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International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY)

Low-density parity-check codes based on the independent subgroups

Fedor I. Ivanov, Victor Zyablov, В. Г. Потапов

Published Sep 1, 2012• 3 citations
Publisher

Abstract

Two criteria of cyclic subgroups independence are proved. The ensemble of regular binary LDPC codes which are based on independent subgroups, is built. The condition of absence of the cycles of the length 4 is proved for the resulting code construction. The results of the received code constructions are presented for the iterative algorithm Sum-Product when the codeword is transmitted over channel with additive Gaussian white noise (AGWN).

DOI
10.1109/red.2012.6338401

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Two criteria of cyclic subgroups independence are proved. The ensemble of regular binary LDPC codes which are based on independent subgroups, is built. The condition of absence of the cycles of the length 4 is proved for the resulting code construction. The results of the received code constructions are presented for the iterative algorithm Sum-Product when the codeword is transmitted over channel with additive Gaussian white noise (AGWN).
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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.
An algorithm for generating parity-check matrices of regular low-density paritycheck codes based on permutation matrices and Steiner triple systems S(v, 3, 2), v = 2 m − 1, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm applied in the case of transmission over a binary channel with additive Gaussian white noise and BPSK modulation are presented.