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Journal of Communications

Construction of Quasi-Cyclic LDPC Codes Using a Class of Balanced Incomplete Block Designs with Irregular Block Sizes

Hosung Park

Published Jan 1, 2019• 5 citations
Publisher
DOI
10.12720/jcm.14.7.553-559

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In this paper we propose a novel method for designing irregular quasi-cyclic low-density parity-check (LDPC) codes from Balanced Incomplete Block Designs (BIBDpsilas). The design method hinges around finding the optimum degree profile by minimizing the threshold using density evolution. The approach for designing short block length codes is robust for practical implementation and has been found to exhibit considerable performance gain that may be attributed to a good degree profile for the codes. The design takes into consideration the code rate and code length as variable parameters. The simulation results for the designed codes are compared with regular and irregular quasi-cyclic BIBD based LDPC codes and found a relatively higher performance in terms of BER.

IEEE Region 10 Conference (TENCON)•Nov 1, 2008•0 citations
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.
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.
In this paper we propose a novel method for designing irregular quasi-cyclic low-density parity-check (LDPC) codes from Balanced Incomplete Block Designs (BIBDpsilas). The design method hinges around finding the optimum degree profile by minimizing the threshold using density evolution. The approach for designing short block length codes is robust for practical implementation and has been found to exhibit considerable performance gain that may be attributed to a good degree profile for the codes. The design takes into consideration the code rate and code length as variable parameters. The simulation results for the designed codes are compared with regular and irregular quasi-cyclic BIBD based LDPC codes and found a relatively higher performance in terms of BER.