CN104052501A - Multi-system LDPC decoding method low in complexity - Google Patents
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Abstract
The invention provides a multi-system LDPC decoding method low in complexity, and belongs to the technical field of communication. In the method, the representation mode that the binary system with multi-system symbols is used for representing the simplified codon information confidence coefficient is adopted, the confidence coefficient of side information is updated through calculation of check nodes during each time of iteration, using efficiency for the side information by weighted and strengthened variable nodes is introduced into calculation of the variable nodes, and codon information and extrinsic information are calculated by adopting the information updating mode of the binary system. According to the method, the information length of each symbol of codons is far smaller than the length 2r in an existing method, the side information only has one finite field symbol and the confidence coefficient of the finite field symbol, the storage complexity is very low, calculation of the variable nodes and the check nodes is mainly integer addition and integer comparison operation, only little finite field operation and multiply operation are adopted, calculation complexity is very low, and very good decoding performance can be achieved for codes with various lengths and weights.
Description
Technical field
The m-ary LDPC code coding method that the present invention relates to a kind of low complex degree, belongs to communication technical field.
Background technology
Low-density checksum (LDPC) code is a kind of important error correcting code, and its parity matrix has sparse characteristic, and while adopting belief propagation (BP) algorithm, the performance of LDPC code can approach shannon limit.Had at present plurality of communication systems, such as digital satellite television (DVB-S2), the 4th Generation Mobile Communication System (4G), GPS (Global Position System) (GPS) etc. adopts LDPC code to carry out error control in its transfer of data.Non-Binary LDPC Coded can obtain than the more excellent performance of binary system LDPC code, but obtain as binary system LDPC code rapidly, does not promote.This is mainly because do not have at present a kind of Non-Binary LDPC Coded decoding algorithm that can take into account decoding performance and calculating, storage complexity.
The bipartite graph of the decoding of Non-Binary LDPC Coded based on code check matrix, or be called Tanner figure, shown in Fig. 1, being two branches of a LDPC code, it consists of the limit of variable node, check-node and two kinds of nodes of connection.Its decode procedure is mainly divided into 4 parts: the storage of codeword information, the storage of side information, the calculating of check-node and the calculating of variable node.Existing m-ary LDPC code coding method mainly contains two kinds, a kind of based on belief propagation (BP) algorithm, another kind of based on majority-logic decoding (MLgD) algorithm.These two kinds of methods have similar codeword information, suppose that m-ary LDPC code check battle array is finite field gf (2
r) under matrix, to be a length be 2 to the information of each code-word symbol
rconfidence level vector, characterize this symbol and be respectively finite field gf (2
r) lower all 2
rthe possibility tolerance of individual element, need to store 2
rindividual confidence information.And m-ary LDPC code coding method based on MLgD algorithm has than the simple many side informations of the m-ary LDPC code coding method based on BP algorithm.The side information of the m-ary LDPC code coding method based on BP algorithm, the different implementations based on BP algorithm, can equal the information vector of code word, and its length is 2
r, every limit need to store 2
rthe confidence level of individual finite field element; Also can only get the Partial Elements that confidence level is larger according to the confidence level size of different elements in codeword information vector, suppose that its length is n
m(n in reality
m> > 1), n need to be stored in every limit like this
mthe value of individual finite field element and corresponding n
mthe value of individual confidence level.The side information of the m-ary LDPC code coding method based on MLgD algorithm only in codeword information that element of confidence level maximum form, the value of 1 finite field element and 1 confidence level only need to be stored in every limit.In Non-Binary LDPC Coded decoding, the calculating of check-node and the calculating of variable node are carried out based on codeword information and side information.In m-ary LDPC code coding method based on BP algorithm, check-node is q to the computation complexity of the side information of every two inputs
2magnitude (or
m magnitude is n for side information length
mrealization), variable node is q magnitude (or 2n to the computation complexity of the side information of every two inputs
m, for side information length, be n
mrealization).Because the side information of the m-ary LDPC code coding method based on MLgD algorithm is more simple, so its check-node and variable node be 1 to the computation complexity of the side information of every two inputs, is the 1/q of the m-ary LDPC code coding method based on BP algorithm
2(or
).
