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IEEE Region 10 Conference (TENCON)

Improved performance irregular quasi-cyclic LDPC code design from BIBD’s using threshold minimization

Siddarama R. Patil, Sant Saran Pathak

Published Nov 1, 2008• 0 citations
Publisher

Abstract

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.

DOI
10.1109/tencon.2008.4766569

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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.
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.
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.
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 simple mathematical structure to improve the BER (bit error rate) performance of quasi-cyclic low-density parity-check (QC-LDPC) codes. Since the proposed structure can be defined in-between those of random codes and structured codes, these proposed QC-LDPC codes not only perform as well as random-LDPC codes, but also preserve the advantage of structured LDPC codes which is easier to implement over coding hardware. Moreover, the proposed structure, constructed from balanced incomplete block design (BIBD), can reduce the density of parity-check matrix and hence reduce the number of short cycles, which generally lead to better performance. At the end, we show that the error floor performance of QC-LDPC codes can be improved by proposed hybrid structures and perform well over binary-input additive white Gaussian noise (BI-AWGN) channel.
This paper presents a method to construct regular low-density parity-check (LDPC) codes of short block length and high rate based on a special type of combinatoric designs, i.e., balanced incomplete block designs (BIBDs) with lambda = 2 whose construction are based on cyclic difference families. Although the Tanner graph of the codes constructed contains some cycles of length 4, simulation results show that they perform well under belief propagation (BP) decoding. Further, these codes are quasi-cyclic (QC) codes and hence can be encoded efficiently
The existing design of quasi-cyclic(QC) low-density parity-check(LDPC) codes has not considered the problems of short length girths and the rows' dependency.The first problem leads to the BER performance of QC LDPC codes to be much poorer than that of randomly constructed LDPC codes,while the second problem leads to the difficulty of construction of generator matrices from parity-check matrices.To solve the first problem,the constraint conditions for designing the QC LDPC codes are proposed,and the dimension and shift factors of the circulant matrices of the given sparse parity-check matrix are adjusted according to the test results of both girth 4 and girth 6.To solve the second problem,an approach of irregular QC LDPC codes is proposed.The proposed approach is to replace some sub-matrices by zero matrices and identity matrices at special positions in the given sparse parity-check matrix so as to get a nonsingular square matrix for the construction of the generator matrix.Though adopting bidiagonal submatrices in parity-check matrix can solve the rows' dependency problem,many code words with low weights will occur,which leads to the BER performance can not be better by increasing code lengths.Examples are provided for the proposed design of QC LDPC codes,and computer simulation results show that the proposed QC LDPC codes achieve good BER performance.