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International Conference on Signal Processing and Communications (SPCOM)

Construction of Regular and Irregular LDPC Codes using (n, {k1, k2}, 1) Block Design

Siddarama R. Patil, Sant Saran Pathak

Published Jan 1, 2007• 0 citations
Publisher

Abstract

In this paper, we construct regular and irregular LDPC codes using (n, {k1,k2}, 1)block design. The problem of designing regular and irregular structured LDPC codes that have good overall error performance for wide range of code rates and block sizes with attractive storage requirements is attempted. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Further we analyze the constructed codes based on number of short cycles of the corresponding Tanner graph. The analysis shows that codes having small number of short cycles and a cycle structure which is not overly regular in their Tanner graph perform better. The presented codes are well structured and unlike random codes can lend themselves to a very low-complexity encoder and decoder implementation.

DOI
10.1109/icspc.2007.4728629

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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.
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
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Based on the optical orthogonal codes, a method for constructing irregular LDPC (low-density parity check) codes was presented. These LDPC codes are quasi-cyclic codes and can be encoded with low complexity with a linear relationship to code length. These codes have Tanner graphs free of 4-cycles. They perform well with the sum-product iterative decoding. Compared with random codes and regular LDPC codes based on the optical orthogonal codes with similar parameters, they have decoding performance gains respectively about 0.3 and 0.15 dB when bit error rate is 10~(-5).