding output of receiving sequence Euclidean apart from minimum from the front.

2. low density odd-even check code iterative sequencing statistical decoding method according to claim 1 is characterized in that the iterative decoding of low density parity check code can be expressed as the step of carrying out in the following order:

The generator matrix G and the check matrix H of definition low density parity check code _{M * N}=[h _{M, n}], corresponding bipartite graph variable node and check-node set are V={v _n, n ∈ [1, N] }, S={s _m, m ∈ [1, M] }; Defined variable node v _nCheck-node set A (n)={ j, the h that participates in _{J, n}=1} is contained in check-node s _mVariable node set B (m)={ i, h _{M, i}=1}; Remove check-node s in the definition check-node set A (n) _mNode set A (n) m, remove variable node v among the defined variable node set B (m) _nNode set B (m) n, coded sequence C={c _n, n ∈ [1, N] };

Step (1) initialization: BPSK modulates x _n=1-2c _n, n ∈ [1, N] is through the zero-mean variances sigma ²The white Gaussian noise channel, obtain received signal sequence Y={y _n| y _n=x _n+ w _n, n ∈ [1, N] }, initial variable node v _n, n ∈ [1, N] is to check-node s _m, m ∈ A (n) output information $L_{\mathrm{nm}}^0=2y_n/{\mathrm{\σ}}^2,$ And declare firmly according to the symbol of signal among the Y and to obtain sequence C ⁰, the accumulation likelihood ratio data of simultaneously initial each variable node $L_n^{\mathrm{sum}}=0,$ And iterations k=1, the beginning iterative decoding;

The information output of step (2) check-node and variable node is upgraded: each check-node s _mVariable node output information L with the k-1 time iteration _{N ' m} ^K-1, calculate iteration node s the k time according to following formula _mTo variable node v _nThe information of output,

$L_{\mathrm{mn}}^k=2a\tanh \underset{n^{\′}\∈B\left(m\right)\backslash n}{\mathrm{\Π}}\tanh (L_{n^{\′}m}^{k-1}/2);$

Each variable node v _nWith the verification formula output information L that participates in _{M ' n} ^kAddition is as variable node v _nTo check-node s _mOutput,

$L_{\mathrm{nm}}^k=\underset{m^{\′}\∈A\left(n\right)\backslash m}{\mathrm{\Σ}}{L}_{m^{\′}n}^k;$

The output of the k time iteration of step (3): each variable node v _nCheck-node s with all participations _m, the output L of m ∈ A (n) _Mn ^kAddition is always exported L as the variable node of current iteration _n ^k, simultaneously according to following formula add up the accumulation likelihood ratio output up to the present of each node, wherein parameter alpha ^k, 0≤α ^k≤ 1 is weight coefficient,

$L_n^{\mathrm{sum}}={\mathrm{\α}}^k\·L_n^{\mathrm{sum}}+L_n^k;$

Step (4) is according to the output information L of each variable node of current iteration _n ^k, make symbol according to following formula and declare firmly and obtain output sequence C _IT ^k,

$\left\{\begin{array}{ccc}{c}_{\mathrm{IT},n}^k=0& \mathrm{if}& L_n^k>0\\ c_{\mathrm{IT},n}^k=1& \mathrm{if}& L_n^k\≤0\end{array}\right.;$

If this sequence satisfies all check equations, then the iterative decoding result will be as final decoding output

Stop the decoding of this frame simultaneously, if can not satisfy all check equations and iterations k equals maximum iteration time, then decoding failure stops decoding, current iteration number of times k satisfies else if, mod (k, I)=0, wherein parameter I is the iteration interval of sequencing statistical decoding, then starting sequencing statistical decoding handles, continue iterative decoding simultaneously, jump to step (2), k++.

