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IEEE International Conference on Industrial and Information Systems (ICIIS)

Construction of irregular LDPC codes based on Balanced Incomplete Block Designs

Siddarama R. Patil, Sant Saran Pathak

Published Jan 1, 2007• 0 citations
Publisher

Abstract

In this paper, we present a method to design irregular structured low-density parity-check (LDPC) codes based on balanced incomplete block designs (BIBD). The problem of designing irregular structured LDPC codes that have good overall error performance for a wide range of code rates and block sizes with attractive storage requirements is attempted. The proposed codes are well structured and unlike random codes can lend themselves to a very low-complexity implementation. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance. The proposed LDPC codes demonstrate performance that is better than an average random LDPC code of similar block length, code rate and parity check matrix sparsity.

DOI
10.1109/iciinfs.2007.4579179

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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.
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.
In this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based on these designs. By analyzing the incidence relations between points and blocks within a BIBD, we prove that the resulting LDPC codes possess a girth of 6. Subsequently, we provide a detailed analysis of the cycle structure of the constructed LDPC codes and introduce a systematic approach for enumerating their short cycles. Using this method, we determine the exact numbers of cycles of lengths 6 and 8. Simulation results demonstrate that the constructed LDPC codes exhibit excellent performance.