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Quasi-cyclic LDPC codes from difference families

Sarah J. Johnson, Steven R. Weller

Published Jan 1, 2002• 16 citations
OpenAlex

Abstract

Abstract — We consider in this paper regular and nearly regular quasi-cyclic low-density parity-check (LDPC) codes, derived from families of dif-ference sets. The codes have girth at least 6, and sparse parity-check matrices. They are designed to perform well when iteratively decoded with the sum-product decoding algorithm and to allow low complexity encoding. I.

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Abstract — We consider in this paper regular and nearly regular quasi-cyclic low-density parity-check (LDPC) codes, derived from families of dif-ference sets. The codes have girth at least 6, and sparse parity-check matrices. They are designed to perform well when iteratively decoded with the sum-product decoding algorithm and to allow low complexity encoding. I.
Difference sets are used to give a novel method for constructing structured regular quasi-cyclic low-density parity-check codes. Let Fqbe a field with q elements and assume that D={d1,..., dk} is a (v,k,1)-difference set for Zvwith d12k. Depending on v=q-1, v≥ 2dkor v≥ 2dk-1, three code construction methods are given that produce regular 4-cycle free codes, that is codes with girth at least 6. Simulation results show that the constructed codes perform well over the AWGN channel with an iterative sum-product message-passing decoding algorithm.
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.