CN101807929A - Minimum sum decoding method of selective annealing of low density parity check code - Google Patents
Minimum sum decoding method of selective annealing of low density parity check code Download PDFInfo
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Abstract
The invention relates to a minimum sum decoding method of selective annealing of a low density parity check code, which is suitable for soft decision decoding of the low density parity check codes and replaces the traditional multiplicative revise minimum sum decoding method. Based on the minimum sum decoding method, the invention adopts a multiplicative factor smaller than 1 to revise output of check nodes with unsuccessful check. The method comprises the following implementation steps of: merging external information quantity input by the check nodes and information from a channel by a variable node as decision soft information of iteration; probing whether a decision sequence satisfies a check equation; taking down or updating a node sequence set U with unsuccessful check, if U is empty, finishing decoding, and if U is not empty, updating and outputting information to the variable node by the check nodes based on minimum sum regulations; carrying out annealing treatment on check node output information belonging to U plus a factor smaller than 1; and turning to next iterative decoding. In the method, the performance is obviously superior to other improved minimum sum decoding method, and the calculation complexity is far lower than a sum-product algorithm.
Description
Technical field
The present invention is that the soft-decision iterative decoding of low density parity check code is simplified interpretation method, belongs to the decoding technique field of channel error correction coding.
Background technology
At low-density checksum (Low-Density Parity-Check, LDPC) in the middle of Ma the interpretation method, iteration soft-decision decoding method based on bipartite graph has good bit error rate performance, and the irregular LDPC codes for long can reach the performance near shannon limit.The soft-decision algorithm of standard is referred to as sum-product algorithm, and no matter this algorithm is the probability territory or the decoding in log-likelihood ratio territory in the output of calculation check nodal information, always relate to a large amount of additions, multiplication, logarithm and exponent arithmetic, add that interstitial content is more, computational complexity is bigger.Minimum and interpretation method is a simplification to this algorithm, directly minimum the or inferior low information of importing with check-node of reliability is as output, save computings a large amount of in the sum-product algorithm, but performance has been compared certain gap with sum-product algorithm.
The improved one's methods offset correction or the property the taken advantage of method for normalizing of minimum-sum algorithm are on the minimum value or sub-minimum information of output, deduct a modifying factor or are multiplied by a normalization factor, thereby reach the result who exports near sum-product algorithm.This class methods performance compares minimum and interpretation method improvement amplitude is bigger, and complexity does not increase a lot.Because communication system is to transmission rate, bit error rate performance requires further to improve, and a lot of systems begin to gradually adopt length at the irregular LDPC codes more than 8000.Along with the increase of code length and the influence of non-regular distribution, the minimum of offset correction or the property taken advantage of normalization correction and the performance of interpretation method be deterioration to some extent also, increases gradually at a distance of the sum-product algorithm performance gap of standard.
Summary of the invention
Technical problem: the selective annealing minimum and the interpretation method that the purpose of this invention is to provide a kind of low density parity check code, this method is a kind of improved minimum and interpretation method, solve the existing LDPC sign indicating number soft-decision decoding method of simplifying poor-performing when handling long non-regular code, and existing sum-product algorithm complexity problem of higher still; This method is to channel estimating parameter robust more simultaneously.
Technical scheme: a kind of selective annealing minimum and the interpretation method of low density parity check code, it is characterized in that: it is characterized in that: in the minimum and iterative decoding process of low density parity check code, variable node and check-node carry out soft amount of information successively to be upgraded; In iterative process, variable node is declared firmly to gross information content, judges whether success of each verification formula verification; If the verification of verification formula is success all, then iterative decoding stops automatically, otherwise when the soft value of the check-node that carries out is immediately upgraded, check-node to verification succeeds carries out soft value renewal according to original minimum and principle, finishes annealing in process and the unsuccessful check-node of verification be multiply by a factor beta less than 1 on the basis of minimum and the soft value renewal of principle.
Annealing coefficient β can optimize definite by emulation, and preestablishes storage before iterative decoding begins.
