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Jisuanji gongcheng

Coset-based Quasi-Cyclic LDPC Code Construction

Yuansheng Tang

Published Jan 1, 2009• 0 citations
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Abstract

This paper proposes a coset-based Quasi-Cyclic Low Density Parity Check(QC LDPC) construction method and similar SFT-LDPC code construction method in order to guarantee the girth under high bitrate.It gives two necessary conditions of girth at least 6 when the size of cyclic permutation matrix is a composite number.This construction method with various lengths,rates and girth at least 6 can be flexiblely constructed.Simulation results show that the code constructed by this method is comparable to random ones in error correction performance over additive white Gaussian noise channel.

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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.

International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)•Jul 1, 2016•1 citation
This paper proposes a coset-based Quasi-Cyclic Low Density Parity Check(QC LDPC) construction method and similar SFT-LDPC code construction method in order to guarantee the girth under high bitrate.It gives two necessary conditions of girth at least 6 when the size of cyclic permutation matrix is a composite number.This construction method with various lengths,rates and girth at least 6 can be flexiblely constructed.Simulation results show that the code constructed by this method is comparable to random ones in error correction performance over additive white Gaussian noise channel.
We propose a construction method for constructing quasi-cyclic low-density parity-check (QC LDPC) codes based on subgroup's coset. Our construction method is available not only for the prime circulants size, but also for the nonprime circulants size in some conditions. And it is showed that these conditions are easy to satisfy. Regular QC LDPC codes with various lengths and rates can be easily constructed with girth at least 6. Simulation results show that they are have almost the same performance as random regular LDPC codes over AWGN channel.
This article presents a highly flexible method for constructing high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes. The proposed algorithm constructs a Tanner graph formed by connecting groups of rows (check nodes) and columns (variable nodes) of the constructed code. To obtain a sub-matrix structure, rows and columns are divided into groups of equal sizes. Rows and columns in a group are connected in their numerical (positional) order to obtain a cyclic structure. Connected rows and columns must satisfy the desired minimum cycle length. We present conditions that guarantee desired girths. The proposed algorithm is by far more flexible in constructing a wide range (rates and lengths) of regular and irregular QC-LDPC codes compared to existing methods. The algorithm, which has linear complexity with respect to the number of rows or columns, provides an easy and fast way to construct QC-LDPC codes. Constructed codes show good bit error rate performances.
For arbitrary code lengths of the form PL(P≥3L2/4+L?1),a new family of(4,L)-regular quasi-cyclic(QC) low-density parity-check(LDPC) codes was proposed explicitly with girth eight.Employing the new code as a compo-nent code in the construction method of Chinese remainder theorem(CRT),a novel class of compound QC-LDPC codes was presented with both girth at least eight and very flexible code lengths.Simulation results show that the new compound codes with rate 1/2 and moderate code lengths perform very well over the additive white Gaussian noise(AWGN) channel.
A simple and efficient search method based on the coset concept is proposed to construct (3, L ) quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes without small cycles. Compared with the random search method, the chance to find large‐girth codes is remarkably increased for the new method. Compared with Tanner's construction, the proposed method is much more flexible in the selection of row weight L . Some new codes are constructed with the shortest lengths compared with those constructed by the existing well‐known methods. Simulation results show that the novel codes with moderate length perform well in the additive white Gaussian noise channel.
This paper proposes a construction method of regular(j, k) Lucas quasi-cyclic low-density parity-check(L-QC-LDPC) codes with girth at least eight based on the Lucas sequence. By this method, the girth of L-QC-LDPC codes is large, which can effectively eliminate short cycles. Besides, lower bound of circulant permutation submatrix dimension p is allowed continuous values. In addition, it can save the storage space in terms of hardware implementation which reduces the cost and complexity of hardware realization correspondingly. Simulation results show that the L-QC-LDPC codes have net coding gain(NCG) of about 2d B and 0.8d B compared with one-coincidence sequence quasi-cyclic LDPC(OCS-LDPC) codes and deterministic codes, respectively, at code rate of 1/2, code length of 1302 and bit error rate(BER) of 10?6. At the same condition, the performance of L-QC-LDPC codes is slightly better than that of the quadratic function LDPC(QF-LDPC) codes, which has an NCG improvement of around 0.1d B. Meanwhile, at code rate of 1/2, similar code length and BER of 10~(-6), the NCG of L-QC-LDPC codes outweigh about 0.5d B compared with that of QC-LDPC codes based on cyclic subgroups of finite fields.
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.