Although the storage of the m-ary LDPC code coding method based on MLgD algorithm and computation complexity are all far below the interpretation method of the Non-Binary LDPC Coded based on BP algorithm, the performance of the m-ary LDPC code coding method based on MLgD algorithm depends on the column weight of LDPC code check matrix very much.When the column weight lower (being less than 6) of code, its performance loss is very serious, and in bit error rate (BER) up to 10
-6may there is wrong platform in left and right.Not having at present a kind of m-ary LDPC code coding method can be pervasively when the LDPC code decoding to various parameters, before decoding performance and calculating, storage complexity, obtains good equilibrium.
Summary of the invention
The object of the invention is the problem that cannot take into account in order to solve polynary territory LDPC code decoding complexity and performance, propose a kind of m-ary LDPC code coding method of low complex degree.Interpretation method of the present invention is a kind of interative encode method based on bipartite graph, this method adopts the binary representation of multi-system symbol to simplify the expression mode of codeword information confidence level in iteration, in each iteration, by the calculating of check-node, upgrade the confidence level of side information, in the calculating of variable node, introduce weighting and strengthen the service efficiency of variable node to side information, and adopt binary information updating mode compute codeword information and external information.
First LDPC code coding method carries out decoding initialization, and then iteration is carried out following steps: hard decision, calculating side information, check node calculation and variable node calculate, until successfully decoded or failed.The m-ary LDPC code coding method of low complex degree provided by the invention, to codeword information, all adopts binary form to represent code-word symbol, in decode procedure, has carried out the improvement of following aspect:
1) during decoding initialization, set weighted factor, use bit confidence coefficient that codeword information is carried out to initialization;
2) the outside verification of check-node and variable node fillet and confidence level convert bit confidence coefficient vector to, participate in variable node and calculate;
3) codeword information that each iteration is upgraded and the external information of check-node are all bit confidence coefficient vector.
Interpretation method of the present invention, while carrying out variable node calculating, the information of check-node input variable node, the confidence level weighting scheme of employing based on Hamming distance obtains, specifically: according to the outside verification of check-node and variable node fillet and binary representation and the size of the Hamming distance between the binary representation of code-word symbol hard decision set weighted factor, use weighted factor to the outside verification of fillet and confidence level be weighted.
Interpretation method of the present invention, when side information calculates, side information comprises the multi-system hard decision symbol of code word external information and the confidence level of this symbol; Wherein, all minimizations of the sum of absolute value in the binary digit external information that the confidence level of symbol is code word.
In interpretation method of the present invention, all codeword information, code word external information, outside verification and confidence level and the check-node information that inputs to variable node be integer.
Advantage of the present invention and good effect are:
(1) in the present invention, the message length of each symbol of code word is only r, far below the code-word symbol message length 2 of existing algorithm
r; Meanwhile, its side information only has a finite field symbol and confidence level thereof, has very low storage complexity;
(2) calculating of variable node of the present invention and check-node is mainly addition of integer and integer comparison operation, only has a small amount of finite field operations and multiplying, has very low computation complexity;
(3) the present invention is heavy insensitive for the code of Non-Binary LDPC Coded, for various code lengths and the heavy code of code, all can obtain good decoding performance.
Accompanying drawing explanation
Fig. 1 is that the bipartite graph of the LDPC code check matrix of 5 row 10 row represents;
Fig. 2 is the flow chart of m-ary LDPC code coding method of the present invention.
Embodiment
Below in conjunction with accompanying drawing and embodiment, the present invention is described in further detail.
As shown in Figure 2, be the overall flow figure of m-ary LDPC code coding method, first carry out decoding initialization, then iteration is carried out: hard decision, calculating side information, check node calculation and variable node calculate, until successfully decoded or failed.The m-ary LDPC code coding method of low complex degree of the present invention, all adopts binary form to represent to the code-word symbol of codeword information, in decode procedure, has carried out the improvement of following aspect:
1) use bit confidence coefficient that codeword information is carried out to initialization;
2) the outside verification of check-node and variable node fillet and confidence level convert bit confidence coefficient vector to, participate in variable node and calculate;
3) codeword information that each iteration is upgraded and the external information of check-node are all bit confidence coefficient vector.
Below in conjunction with instantiation, m-ary LDPC code coding method of the present invention is described.