Low density parity check code minimum and interpretation method based on selective annealing can be expressed as the step of carrying out in the following order:
1) initialization: BPSK modulates x
n=1-2u
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 c
m, m ∈ A (n) exports side information
Initial check-node c
m, m ∈ [1, M] is to variable node v
n, n ∈ B (m) exports side information
Iterations k=0;
2) variable node calculates: 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 c
mThe output side information:
Variable node v
nCheck-node c with all participations
m, the output side information L of m ∈ A (n)
Mn kAddition is always exported as the variable node of current iteration
Output information L according to each variable node of current iteration
n k, make symbol according to following formula and declare firmly and obtain output sequence
3) check node calculation preliminary treatment: whether by declaring sequence firmly, it is successful to calculate each verification formula:
The operation that adds up of expression XOR.Write down the check-node sequence number that all do not satisfy verification
With season
Represent that all satisfy the check-node sequence number collection of verification.If not satisfying the node number of verification is 0, also being | U|=0, then step (2) output result will be as final decoding output
Stop the decoding of this frame simultaneously, if can not satisfy and iterations k equals maximum iteration time, then decoding failure stops decoding, otherwise continues iterative decoding, k++;
4) check node calculation: each check-node c
mVariable node output side information L according to the k-1 time iteration
N ' m K-1, calculate iteration node c the k time according to minimum and principle
mTo variable node v
nThe side information of output if check-node m belongs to set U, then carries out annealing in process, otherwise unannealed; Also promptly carry out following operation:
Jump to step 2 then).
Beneficial effect: whether successful main innovate point of the present invention be the unsuccessful check-node lastest imformation of verification to be annealed on the basis of minimum and rule according to verification mensuration.
Be mainly reflected in the following aspects:
1) whether case of successful is annealed selectively according to verification, and feasible minimum of this new mechanism and decoding algorithm performance are better.
2) compare with method with the existing property taken advantage of correction is minimum, correction effect is better, and the decoding convergence rate is faster.
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 method flow diagram of a variable node computing unit.
Fig. 3 is total interpretation method flow chart of a check node calculation output unit.
Fig. 4 is a check-node unit calculated minimum, the method flow diagram of sub-minimum and minimum index.
Fig. 5 is the method flow diagram that the check-node unit is minimum and the annealing renewal is exported.
Fig. 6 is the bit error rate curve of 1/2 code check irregular LDPC codes under each interpretation method of (8064,4032).
Fig. 7 is the frame error rate curve of 3/4 code check irregular LDPC codes under each interpretation method of (8064,6048).
All explanation of symbols:
v
n: n variable node;
c
m: m check-node;
A (n): variable node v
nThe check-node set that participates in;
B (m): variable node c
mThe variable node set that comprises;
L (v
n→ c
m)=(L (v
n→ c
m), z
n): variable node v
nTo check-node c
mThe likelihood ratio information L (c that transmits
m→ v
n) and symbolic information z
n
L (c
n→ v
n): variable node c
mTo check-node v
nThe likelihood ratio information of transmitting;
| L (v
n→ c
m) |: variable node v
nTo check-node c
mThe reliability of the likelihood ratio information of transmitting;
Sign (L (v
n→ c
m)): variable node v
nTo check-node c
mTransmit the sign symbol of likelihood ratio information;
Sign (c
m): check-node c
mThe sign symbol of output signal;
Min (c
m): check-node c
mThe minimal reliability of output signal;
Sub-min (c
m): check-node c
mThe inferior minimal reliability of output signal;
Min-ind (c
m): check-node c
mOutput minimal reliability signal corresponding variable node sequence number
MSA: minimum and interpretation method;
NMSA: the property taken advantage of correction minimum and interpretation method;
AN-MSA: wash and select annealing minimum and interpretation method.
Embodiment
The information that the minimum and interpretation method of selective annealing of the present invention merges the external information amount of check-node inflow by variable node and comes self-channel is as the soft information of the judgement of this time iteration, sound out the judgement sequence and whether satisfy check equations, write down or upgrade the set of the unsuccessful node ID of verification, if the unsuccessful check-node sequence number of verification collection is empty, then decoding finishes; If the unsuccessful check-node sequence number of verification collection non-NULL, then check-node upgrades output information according to minimum and rule to variable node, the unsuccessful check-node output information of verification be multiply by one carry out annealing in process, change next iterative decoding over to less than 1 the factor.
Its concrete steps are as follows:
Step 1: the symbolic variable s of this check-node of initialization
m=1, sign
k(c
m)=1, minimum value min
k(c
m)=100 and sub-minimum sub-min
k(c
m)=100.
