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Journal of China Institute of Communications

Low-density parity-check codes based on sparse binary sequences

Ming Jiang

Published Jan 1, 2005• 2 citations
OpenAlex

Abstract

A novel and simple construction of regular LDPC codes was proposed, which used sparse binary sequences, through studying construction methods of LDPC codes. The distribution matrix of ones in parity-check matrix was introduced into the new construction. The cyclic cross correlation function and the cyclic auto correlation function were utilized to ensure that the girth of Tanner graph was eight. The new codes perform well using the sum-product algorithm for iterative decoding. Low encoding complexity can also be achieved due to the inherent quasi-cyclic structure of the LDPC codes.

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•Oct 15, 2004•6 citations
A novel and simple construction of regular LDPC codes was proposed, which used sparse binary sequences, through studying construction methods of LDPC codes. The distribution matrix of ones in parity-check matrix was introduced into the new construction. The cyclic cross correlation function and the cyclic auto correlation function were utilized to ensure that the girth of Tanner graph was eight. The new codes perform well using the sum-product algorithm for iterative decoding. Low encoding complexity can also be achieved due to the inherent quasi-cyclic structure of the LDPC codes.
In this paper, we propose a novel and simple construction of regular LDPC codes using sparse binary sequences. The distribution matrix of ones in a parity-check matrix is introduced into this new construction. The cyclic cross correlation function and the cyclic auto correlation function are employed to ensure that the girth of Tanner graph is at least eight. The new codes perform well using the sum-product algorithm for iterative decoding. Low encoding complexity can also be achieved due to the inherent quasi-cyclic structure of the 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.
This paper gives a new random construction for LDPC codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has low complexity and great flexible choice in LDPC code parameters including code length, code rate, least girth of the graph, and the weight of column and row in the parity-check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Simulations show that the method performs well with iterative decoding.
A new approach is proposed for constructing regular low-density parity-check (LDPC) codes based on tensor product of matrices. In this paper, first a general construction method of regular LDPC codes exploiting permutation matrices is described. Constructed codes have a quasi-cyclic structure with no short cycles of length 4 in their Tanner graph, hence simple encoding while maintaining good performance is achieved. The paper also demonstrates a generalized design, which covers a large family of LDPC codes and number of other construction methods. The new generalized LDPC codes are defined by a small number of parameters and cover a large set of code lengths and rates. Using these codes, LDPC matrices of any column weight and row weight can be constructed. Performance of these codes under iterative decoding compares well with other well-structured as well as random LDPC codes
This paper presents a new family of low-density parity-check (LDPC) code, the sparse parity-check matrix of which is constructed by self-defining non-diagonal identity sub-matrix that is a solution of the "n-queen problem". So this sub-matrix is called the Q-matrix and these LDPC codes are called the Q-matrixes LDPC codes. The Q-matrixes LDPC codes are good or very good codes with iterative decoding and their Tanner graphs are free of 4-lines cycle. Furthermore, they can be created in cycle form. Their encoding can be achieved in linear time. Especially, their code length and code rate can be flexible and quickly adjusted according to the practical situation, and the performance of high rate is also very good. The other unique excellence is that the large sparse parity-check matrixes of long Q-matrixes LDPC codes require very small storage space. The result of this paper is very significant not only for designing low complexity encoder, improving performance and reducing the complexity of the sum-product iterative decoding algorithm, but also for building practice system of encodable and decodable LDPC code.