Suppose that a Non-Binary LDPC Coded is by its finite field gf (2
r) lower size is that the kernel of the parity check matrix H of m * n defines, the code word of this Non-Binary LDPC Coded is the GF (2 that a length is n
r) under vector, the binary vector that this codeword vector can be nr by a length is equivalently represented.With c=(c
1, c
2..., c
n) represent multi-system code word, use c
j(1≤j≤n) represents j symbol of code word, uses c
j=(c
j, 1, c
j, 2..., c
j,r) represent the binary representation of j symbol, c
j,tt the binary digit that represents j symbol, value is 0 or 1.When communication system is used BPSK modulation system to transmit, each bit of code word binary representation is done to following mapping: 0 →+1V, 1 →-1V.After binary system input additive white Gaussian noise (BI-AWGN) channel, the codeword information that system receives is y=(y
1, y
2..., y
n), y wherein
j=(y
j, 1, y
j, 2..., y
j,r) be the log-likelihood ratio of a j code-word symbol r bit
1≤j≤n, 1≤t≤r.M-ary LDPC code decoder is used y and H to carry out decoding.Decode procedure carries out according to the following steps:
Step 1, carry out decoding initialization setting.Set weighted factor θ
0, θ
1..., θ
r.Set maximum iteration time I
max.Current iteration number of times k is made as 1.
Using bit confidence coefficient that codeword information is carried out to initialization, is that y be take to quantized interval Δ and quantizing bit number ω uniform quantization is that integer assignment is to the codeword information of the 1st iteration.The embodiment of the present invention is initialized as integer by following quantification manner by codeword information:
1≤j≤n wherein, 1≤t≤r, ω, Δ are respectively quantizing bit number and quantized interval, and N is integer, and-(2
ω-1-1) < N < 2
ω-1-1, y
j,tt binary piece of information of j the code-word symbol of the binary code word information y that expression system receives,
superscript 1 represent current iteration number of times,
represent t binary piece of information of j code-word symbol in the 1st iteration.
Through type (1) obtains j code-word symbol information of the 1st iteration
and then obtain the codeword information of the 1st iteration
Step 2, the codeword information of the k time iteration is carried out to hard decision:
Wherein
the codeword information of the k time iteration, if k=1,
in step 1, initialization obtains, otherwise
in the step 5 of upper once iteration, upgrade and obtain,
expression t binary piece of information of j code-word symbol to the k time iteration
hard decision result.Suppose
it is multi-system symbol
binary representation,
it is the hard decision result of j code-word symbol of code word.By multi-system hard decision vector
by check matrix H, carry out verification.If z
(k)h
t=0, successfully decoded; If z
(k)h
t≠ 0 and k > I
max, decoding failure; Otherwise, carry out step 3.In Fig. 2, judge that whether parity check result is 0 is exactly to judge z
(k)h
twhether be 0, when judging iterations, surpass maximum iteration time and judge exactly whether k is greater than I
max.
Step 3, for all 1≤j≤n, i ∈ M
j, calculate j variable node to the side information of i check-node, wherein, M
jrepresent that the j of check matrix H is listed as the set of all nonzero element line positions, suppose that the element of the capable j row of i of H is h
i,j, M
j={ i:1≤i≤m, h
i,j≠ 0}.
First, calculate the code word external information of the k time iteration.If this iteration is iteration for the first time, i.e. k=1, code word external information equals codeword information.The binary digit external information of j code-word symbol of check-node
equal the binary piece of information of j code-word symbol of iteration for the first time
suc as formula (3):
During the inferior iteration of k (k>=2), code word external information is by the codeword information of this iteration
while deducting last iteration, check-node inputs to the information of the variable node corresponding with this code-word symbol
obtain:
Wherein, 1≤t≤r,
while representing the k time iteration, for i check-node, the external information of t binary digit of j code-word symbol.
during for last iteration, i check-node inputs to t binary piece of information of the variable node corresponding with j code-word symbol.Variable node corresponding to j code-word symbol be j variable node namely.(3) required in formula and (4) formula
number range be limited to (2
ω-2+ 1,2
ω-2-1), in scope, when required result exceeds this scope, set
value be immediate boundary value.
