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Computer Engineering and Applications Journal

Construction of a class of quasi-cyclic LDPC codes

Tang Yuan-shen

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

This paper constructs Partially Balanced Incomplete Block Designs (PBIBD) based on finite fields,and uses them to construct regular Low-Density Parity-Check(LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for the choosing of the code rate.Further,the paper even constructs QC-LDPC codes with girth at least 8,they can also be quasi-cyclic.Simulation results show that some of the codes can have slightly better performance than random regular LDPC codes over AWGN channel.

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International Conference on Computer, Control and Communication•Feb 1, 2009•0 citations
This paper constructs Partially Balanced Incomplete Block Designs (PBIBD) based on finite fields,and uses them to construct regular Low-Density Parity-Check(LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for the choosing of the code rate.Further,the paper even constructs QC-LDPC codes with girth at least 8,they can also be quasi-cyclic.Simulation results show that some of the codes can have slightly better performance than random regular LDPC codes over AWGN channel.
In this paper,two classes of partially balanced incomplete block designs (PBIBD) based on finite fields is constructed,and they are used to construct the regular low-density parity-check (LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for choosing the code rate.In particular,they can also be quasi-cyclic.Simulations show that the constructed LDPC codes under sum-product iterative decoding perform very well over additive white Gaussian noise (AWGN) channels with BPSK modulation.
A method to construct a flexible length or rate of quasi-cyclic Low Density Parity Check(LDPC) codes based on Balanced Incomplete Block Design(BIBD) and cycle permutation matrix is proposed.Based on actual demand,the corresponding template matrix is constructed by BIBD method.The template matrix is extended by the appropriate cycle permutation matrix.The quasi-cyclic LDPC codes constructed by the proposed method have a good structure and flexibility.This method improves the efficiency of construction good codes which meet the needs of a practical application.Simulations show that quasi-cyclic LDPC codes constructed by the proposed method perform well over AWGN channels with iterative decoding and have a lower error floor.
Two classes of well-structured binary low-density parity check codes (LDPC) are described. The first class is based on a branch of combinatorial mathematics, known as the balanced incomplete block design (BIBD). Construction of three types of codes derived from BIBD designs is illustrated in addition to a family of LDPC codes constructed by decomposition of incidence matrices of the proposed BIBD designs. The decomposition technique reduces the density of the parity check matrix and hence reduces the number of short cycles, which generally lead to better performing LDPC codes. The second class of well-structured LDPC codes, Vandermonde or array LDPC codes, are defined by a small number of parameters and cover a large set of code lengths and rates with different column weights. The presented LDPC codes are quasi-cyclic with no cycles of length four; hence simple encoding while maintaining good performance is achieved. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance/complexity trade-offs. It is shown that well-structured LDPC codes perform very similar to the known 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.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes require less hardware resources due to the quasi-cyclic structure of parity-check matrices.In this paper, two improved methods for constructing QC-LDPC codes are proposed.Firstly, in order to make sure the masked LDPC codes have flexible code rate and code length, an improved construction of masking matrix is presented.The proposed regular masking matrix of QC-LDPC codes have the girth at least 6.Then, the irregular codes are constructed by using improved finite field approach and PEG algorithm, which result in large girth and less short cycles.Simulations demonstrate that the proposed QC-LDPC codes have both lower error floor and good waterfall performance.
We propose a construction method for constructing quasi-cyclic low-density parity-check (QC LDPC) codes based on subgroup's coset. Our construction method is available not only for the prime circulants size, but also for the nonprime circulants size in some conditions. And it is showed that these conditions are easy to satisfy. Regular QC LDPC codes with various lengths and rates can be easily constructed with girth at least 6. Simulation results show that they are have almost the same performance as random regular LDPC codes over AWGN channel.