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IEEE Transactions on Information Theory

Regular and irregular progressive edge-growth tanner graphs

Xiao-Yu Hu, Evangelos S. Eleftheriou, Donald M. Arnold

Published Jan 1, 2005• 1,489 citations
Publisher

Abstract

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.

DOI
10.1109/tit.2004.839541

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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 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.
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.
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.
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.