CN108055046B - LDPC decoder based on double correction factors - Google Patents

LDPC decoder based on double correction factors Download PDF

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CN108055046B
CN108055046B CN201810093380.6A CN201810093380A CN108055046B CN 108055046 B CN108055046 B CN 108055046B CN 201810093380 A CN201810093380 A CN 201810093380A CN 108055046 B CN108055046 B CN 108055046B
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赵良
周华
彭文凯
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Nanjing University of Information Science and Technology
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
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Abstract

The invention discloses an LDPC decoder based on double correction factors, which adopts addition operation to replace product operation in the process of calculating all residue values, simplifies operation steps, greatly reduces calculation complexity, introduces correction factors and corrects the residue values of each edge in order to ensure that the decoding performance of modified RBP and NW RBP algorithms is not reduced, so as to reduce the error rate of decoding after the algorithms are simplified.

Description

LDPC decoder based on double correction factors
Technical Field
The invention relates to the technical field of electronics, communication and information engineering, in particular to an LDPC decoder based on double correction factors.
Background
A Low-Density Parity-Check (LDPC) code is a linear block code. Because of the characteristic of being close to the aroma limit, the LDPC code is widely applied to the fields of deep space communication, optical fiber communication, satellite digital video, audio broadcasting, data storage and the like. In each iteration process, all information from variable nodes to check nodes is updated at the same time, and then all information from check nodes to variable nodes is updated at the same time. The convergence rate of the decoding method is slow, in order to improve the convergence rate of decoding, Casado et al apply the concept of residual degree to belief propagation, and propose two decoding timings: decoding is propagated based on Residual Belief Propagation (RBP), and decoding is propagated based on Residual Belief Propagation (NWRBP) of check nodes. The difference between the two is that the RBP dynamically selects the edge where the maximum residue degree is located for updating, and the NWRBP dynamically selects the check node where the maximum residue degree is located for updating.
The convergence rate of LDPC decoding is effectively improved by both RBP algorithm and NW RBP decoding, but the RBP algorithm and NW RBP decoding have the disadvantages that a large number of floating point type logarithm and exponential operations are required in the decoding process, so that the operation amount is large, the complexity is high, and the hardware realization is not facilitated.
Disclosure of Invention
The invention aims to solve the problems that in the prior art, an RBP decoding algorithm is high in complexity and not beneficial to hardware implementation, and provides an LDPC decoder based on double correction factors.
The technical scheme adopted by the invention is as follows: an LDPC decoder based on double correction factors comprises the following procedures:
1) initialization: setting correction factors alpha and beta;
all information m from check node to variable nodec→vSet to 0; where subscripts c and v are check nodes and variable nodes respectively,
all information L from variable node to check nodev→cSet to its corresponding channel information ri；Lv→cSubscripts are denoted as the v-th variable node through the c-th check node;
setting the total number of information from the check node to the variable node in each iteration as T, wherein the variable T is 0;
m denotes check node to variable node information, where subscripts denote from the number of check nodes to the number of variable nodes;
2) calculating all residual values
Figure BDA0001564316330000021
The calculation process is as follows:
Figure BDA0001564316330000022
Figure BDA0001564316330000023
Figure BDA0001564316330000024
Figure BDA0001564316330000025
and is
Figure BDA0001564316330000026
Figure BDA0001564316330000027
Figure BDA0001564316330000028
Figure BDA0001564316330000029
Figure BDA00015643163300000210
Figure BDA00015643163300000211
And representing the information before updating from the ith check node to the jth variable node.
3) Finding the maximum value of the residue value
Figure BDA00015643163300000212
4) The method is divided into two types, the first type is: generating check node to variable node information
Figure BDA00015643163300000213
Recording the updating times t as t + 1; c hereinmaxAnd vmaxIs a specific node;
and (4) subsequent updating:
FOR each ca∈N(vmax)DO
Generate and propagate
Figure BDA00015643163300000214
V hereinmaxAnd caIs a specific node;
END FOR
the second method is as follows: for each vj∈N(cmax) Generating and propagating check node cmaxInformation to all edge nodes
Figure BDA00015643163300000215
Recording the updating times t as t + 1;
and (4) subsequent updating:
FOR each ca∈N(vj)DO
Generate and propagate
Figure BDA0001564316330000031
END FOR
5) And (4) trial judgment:
IF t＜T
returning to the step 2);
ELSE
after the decoding is finished, outputting a decoding result;
END。
preferably, the correction factor α ∈ (0,1), the correction factor β ∈ (0,1), and β < α.
Preferably, said N (c)m)＝{vn:h mn1 represents and checks node cmA set of all connected variable nodes; n (c)m)\vnA set of representations N (c)m) Removing variable node vnSet of (d), N (v)n)＝{cm:h mn1 represents a variable node vnA collection of all check nodes connected.
