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Jisuanji gongcheng

LDPC Code Based on Balanced Incomplete Block Design and Cycle Permutation Matrix

Yanhu Shan

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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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.
The algebraic method for constructing nonbinary quasi-cyclic(QC) low-density parity-check(LDPC) codes based on balanced incomplete block designs(BIBD) is presented.The generalized nonbinary location vector is proposed on constructions.A nonbinary matrix,which consists of nonbinary circulant submatrices,is formed by generalized two-dimensional matrix dispersion considering the generalized nonbinary location vector and BIBD method.The codes constructed by this method have girths at least 6.Experimental results show that significant coding gains are achieved over Reed-Solomon codes of the same parameters under the Additive White Gaussian Noise(AWGN) channel with iterative decoding Fast Fourier Transform based q-ary Sum-Product Algorithm(FFT-QSPA).And a good performance is also achieved over nonbinary Mackay LDPC codes with almost the same conditions.
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.
This paper constructs Partially Balanced Incomplete Block Designs (PBIBD) based on finite fields,and uses them to construct regular Low-Density Parity-Check(LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for the choosing of the code rate.Further,the paper even constructs QC-LDPC codes with girth at least 8,they can also be quasi-cyclic.Simulation results show that some of the codes can have slightly better performance than random regular LDPC codes over 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
In this paper,two classes of partially balanced incomplete block designs (PBIBD) based on finite fields is constructed,and they are used to construct the regular low-density parity-check (LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for choosing the code rate.In particular,they can also be quasi-cyclic.Simulations show that the constructed LDPC codes under sum-product iterative decoding perform very well over additive white Gaussian noise (AWGN) channels with BPSK modulation.