Study of doubly-generalized low-density parity-check codes

Pao Yue-kong Library Electronic Theses Database

Study of doubly-generalized low-density parity-check codes

 

Author: Min, Yue
Title: Study of doubly-generalized low-density parity-check codes
Degree: M.Phil.
Year: 2013
Subject: Coding theory -- Mathematics.
Error-correcting codes (Information theory)
Hong Kong Polytechnic University -- Dissertations
Department: Dept. of Electronic and Information Engineering
Pages: xix, 125 p. : ill. ; 30 cm.
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b2681799
URI: http://theses.lib.polyu.edu.hk/handle/200/7363
Abstract: Low-density parity-check (LDPC) codes were proposed in the 1960{174}s but were left un-noticed. In the mid-1990's, David Mackay re-discovered the codes. The LDPC codes have since become very well-known because of their superior error-correction performance when decoded by the belief propagation (BP) algorithm. The original LDPC codes use repetition codes at the variable nodes and single-parity-check (SPC) codes at the check nodes. By introducing more powerful component codes into the LDPC codes, doubly-generalized low-density parity-check (DGLDPC) codes are formed. Due to their better cycle properties, DGLDPC codes can outperform the traditional LDPC codes in terms of error performance. However, when the more complex component codes are introduced, decoders with higher computational complexity are required. Additionally, the techniques used to optimize LDPC codes, such as Density Evolution (DE) and Extrinsic Information Transfer (EXIT) chart, become much more complex when applied to optimize DGLDPC codes. This research aims to design DGLDPC codes that require relatively low decoding complexity. The other aim of this thesis is to derive closed-form EXIT functions for the proposed DGLDPC codes such that optimization of their degree distributions can be made simple. One factor that determines the overall error-correction capability of a DGLDPC code is the minimum distance. It has been shown that the minimum distance increases exponentially with the girth (minimum cycle length) of the code's corresponding adjacency matrix. Further, component codes having a larger minimum distance lead to an increase of the base of the exponent. In this thesis, we propose using single-parity-check product-codes (SPC-PCs) in the super-check nodes (SCNs) of DGLDPC codes. The reason is that SPC-PCs have excellent distance properties their minimum distance increases exponentially with the number of dimensions. We also proposing using a turbo local decoder at the super-check nodes during the decoding process. The aim is to reduce the computation complexity. We further apply SPCs at the super-variable nodes (SVNs) of the DGLDPC code such that the overall code rate can be improved. Simulation results show that the proposed codes achieve very good error performance with relatively low decoder complexity and fast convergence rates. When all SCNs use the same SPC-PC and all SVNs use the same SPC, properties of the DGLDPC code such as the rate and the threshold are fixed once the constituent codes are selected. To provide flexibility in designing the codes, we study another class of DGLDPC codes, in which the SCNs consist of SPC-PCs and SPCs while the SVNs consist of SPCs and repetition codes. We then derive the closed-form EXIT functions for the new DGLDPC codes over the binary erasure channel (BEC) and the binary-input additive-white-Gaussian-noise (BI-AWGN) channel. With the closed-form functions, we vary the degree distributions of the SVNs and SCNs of the new DGLDPC codes so as to optimize the decoding threshold. Simulation results show that the new DGLDPC codes, after optimization, possess very good thresholds.

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