The invention has the beneficial effects that: in the RBP and NWRBP algorithm, because floating-point logarithm and exponent operation are needed when the residue value of each edge is calculated, the operation amount of all the edges from the check node to the variable node is much higher than that of the traditional BP algorithm after the edges are updated; in addition, in order to ensure that the decoding performance of the modified RBP and NW RBP algorithm is not reduced, a correction factor is introduced and the residual value of each edge is corrected, so that the decoding performance is improved on the premise of reducing the operation amount.
Drawings
FIG. 1 is a functional block diagram of the present invention;
FIG. 2 is a diagram illustrating a relationship between a frame error rate and an iteration number when a signal-to-noise ratio is 3.0dB in a white Gaussian noise channel environment by an improved RBP algorithm;
FIG. 3 is a diagram illustrating a relationship between a frame error rate and an iteration number when a signal-to-noise ratio is 3.5dB in a white Gaussian noise channel environment by an improved RBP algorithm;
FIG. 4 is a diagram illustrating a relationship between a frame error rate and an iteration number when a signal-to-noise ratio is 3.0dB in a Gaussian white noise channel environment by an improved NW RBP algorithm;
FIG. 5 is a diagram illustrating a relationship between a frame error rate and an iteration number when a signal-to-noise ratio is 3.5dB in a Gaussian white noise channel environment by an improved NW RBP algorithm;
Detailed Description
The invention will be further described with reference to the drawings in the following examples.
Example 1:
referring to fig. 1-3, an embodiment of the present invention is provided:
step 1, firstly, initializing, and setting correction factors alpha and beta; all information m from check node to variable nodec→vSet to 0; all information L from variable node to check nodev→cSet to its corresponding channel information ri(ii) a Setting the total number of information from the check node to the variable node as T, wherein the variable T is 0;
step 2, calculating the residual value of all edges
Figure BDA0001564316330000041
Original source
Figure BDA0001564316330000042
The calculation method comprises the following steps:
Figure BDA0001564316330000043
Figure BDA0001564316330000044
will be original
Figure BDA0001564316330000045
The calculation method is modified as follows:
Figure BDA0001564316330000046
then through correction factors alpha and beta
Figure BDA0001564316330000047
Making correction and final calculation
Figure BDA0001564316330000048
Step 3, finding the maximum value of the residue value
Figure BDA0001564316330000049
Generating check node to variable node information
Figure BDA00015643163300000410
And for each ca∈N(vmax) Generating and propagating
Figure BDA00015643163300000411
Recording the updating times T as T +1, returning to the step 2 to continuously update when T is less than T, and finishing one iteration when T as T; the repeated decoding interruption condition is as follows: the number of successful decoding or iterations reaches a set maximum.
Example 2:
referring to fig. 1, 4 and 5, an embodiment of the present invention is provided:
step 1, firstly, initializing, and setting correction factors alpha and beta; all information m from check node to variable nodec→vSet to 0; all information L from variable node to check nodev→cSet to its corresponding channel information ri(ii) a Setting the total number of check nodes as T, and setting a variable T as 0;
step 2, calculating the residual value of all edges
Figure BDA00015643163300000412
Original source
Figure BDA00015643163300000413
The calculation method comprises the following steps:
Figure BDA0001564316330000051
Figure BDA0001564316330000052
will be original
Figure BDA0001564316330000053
The calculation method is modified as follows:
Figure BDA0001564316330000054
then through correction factors alpha and beta
Figure BDA0001564316330000055
Making correction and final calculation
Figure BDA0001564316330000056
Step 3, finding the maximum value of the residue value
Figure BDA0001564316330000057
For each vj∈N(cmax) Generating and propagating check node cmaxInformation to all edge nodes
Figure BDA0001564316330000058
And for each ca∈N(vj) Generating and propagating
Figure BDA0001564316330000059
Recording the updating times T as T +1, returning to the step 2 to continuously update when T is less than T, and finishing one iteration when T as T; the repeated decoding interruption condition is as follows: the number of successful decoding or iterations reaches a set maximum.
The computer used for the experiment is configured to be an internal memory of 8GB, the CPU is a desktop computer of Intel Core i 5-65003.20 GHz, the code is developed by C + + language, and the compiler is Visual Studio 2012. The LDPC code used to test the inventive scheme was a (155,3,5) LDPC code. All simulations in the invention are performed in binary input additive white gaussian noise (BI-AWGN) channel, the correction factor α is 0.9, the correction factor β is 0.1, the maximum number of iterations is 200, and the modulation mode is BPSK. By analyzing the performance of each coding scheme, the following conclusions can be drawn:
first, in calculating the residual value
Figure BDA00015643163300000510
In the process, the floating-point product operation is replaced by the addition operation, and compared with the traditional RBP and NW RBP algorithm, the complexity of the improved RBP and improved NW RBP decoding algorithm is greatly reduced, and the hardware implementation difficulty is reduced.
Secondly, as shown in fig. 2 and fig. 3, the frame error rate of the modified RBP decoding algorithm is significantly lower than that of the conventional RBP algorithm, and as shown in fig. 4 and fig. 5, the frame error rate of the modified NW RBP algorithm is also slightly lower than that of the conventional NW RBP algorithm, so that the algorithm achieves the effect of improving decoding performance while reducing complexity.
The above are only typical examples of the present invention, and besides, the present invention may have other embodiments, and all the technical solutions formed by equivalent substitutions or equivalent changes are within the scope of the present invention as claimed.

