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IEEE International Symposium on Information Theory (ISIT)

Irregular progressive edge-growth (PEG) Tanner graphs

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

Published Jun 25, 2003• 41 citations
Publisher

Abstract

A general method for constructing Tanner graphs having a large girth by progressively establishing edges between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) construction, is proposed. Such an approach is powerful for generating good regular and irregular LDPC codes of short and moderate block lengths.

DOI
10.1109/isit.2002.1023752

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A general method for constructing Tanner graphs having a large girth by progressively establishing edges between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) construction, is proposed. Such an approach is powerful for generating good regular and irregular LDPC codes of short and moderate block lengths.
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 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.
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.