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IEEE International Conference on Communication Systems (ICCS)

Compressing construction of QC-LDPC codes

Shuqi Sun, Wuyang Zhou

Published Nov 1, 2008• 0 citations
Publisher

Abstract

Two compressing construction methods of Quasi-Cyclic LDPC (QC-LDPC) codes are proposed, which can be called recursive-compressing and single-compressing respectively. Selecting a good QC-LDPC code as the Mother, the son codes constructed through the compressing methods are still good codes, i.e., have high girth and few short cycles, moreover, they have continuous code length and require smaller memory space. Analysis and simulation results show they can perform well over the AWGN channel.

DOI
10.1109/iccs.2008.4737397

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Two compressing construction methods of Quasi-Cyclic LDPC (QC-LDPC) codes are proposed, which can be called recursive-compressing and single-compressing respectively. Selecting a good QC-LDPC code as the Mother, the son codes constructed through the compressing methods are still good codes, i.e., have high girth and few short cycles, moreover, they have continuous code length and require smaller memory space. Analysis and simulation results show they can perform well over the AWGN channel.
A compressing method for the construction of quasi-cyclic LDPC(QC-LDPC)codes was proposed,which used a QC-LDPC code with large girth as mother code.By compressing circulant permutation matrices of the mother code,shorter QC-LDPC codes would be generated.After optimization,the generated codes would have large girth and few cycles,whose lengths varied continuously in a large range.Analysis and simulation results show that these LDPC codes have good performance and can greatly reduce the size of code storage.
In this paper, we present two simple methods to construct a quasi-cyclic LDPC (QC-LDPC) code of larger length by lifting a given QC-LDPC code. We show that its girth is always larger than or equal to that of the given QC-LDPC code. Applying the methods recursively, it is possible to construct a sequence of QC-LDPC codes generated from a single exponent matrix by proper floor or modulo operations. Simulation results show that they have no serious performance degradation, as compared with randomly constructed LDPC codes
In this paper, we analyze some cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes and show that the girth of a QC-LDPC code is upper bounded by a certain number introduced by the structure of its mother matrix. We also propose a simple method to extend QC-LDPC codes of large length by lifting QC-LDPC codes of smaller length. In particular, it is possible to generate them from a single exponent matrix by a proper modulo-operation. Simulation results show that the more we apply the lifting to QC-LDPC codes, the more memory efficiency becomes better, but it may induce a little performance degradation
In this paper, we proposed a novel method for constructing quasi-cyclic low-density parity-check (QC LDPC) codes based on cyclic subgroup over GF(q) . LDPC codes constructed by this method are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN) with sum product algorithm (SPA). 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. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.
Designs and constructions of quasi-cyclic (QC) LDPC codes for the AWGN channel are presented. The codes are constructed based on the conventional parity-check matrices of Reed-Solomon (RS) codes and are referred to as RS-QC-LDPC codes. Several classes of RS-QC-LDPC codes are given. Cycle structural properties of the Tanner graphs of codes in these classes are analyzed and specific methods for constructing codes with girth at least eight and reducing their short cycles are presented. The designed codes perform well in both waterfall and low error-rate regions.
In this paper, we present an improved method for obtaining quasi-cyclic low-density parity-check (QC-LDPC) codes of larger length by combining some component QC-LDPC codes of smaller length.Large girth can be obtained by carefully designing one large girth component code of smaller length.The other component codes are properly designed to obtain a lot of QC-LDPC codes with much few short cycles.Simulations show that compared with CRT based QC-LDPC codes and PEG based QC-LDPC codes, the proposed QC-LDPC codes have much less short cycles and better performance.