Then, according to code word external information, calculate variable node to the side information of check-node.Side information in this step is divided into two parts, and first is the multi-system hard decision symbol of code word external information
and
each of binary representation be all the hard decision of the corresponding binary digit of code word external information:
Wherein
represent
the t position of binary representation, 1≤t≤r; The second portion of side information is the minimum value of r binary digit external information absolute value of code word,
it represents symbol
confidence level.Here, footmark j → i represents to connect the limit of j variable node and i check-node.
Step 4, check node calculation.First, for all 1≤i≤m, the verification of calculating i check-node with
N
irepresent the set of the capable all nonzero element line positions of i of check matrix H, N
i={ j:1≤j≤n, h
i,j≠ 0}.
The limit that connects check-node and variable node comprises two parts information: the outside verification that first is this limit and, second portion be this limit outside verification and confidence level; Wherein, the outside verification in limit and definite method of confidence level be: first, obtain the minimum value MIN of the confidence level on all limits that are connected with check-node
1with sub-minimum MIN
2, the outside verification on the limit of the confidence level minimum being connected with check-node and confidence level be MIN
2, the outside verification on the limit that is connected with check-node of residue and confidence level be MIN
1.Information with the limit that is connected with i check-node describes below.
Minimum value and the sub-minimum of the confidence information on all limits that calculating is connected with i check-node.The minimum value of the confidence level of side information and sub-minimum are designated as respectively
with
and the sequence number on the limit of confidence level minimum in all limits that are connected with i check-node is designated as to j
i.
Then, for check-node i, 1≤i≤m, connected all limit i → j, j ∈ N
i={ j:1≤j≤n, h
i,j≠ 0}, calculates the side information on every limit.The side information of this step is divided into two parts equally, first be outside verification corresponding to every limit and
Second portion be the outside verification in this limit and confidence level
by following formula, tried to achieve:
Here, footmark i → j represents to connect the limit of i check-node and j variable node.
Step 5, variable node calculate.The calculating of variable node is divided into two parts.
First, the information of calculation check node input variable node, adopts the confidence level weighting scheme based on Hamming distance to obtain.According to the outside verification of check-node and variable node fillet and binary representation and the size of the Hamming distance between the binary representation of code-word symbol hard decision set weighted factor, use weighted factor to the outside verification of fillet and confidence level be weighted.For all 1≤j≤n and i ∈ M
j, in calculation procedure four the outside verification of every side information and
with the codeword information hard decision result z in this iterative step two
(k)the Hamming distance of binary representation, by this apart from use
represent; Conventional letter
binary form be shown
the information that i check-node inputs to t binary digit of j variable node is
Wherein, 1≤t≤r, this information will be used for compute codeword external information in the step 3 of next iteration.
for weighted factor, concrete value is set in step 1, according to obtained distance
determine the value of weighted factor.In addition, this step is by required
number range be limited to (2
ω-2+ 1,2
ω-2-1) in scope, if required result is greater than 2
ω-2-1, will
value be taken as 2
ω-2-1, if required result is less than-2
ω-2+ 1, will
value be taken as-2
ω-2+ 1.
The renewal that the second portion that variable node calculates is codeword information, carry out according to the following formula:
Wherein, 1≤j≤n, 1≤t≤r, the codeword information of renewal is carried out hard decision and parity check by being used in the step 2 of next iteration.From formula (10), the binary piece of information of j code-word symbol during the k+1 time iteration, by two parts summation, obtained, first is the binary piece of information of j code-word symbol during iteration for the first time, and the binary piece of information that second portion each check-node when to the k time iteration inputs to j variable node is sued for peace and obtained.
In addition, this step is required
number range be limited to (2
ω-1+ 1,2
ω-1-1) in scope, if required result is greater than 2
ω-1-1, will
value be taken as 2
ω-1-1, if required result is less than-2
ω-1+ 1, will
value be taken as-2
ω-1+ 1.
Step 6, enter next iteration, that is, make k=k+1, re-execute step 2.
When decoding successfully decoded or when failed, decoding finishes in step 2.
Claims (8)
1. a m-ary LDPC code coding method for low complex degree, first carries out decoding initialization, and then iteration is carried out following steps: hard decision, side information calculating, check node calculation and variable node calculate, until successfully decoded or failed; It is characterized in that, described interpretation method, code-word symbol adopts binary form to represent, and comprises following aspect:
1) during decoding initialization, set weighted factor, use bit confidence coefficient that codeword information is carried out to initialization;
2) the outside verification of check-node and variable node fillet and confidence level convert bit confidence coefficient vector to, participate in variable node and calculate;
3) codeword information that each iteration is upgraded and the external information of check-node are all bit confidence coefficient vector.