Step 2: the sign bit for input is done the verification computing
s
m=s
m·z
n;
Signal L to input
k(v
i→ c
m), i ∈ B (m) gets symbol and absolute value, then takes turns doing following symbolic operation, and minimum value, the comparison operation of sub-minimum.
sign
k(c
m)=sign
k(c
m)·sign(L
k(v
i-c
m));
sub-min
k(c
m)=min{sub-min
k(c
m),|L
k(v
i→c
m)|};
Min
k(c
m)=min{min
k(c
m), sub-min
k(c
m), write down corresponding min-ind (c simultaneously
m).
Step 3: successively to participating in check-node c
mVariable node upgrade output:
If i=min-ind
k(c
m),
L then
k(c
m→ v
i)=sign
k(c
m) sign (L
k(v
i→ c
m)) sub-min
k(c
m) otherwise L
k(c
m→ v
i)=sign
k(c
m) sign (L
k(v
i→ c
m)) min
k(c
m)
If s
m=-1,
L then
k(c
m→ v
i)=β L
k(c
m→ v
i).
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 c respectively.(b) be variable node v
nBe connected signal with the check-node that participates in, and the likelihood ratio information of transmitting between node.(c) be check-node c
mBe connected signal with the variable node that it comprises, and the likelihood ratio information of transmitting between node.
Fig. 2 is the method flow of certain iteration of check node calculation unit.First step initialization sign (c
m) and s
mThe variable node that second step will participate in this check-node is one by one gathered input information and is done and get symbol and comparison operation, obtains the minimum value of input information absolute value, sub-minimum, the symbol product of minimum index and each input information.The 3rd step was pressed the minimum-sum algorithm rule, to the variable node of each input, upgraded the output information of feedback, according to symbol s
mValue, carry out selectively annealed to output information.
Fig. 3 is the detailed description of second step of check-node unit process.At first Shu Ru signal code and current verification formula symbol multiply each other and upgrade verification formula symbol, then will import the absolute value of data and current sub-minimum compares, if input data absolute value is less than sub-minimum then upgrade sub-minimum, at last the sub-minimum data of renewal and current minimum value data are compared, according to the input size of data, upgrade sub-minimum and minimum value respectively or remain unchanged,, then the minimum value index is designated as the node ID of present input data if the renewal of minimum value takes place.
Fig. 4 calculates in the 3rd step of check-node unit, upgrades the detailed description of output information to each variable node.At first corresponding variable node input information symbol and the total output symbol of verification formula are multiplied each other, as information symbol to this node output, if this variable node sequence number equals the minimum value index, then the absolute value of output information is a sub-minimum, and the absolute value of output information is a minimum value if fruit is not waited then.Thereafter, according to symbol s
mValue carry out selectively annealed to output information: if s
m=-1, then output information takes advantage of one to carry out annealing in process less than 1 parameter.
Fig. 5 is that the variable node unit calculates current output and upgrades the method flow of output information to check-node.At first the variable node unit is with each check-node input information addition, and whether as the output of this variable node current iteration, this output directly obtains current decoding output as hard decision, and correct with verification formula check output.If this iteration does not obtain correct decoding output, then the variable node unit deducts the input of each check-node originally respectively with total output, upgrades the output information to corresponding check-node.
Fig. 6 is under the awgn channel, length overall 8064, and the irregular LDPC codes of message length 4032,1/2 code checks is in the NMSA method, and the errored bit code check performance under the AN-MSA method is relatively.The variable node of irregular LDPC codes is distributed as λ (x)=4032x+2688x
2+ 1344x
8, check-node is distributed as ρ (x)=4032x
6Wherein, x
D-1Preceding coefficient table indication number is the node number of d.As can be seen from the figure, the performance of AN-MSA method (annealing coefficient β=0.75) has improved about 0.1-0.2dB than NMSA method (property the taken advantage of modifying factor 0.85 of optimization), is better than improving one's methods of other.
Fig. 7: be under the awgn channel, length overall 8064, irregular LDPC codes λ (the x)=1008x+6048x of message length 6048,3/4 code checks
2+ 1008x
7, ρ (x)=2016x
27In the NMSA method, the frame error rate performance under the AN-MSA method (annealing coefficient β=0.75) relatively.The amendment scheme that we provide makes decoding performance improve about 0.1-0.2dB than NMSA method (property the taken advantage of modifying factor 0.85 of optimization).
