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On the Low Complexity Construction of Quasi-Cyclic Low-Density Parity-Check Codes by Progressive-Block Growth

Qiangy Yuan, Pinyi Ren, Yilin Feng, Jun Wang

Published Jan 1, 2009• 1 citation
Publisher

Abstract

In this paper, we propose a novel method with low complexity for constructing quasi-cyclic LDPC codes. The algorithm chooses every circulant permutation matrix sequentially, and makes sure that the current circulant permutation matrix forms no cycles of length 4 and 6 with the existent matrices, finally a family of $(3,L)$ QC-LDPC codes with girth at least 8 is obtained. The main complexity of the algorithm is checking cycles of length 6, the number of which is no more than $L^2$. Simulation results show that, when block length is 1008 and using the iterative belief propagation decoding, the LDPC code constructed by the proposed algorithm out performs the random code about 0.1dB at the bit-error-rate of $ 10^{ - 5}$.

DOI
10.1109/cmc.2009.205

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In this paper, we propose a novel method with low complexity for constructing quasi-cyclic LDPC codes. The algorithm chooses every circulant permutation matrix sequentially, and makes sure that the current circulant permutation matrix forms no cycles of length 4 and 6 with the existent matrices, finally a family of (3,L)(3,L)(3,L) QC-LDPC codes with girth at least 8 is obtained. The main complexity of the algorithm is checking cycles of length 6, the number of which is no more than L2L^2L2. Simulation results show that, when block length is 1008 and using the iterative belief propagation decoding, the LDPC code constructed by the proposed algorithm out performs the random code about 0.1dB at the bit-error-rate of 10−5 10^{ - 5}10−5.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.
In this paper a new low complexity method for constructing binary quasi-cyclic low-density parity-check (QC-LDPC) codes is introduced. In the proposed method, each block-column of the parity check matrix H is made by a circulant matrix in a way that the associated Tanner graph is free of cycle four. Each circulant matrix in H is made by a generator column. The generator columns should be selected in a way that each associated circulant matrix and every two distinct circulant matrices are free of cycle four. The generator columns are made by row distance sets. An algorithm for generating distance sets and obtaining circulant matrices with columns of weight three is presented separately. Simplicity of construction and having a good flexible family of quasi cyclic LDPC codes both in rate and length are the main properties of the proposed method. The performance of the proposed codes is compared with that of the random-like and Array LDPC codes over an AWGN channel. Simulation results show that from the performance perspective, the constructed codes are competitive with random-like and Array LDPC codes.
In this paper, we propose an algorithm for removing short-cycles in Quasi-Cyclic (QC) Low-density parity-check (LDPC) codes. First using an algorithm with lower computational complexity, all the cycles in the parity check matrix H are found. Then following a ruler, we adjust the shift value of circulant permutation matrix (CPM) to remove the short-cycles. This algorithm could ensure that the code after cycle removal process preserves the quasi-cyclic structure. Simulation results show that: comparing with the codes (504,252) and (1008, 504), we achieve 0.1dB improvement both.
In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.
In this paper, we proposed a novel method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on circulant permutation matrices via a simple quadratic congruential equation. The main advantage is that QC-LDPC codes with a variety of block lengths and rates can be easily constructed with no cycles of length four or less. Simulation results show that the proposed QC-LDPC codes perform slight better than the random regular LDPC codes for short to moderate block lengths and have almost the same performance as Sridara-Fuja-Tanner codes.
In this paper, we proposed a new method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on circulant permutation matrices via the one-coincidence sequences. The main advantage is that QC-LDPC codes with a variety of block lengths and rates can be easily constructed with no cycles of length four or less. Simulation results show that the proposed QC-LDPC codes perform slight better than the random regular LDPC codes for short to moderate block lengths and have almost the same performance as Sridara- Fuja-Tanner codes.