2. m-ary LDPC code coding method according to claim 1, it is characterized in that, described interpretation method, when variable node calculates, the information of check-node input variable node, the confidence level weighting scheme of employing based on Hamming distance obtains, specifically: according to the outside verification of check-node and variable node fillet and binary representation and the size of the Hamming distance between the binary representation of code-word symbol hard decision set weighted factor, use weighted factor to the outside verification of fillet and confidence level be weighted.
3. m-ary LDPC code coding method according to claim 1, is characterized in that, described interpretation method, and when side information calculates, side information comprises the multi-system hard decision symbol of code word external information and the confidence level of this symbol; Wherein, all minimizations of the sum of absolute value in the binary digit external information that the confidence level of symbol is code word.
4. according to the arbitrary described m-ary LDPC code coding method of claim 1～3, it is characterized in that, in described interpretation method, all codeword information, code word external information, outside verification and confidence level and the check-node information that inputs to variable node be integer.
5. m-ary LDPC code coding method according to claim 1, it is characterized in that, described use bit confidence coefficient carries out initialization by codeword information, specifically: it is that integer assignment is to the codeword information of the 1st iteration that the binary message y of the code word that system is received be take quantized interval Δ and quantizing bit number ω uniform quantization.
6. m-ary LDPC code coding method according to claim 1 and 2, it is characterized in that, the external information of described check-node, specifically: during the 1st iteration, the binary digit external information of j code-word symbol of check-node equals the binary piece of information of j code-word symbol of iteration for the first time; During the inferior iteration of k (k >=2), the information that when the binary digit external information of j code-word symbol of check-node deducts the k-1 time iteration by the codeword information of the k time iteration, check-node is inputted j variable node obtains.
7. m-ary LDPC code coding method according to claim 1, it is characterized in that, during described check node calculation, the limit that connects check-node and variable node comprises two parts information: the outside verification that first is this limit and, second portion be this limit outside verification and confidence level; Wherein, the outside verification in limit and definite method of confidence level be: first, obtain the minimum value MIN of confidence level in all limits that are connected with check-node
1with sub-minimum MIN
2, the outside verification on the limit of the confidence level minimum being connected with check-node and confidence level be MIN
2, the outside verification on the limit that is connected with check-node of residue and confidence level be MIN
1.
8. m-ary LDPC code coding method according to claim 6, it is characterized in that, described codeword information, update method is: the binary piece of information of j code-word symbol during the k+1 time iteration, by two parts summation, obtained, first is the binary piece of information of j code-word symbol during iteration for the first time, and the binary piece of information that second portion each check-node when to the k time iteration inputs to j variable node is sued for peace and obtained.
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| CN106936445B (en) * | 2017-03-14 | 2019-06-21 | 西安电子科技大学 | A kind of multielement LDPC code coding method of low complex degree near-maximum-likelihood |
| CN107124186B (en) * | 2017-03-17 | 2020-06-19 | 上海交通大学 | Two-stage decoding method of LDPC code based on grid complexity |
| CN107124186A (en) * | 2017-03-17 | 2017-09-01 | 上海交通大学 | LDPC code two benches interpretation method based on grid complexity |
| CN108768410A (en) * | 2018-06-08 | 2018-11-06 | 中国电子科技集团公司第五十八研究所 | A kind of check-node update method suitable for Non-Binary LDPC Coded |
| CN109714060A (en) * | 2018-12-26 | 2019-05-03 | 西安烽火电子科技有限责任公司 | A kind of adaptive decoding method that LDPC code can be translated suitable for majority logic |
| CN111384975A (en) * | 2018-12-29 | 2020-07-07 | 泰斗微电子科技有限公司 | Optimization method and device of multi-system LDPC decoding algorithm and decoder |
| CN111384975B (en) * | 2018-12-29 | 2023-05-26 | 泰斗微电子科技有限公司 | Optimization method, device and decoder of multi-system LDPC decoding algorithm |
| CN114421972A (en) * | 2022-01-27 | 2022-04-29 | 石家庄市经纬度科技有限公司 | Decoding method of multi-system LDPC code |
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