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Telecommunication Engineering

Design of Parity Check Matrix for Irregular LDPC Codes

Song Wei-jun

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

A design of parity check matrix for Irregular LDPC codes based on permutation matrix is proposed in this paper.The parity-check matrix is composed of blocks of circulant matrices and the purpose is to reduce the number of 1 in the upper triangle by applying matrix transposition,and row and column interchange to avoid the cycle of 4.Simulation result shows that BER can be improved at 10 iterations,and the code rate of 0.930 is obtained.

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A design of parity check matrix for Irregular LDPC codes based on permutation matrix is proposed in this paper.The parity-check matrix is composed of blocks of circulant matrices and the purpose is to reduce the number of 1 in the upper triangle by applying matrix transposition,and row and column interchange to avoid the cycle of 4.Simulation result shows that BER can be improved at 10 iterations,and the code rate of 0.930 is obtained.
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.
To reduce the cycles in the Tanner graph which may affect the code performance,a recursive method to construct low-density parity-check(LDPC) codes was proposed.The method used a parity-check matrix of a short LDPC code as its mother matrix upon which a long code was constructed with circulant permutation matrices.By choosing the circulant permutation matrix parameters properly,the number of cycles having a given length in the Tanner graph of the constructed long codes were equal to or less than that of the short code.Either regular or irregular LDPC codes were constructed.Simulation results show that the LDPC codes constructed by this method have very low error-floor and almost no performance degradation due to their special structure as compared with random LDPC codes.
Low-density Parity-check (LDPC) coding is a class of advanced channel coding techniques. To improve the performance of LDPC codes, a simple and effective method to construct QC-LDPC codes without short cycles (cycles of length four and six) is proposed. The approach is especially effective when the parity-check matrix of QC-LDPC codes is composed of circulant permutation matrices. Firstly, we analyze the shapes of the cycles in the exponent matrix, to get the required conditions of no four-cycles and six-cycles. Then we show how to construct the parity-check matrix without four-cycles and six-cycles by filling rows of the exponent matrix with arithmetic sequences. Simulation results show that the proposed codes have better performance than array codes. Though the performance of the proposed codes is not as well as random codes at higher Eb/N0, they can be applied to practical communications because of being encoded in linear time with shift registers.