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IEEE International Symposium on Parallel and Distributed Processing with Applications (ISPA)

Extended PEG Algorithm for High Rate LDPC Codes

Zhiheng Zhou, Xiangxue Li, Dong Zheng, Kefei Chen, Jianhua Li

Published Jan 1, 2009• 5 citations
Publisher

Abstract

Progressive Edge-Growth(PEG) Algorithm is a good candidate to generate Tanner Graphs with a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner. In this paper, we propose an extended PEG algorithm for constructing Low-Density Parity-Check (LDPC) codes with very high rate when given a lower bound of girth. Simulation results show the bit error rates of constructed LDPC codes with very high rate or large girth.

DOI
10.1109/ispa.2009.80

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Progressive Edge-Growth(PEG) Algorithm is a good candidate to generate Tanner Graphs with a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner. In this paper, we propose an extended PEG algorithm for constructing Low-Density Parity-Check (LDPC) codes with very high rate when given a lower bound of girth. Simulation results show the bit error rates of constructed LDPC codes with very high rate or large girth.
We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.
We propose a general method for constructing Tanner (1981) graphs with large girth by progressively establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) construction. Lower bounds on the girth and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms or parameters of the graphs. Encoding of LDPC codes based on the PEG principle is also investigated. We show how to exploit the PEG graph construction to obtain LDPC codes that allow linear time encoding. The advantages of PEG Tanner graphs over randomly constructed graphs are demonstrated by extensive simulation results on code performance.
We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progres- sive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.
The progressive-edge-growth (PEG) algorithm for constructing Tanner graphs with large girth by progressively establishing edges/connections between symbol nodes and check nodes in an edge-by-edge way is highly known to construct low-density parity-check (LDPC) codes at short block lengths for achieving good performance. This paper proposed an improved PEG construction for irregular codes, which heuristically selects good codes from random graphs for short block lengths. The simulation results are given to demonstrate that the proposed algorithm gians better BER performance for high signal-to-noise (SNR) ratios without performance loss for low-SNR region, i.e. low error floor.
The progressive edge-growth (PEG) algorithm is known to construct low-density parity-check (LDPC) codes at finite code lengths with large girths by establishing edges between symbol and check nodes in an edge-by-edge manner. The linear-encoding PEG (LPEG) algorithm, a simple variation of the PEG algorithm, can be applied to generate linear time encodable LDPC codes whose m parity bits p1, p2, ..., p m are computed recursively in m steps. In this article, we propose modifications of the LPEG algorithm to construct LDPC codes whose number of encoding steps is independent of the code length. The maximum degree of the symbol nodes in the Tanner graph is denoted by ; The m parity bits of the proposed LDPC codes are divided into subgroups and can be computed in only steps. Since , the number of encoding steps can be significantly reduced. It has also been proved that the PEG codes and the codes proposed in this article have similar lower bound on girth. Simulation results showed that the proposed codes perform very well over the AWGN channel with an iterative decoding.
Progressive edge-growth (PEG) algorithm construction builds the Tanner graph for an LDPC code by establishing edges between the symbol nodes and the check nodes in an edge-by-edge manner and maximizing the local girth in a greedy fashion. This approach is simple but the computational complexity of the PEG algorithm scale as O(nm), where n is the number of symbol nodes and m is the number of check nodes. We deal with this problem by first construct a base LDPC code of length n1with the PEG algorithm and then extend this LDPC code into an LDPC code of length n, where n ≥ n1, via the the chinese remainder theorem (CRT). This method increase the code length of an LDPC code generated with the PEG algorithm, without decreasing its girth. Due to the code length reducing in the PEG construction step, the computational complexity of the whole code construction process is reduced. Furthermore, the proposed algorithm have a potential advantage by storing a small parity-check matrix of a base code and extending it “on-the-fly” in hardware.