Claims (3)

1. An LDPC decoder based on dual correction factors, comprising: the method comprises the following steps:
1) initialization: setting correction factors alpha and beta;
all information m from check node to variable nodec→vSet to 0; where subscripts c and v are check nodes and variable nodes respectively,
all information L from variable node to check nodev→cSet to its corresponding channel information ri；
Lv→cSubscripts are denoted as the v-th variable node through the c-th check node;
setting the total number of information from the check node to the variable node in each iteration as T, wherein the variable T is 0;
mc→vinformation representing check nodes to variable nodes, wherein subscripts are represented from the c-th check node to the v-th variable node;
2) calculating all residual values
Figure FDA0002959336200000011
The calculation process is as follows:
Figure FDA0002959336200000012
Figure FDA0002959336200000013
Figure FDA0002959336200000014
Figure FDA0002959336200000015
and is
Figure FDA0002959336200000016
Figure FDA0002959336200000017
Figure FDA0002959336200000018
Figure FDA0002959336200000019
Figure FDA00029593362000000110
Figure FDA00029593362000000111
Representing information before updating from the ith check node to the jth variable node;
3) finding the maximum value of the residue value
Figure FDA00029593362000000112
4) The method is divided into two types, the first type is: generating check node to variable node information
Figure FDA00029593362000000113
Recording the updating times t as t + 1; c hereinmaxAnd vmaxIs a specific node;
and (4) subsequent updating:
FOR each ca∈N(vmax)DO
Generate and propagate
Figure FDA0002959336200000021
V hereinmaxAnd caIs a specific node;
END FOR
the second method is as follows: for each vj∈N(cmax) Generating and propagating check node cmaxInformation to all edge nodes
Figure FDA0002959336200000022
Recording the updating times t as t + 1;
and (4) subsequent updating:
FOR each ca∈N(vj)DO
Generate and propagate
Figure FDA0002959336200000023
END FOR
5) And (4) trial judgment:
IF t＜T
returning to the step 2);
ELSE
after the decoding is finished, outputting a decoding result;
END。
2. the dual correction factor-based LDPC decoder according to claim 1, wherein: the correction factor alpha belongs to (0,1), the correction factor beta belongs to (0,1), and beta is less than alpha.
3. The dual correction factor-based LDPC decoder according to claim 1, wherein: n (c)m)＝{vn：hmn1 represents and checks node cmA set of all connected variable nodes; n (c)m)\vnA set of representations N (c)m) Removing variable node vnSet of (d), N (v)n)＝{cm：hmn1 represents a variable node vnA collection of all check nodes connected.
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