3. low density odd-even check code iterative sequencing statistical decoding method according to claim 1, the sequencing statistical decoding method that it is characterized in that low density parity check code is to combine with interative encode method, utilize the reliability information of the likelihood ratio output of each time iteration accumulation in the iterative decoding as each bit, as the sort by of sequencing statistical decoding, sequencing statistical decoding method can be expressed as the step of carrying out in the following order: according to the accumulation likelihood ratio absolute value on each node | L _n ^Sum| order from big to small, node and corresponding check rectangular array are made an ordering π _K1, obtain new sequence node π _K1(V) and check matrix π _K1(H); New check matrix is made gaussian elimination, because the correlation properties between the check matrix column need be made row and be reset π for the second time _K2, obtain new generator matrix G at last _kAnd corresponding with it check matrix π _K2(π _K1And sequence node π (H)) _K2(π _K1(V)); With sequence node π _K2(π _K1(V)) N-M node is according to L before in _n ^SumSymbol make declaring firmly and obtain information sequence, and by corresponding generator matrix G _kCoding obtains code word

Do twice rearrangement again and obtain code word $C_{\mathrm{OSD}}^k={\mathrm{\π}}_1^{-1}\left({\mathrm{\π}}_2^{-1}\left({\tilde{C}}_{\mathrm{OSD}}^k\right)\right);$ The code word C that utilizes the decoding of initial receiving sequence Y and sequencing statistical to obtain _OSD ^kCompare the Euclidean distance according to following formula, keep the output that Euclidean is deciphered as sequencing statistical apart from the code word of minimum

$C_{\mathrm{OSD}}=\underset{C_{\mathrm{OSD}}^k}{\arg \min }\underset{n,c_{\mathrm{OSD},n}^k\≠c_n^0}{\mathrm{\Σ}}\left|y_n\right|$

If iterative decoding can not get output correctly, the output of sequencing statistical decoding is C as a result _OSDWill be as the final output of system

4. low density odd-even check code iterative sequencing statistical decoding method according to claim 2 is characterized in that iterative decoding is the interpretation method of a class based on belief propagation; Iterative decoding both can be standard or correction and long-pending interpretation method, also can use the minimum and interpretation method and relevant a series of correction minimums and interpretation method thereof of simplification; These Soft decision decodings based on belief propagation can upgrade the likelihood ratio output of each node by iteration, and weaken the reforming phenomena of iterative decoding output by the accumulation of likelihood ratio; On the basis of certain accumulation likelihood ratio amplitude, sequencing statistical decoding method can with above-mentioned interative encode method parallel processing, if iterative decoding can not provide rational decode results, then being that output is finally deciphered by system with the information of reception Euclidean apart from the result of minimum in the sequencing statistical decoding output.

5. low density odd-even check code iterative sequencing statistical decoding method according to claim 1 and 2 is characterized in that the computational methods of accumulating likelihood ratio are: along with parameter alpha ^kDifference choose scheme, following several different way of realization can be arranged; α at first ^kIf do not change with iterations k, then likelihood ratio is tired

Long-pending process is similar to the IIR Filtering Processing of each iteration output likelihood ratio being done a single order; Secondly if parameter alpha ^kBe always 1 or 0, accumulation is equivalent to each time exported addition completely or only choose current likelihood ratio and is output as the reliability sort by; Last if α ^kOnly the iterations in some fixed intervals is to be zero, all the other the time satisfy α ^k∈ (0,1], then the process of this accumulation is equivalent between these iteration interval the fix FIR Filtering Processing of exponent number of likelihood ratio to output.

6. low density odd-even check code iterative sequencing statistical decoding method according to claim 3, it is characterized in that sequencing statistical decoding method can reach the output result who provides sequencing statistical decoding when maximum iteration time finishes in the iterative decoding failure since the k time iteration and interative encode method parallel processing; The scheme of iterative decoding and sequencing statistical decoding algorithm Parallel Implementation can be improved the decoding performance of low density parity check code under the situation that does not increase the low density odd-even check code iterative decoding delay like this; Sequencing statistical decoding method also can serially concatenated in the rear end of iterative decoding process, the likelihood ratio information that such processing mode can the most effective utilization accumulation obtains better bit error rate performance.

7. according to claim 1 or 3 described low density odd-even check code iterative sequencing statistical decoding methods, it is characterized in that the sequence node π after sequencing statistical decoding is according to ordering _K2(π _K1(V)) do and declare coding firmly; Definition is zeroth order sequencing statistical decoding order-0 according to the scheme of declaring sequential coding firmly directly, and the sequencing statistical decoding treatment process that preceding N-M information bit symbol is traveled through upset i bit sign is defined as order-i; Can carry out the high-order upset to the lower node of part reliability and handle, do and mix rank sequencing statistical decoding processing H_order (e ₁, e ₂... e _r), e wherein _iFor doing the interstitial content that order-i handles.

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