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IEEE Transactions on Communications

New Constructions of Quasi-Cyclic LDPC Codes Based on Special Classes of BIBDs for the AWGN and Binary Erasure Channels

Lan Lan, Ying Yu Tai, Shu Lin, Behshad Memari, Bahram Honary

Published Dec 1, 2007• 10 citations
Publisher

Abstract

This paper presents new methods for efficiently constructing encodable quasi-cyclic low-density parity-check (LDPC) codes based on special balanced incomplete block designs (BIBDs). Codes constructed perform well over both the additive white Gaussian noise (AWGN) and binary erasure channels with iterative decoding.
DOI
10.1109/tcomm.2007.910579

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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.