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Electronic Science and Technology

Decoder Design for QC_LDPC Codes with Large Girth Based on FPGA

HU Jua

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

This paper proposes a design of regular check matrix for QC_ LDPC codes with girth 8 with the side effects of cycles,especially the short cycles,on the performance of LDPC decoders in consideration. The proposed construction algorithm for QC_ LDPC codes designs 3 sub matrices with different given shifting functions,then combines them into one matrix,and finally expands the transposed matrix of the combination matrix into a desired parity check matrix using the identity matrix and the cyclic shift matrices of the identity matrix randomly. The layered-decoding algorithm is used for the special structure of check matrix. The design can achieve decoding with 1 /2 code rate, 3456 code length,and( 3,6) regular QC-LDPC codes. The whole design is synthesized under EP3SL340 FPGA of Altera Stratix Ⅲ.

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This paper proposes a design of regular check matrix for QC_ LDPC codes with girth 8 with the side effects of cycles,especially the short cycles,on the performance of LDPC decoders in consideration. The proposed construction algorithm for QC_ LDPC codes designs 3 sub matrices with different given shifting functions,then combines them into one matrix,and finally expands the transposed matrix of the combination matrix into a desired parity check matrix using the identity matrix and the cyclic shift matrices of the identity matrix randomly. The layered-decoding algorithm is used for the special structure of check matrix. The design can achieve decoding with 1 /2 code rate, 3456 code length,and( 3,6) regular QC-LDPC codes. The whole design is synthesized under EP3SL340 FPGA of Altera Stratix Ⅲ.
By analyzing the shapes of 4-cycles and 6-cycles of TG in parity check matrix,this paper presents a method of counting the number of 4-cycles and 6-cycles.Considering the cycles,especially the short cycles,degrade the performance of LDPC decoders,this paper then proposes a design of regular check matrix for Low-Density Parity-Check(LDPC) codes with girth 8.The proposed construction algorithm for LDPC codes is to design 3 submatrices with different given shifting functions,then combine them into one matrix,and finally expand the transposed matrix of the combination matrix into a desired parity check matrix using the identity matrix and the cyclic shift matrices of the identity matrix randomly.The simulation results in the AWGN channel show that the BER performance of these codes obtained by the generation matrix derived from the proposed check matrices in encoding the random information bits is as good as that of the random LDPC codes.
A design algorithm of regular check matrix for Low-Density Parity-Check(LDPC)codes is proposed in this paper.The proposed approach is to design 3 sub-matrices,and each of the sub-matrices is combined by the cyclic shift matrices of the identity matrix,then to combine these sub-matrices into a desired parity check matrix according to our approach.Using the check algorithms of the short cycles to find the combinations of shifting operators by which the parity check matrix desires has no girth- four and no girth-six.The simulation results in AWGN channel show that the BER performance of these codes obtained by the generator matrix derived from the proposed check matrices to encode the random information bits is as good as that of random LDPC codes.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.
The existing design of quasi-cyclic(QC) low-density parity-check(LDPC) codes has not considered the problems of short length girths and the rows' dependency.The first problem leads to the BER performance of QC LDPC codes to be much poorer than that of randomly constructed LDPC codes,while the second problem leads to the difficulty of construction of generator matrices from parity-check matrices.To solve the first problem,the constraint conditions for designing the QC LDPC codes are proposed,and the dimension and shift factors of the circulant matrices of the given sparse parity-check matrix are adjusted according to the test results of both girth 4 and girth 6.To solve the second problem,an approach of irregular QC LDPC codes is proposed.The proposed approach is to replace some sub-matrices by zero matrices and identity matrices at special positions in the given sparse parity-check matrix so as to get a nonsingular square matrix for the construction of the generator matrix.Though adopting bidiagonal submatrices in parity-check matrix can solve the rows' dependency problem,many code words with low weights will occur,which leads to the BER performance can not be better by increasing code lengths.Examples are provided for the proposed design of QC LDPC codes,and computer simulation results show that the proposed QC LDPC codes achieve good BER performance.
The presence of circles would lay a great impact on the quasi-cyclic LDPC decoding.Therefore,the parity check matrix with good girth distribution is beneficial to the performance of code.This paper first makes a analysis on girth distribution of the check matrix.Then a reasonable constraint is set between the mother matrix and shift matrix,thus,by this way,the check matrix could maximize the minimum cycle length of the check matrix and the average length of the cycle.Finally,a method to construct QC-LDPC code with high girth is given.Simulation results show that this method for minimizing the short code cycle could construct good practical codes.