Claims (2)
1. low density parity check code minimum and interpretation method based on a selective annealing is characterized in that: in the minimum and iterative decoding process of low density parity check code, variable node and check-node carry out soft value amount successively to be upgraded; In iterative process, variable node is declared firmly to gross information content, judges whether success of each verification formula verification; If the verification of verification formula is success all, then iterative decoding stops automatically, otherwise when the soft value of the check-node that carries out is immediately upgraded, check-node to verification succeeds carries out soft value renewal according to original minimum and principle, finishes annealing in process and the unsuccessful check-node of verification be multiply by a factor beta less than 1 on the basis of minimum and the soft value renewal of principle.
2. low density parity check code minimum and interpretation method based on selective annealing according to claim 1, it is characterized in that: whether the soft value renewal of check node satisfies verification according to the verification formula is carried out selectively annealed processing, execution is represented based on the bipartite graph of low density parity check code, specifically is expressed as the several steps of carrying out in the following order:
Definition: the check matrix H of low density parity check code
M * N=[h
M, n], wherein, M is the line number of check matrix, N is the columns of check matrix, h
M, nThe capable n column element of m of expression check matrix, m span are 1 to M, and the n span is 1 to N; Corresponding bipartite graph variable node and check-node set are V={v
n, n ∈ [1, N] }, C={c
m, m ∈ [1, M] }; Defined variable node v
nCheck-node set A (n)={ m, the h that participates in
M, n=1} is contained in check-node c
mVariable node set B (m)={ n, h
M, n}=1; Remove check-node c 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, long be the coded sequence u=(u of N
1, u
2..., u
n..., u
N);
Step 1: initialization: two-phase offset keying BPSK modulates x
n=1-2u
n, n ∈ [1, N] obtains received signal sequence Y={y through the white Gaussian noise channel
n| y
n=x
n+ w
n, n ∈ [1, N] }, w wherein
nIt is the zero-mean variances sigma
2White Gaussian noise; Initial variable node v
n, n ∈ [1, N] is to check-node c
m, m ∈ A (n) exports side information
Initial check-node c
m, m ∈ [1, M] is to variable node v
n, n ∈ B (m) exports side information
Iterations k=0;
Step 2: variable node calculates: each variable node v
nCheck-node c with all participations
m, the output side information L of m ∈ A (n)
Mn kAddition is always exported as the variable node of current iteration the k time
Total output information L according to each variable node of current iteration
n k, make symbol according to following formula and declare firmly and obtain output sequence
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 c
mThe output side information:
Be different from minimum-sum algorithm, variable node is to the transmission likelihood ratio information L of check-node
Nm k, this information is except normal side information L
Nm kAlso need increase by 1 outward and declare information, also promptly along limit v than ultrahard
n→ c
mTransmit:
Step 3: check node calculation preliminary treatment: each check-node s
mEarlier to side information
In declare information z firmly
n kHandle, whether the calculation check formula is successful:
The operation that adds up of expression XOR; Write down the check-node sequence number that all do not satisfy verification
With season
Represent that all satisfy the check-node sequence number collection of verification; If not satisfying the node number of verification is 0, also being | U|=0, then the output result that declares firmly of step 2 will be as final decoding output
Stop the decoding of this frame simultaneously, if can not satisfy and iterations k equals maximum iteration time, then decoding failure stops decoding, otherwise continues iterative decoding, k++;
Step 4:: check node calculation: each check-node c
mVariable node output side information L according to the k-1 time iteration
N ' m K-1, calculate iteration node c the k time according to minimum and principle
mTo variable node v
nThe side information of output if check-node m belongs to set U, then carries out annealing in process, otherwise unannealed, also promptly carries out following operation:
Wherein, β<1st, annealing coefficient,
Sign function is got in expression,
Expression belongs to all x of B to subscript
nGet its minimum value; Jump to step 2 after executing.
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CN108155972A (en) * | 2017-12-26 | 2018-06-12 | 厦门大学 | The decoding optimization method of distributed associating signal source and channel system |
CN109586731A (en) * | 2017-09-29 | 2019-04-05 | 奈奎斯特半导体有限公司 | System and method for decoding and error code |
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CN110350923A (en) * | 2019-07-09 | 2019-10-18 | 福建师范大学福清分校 | The building method of the external information transfer figure of five side type low density parity check codes |
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CN110350923A (en) * | 2019-07-09 | 2019-10-18 | 福建师范大学福清分校 | The building method of the external information transfer figure of five side type low density parity check codes |
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