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IEEE Conference on Cybernetics and Intelligent Systems

A novel algorithm of constructing LDPC codes with graph theory

Yan Cui, Xinhui Si, Yanan Shen

Published Sep 1, 2008• 2 citations
Publisher

Abstract

There are many algorithms to construct good low-density parity-check (LDPC) code, the most typical algorithms are bit-filling algorithm, randomly construction algorithm, and PEG (progressive edge growth) algorithm. As shown in [1], the error floor of LDPC Code is decreased by using PEG algorithm, but the error correction performance in waterfall region is compromised since a stopping set with small size will form the codeword with small Hamming weight over AWGN [2]. In this paper, we propose a novel algorithm to construct LDPC Codes. In our algorithm, we construct LDPC Code to avoid small girth and small stopping set by detecting the complete associated matrix of check node (defined in this paper) that converted from bipartite graph of LDPC Code based on the graph theory. Simulation shows that the LDPC code constructed by our algorithm has lower error floor than randomly constructed LDPC Code. The performance improvement of our algorithm is 0.1dB at BER of 10-3compared with PEG algorithm.

DOI
10.1109/iccis.2008.4670752

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There are many algorithms to construct good low-density parity-check (LDPC) code, the most typical algorithms are bit-filling algorithm, randomly construction algorithm, and PEG (progressive edge growth) algorithm. As shown in [1], the error floor of LDPC Code is decreased by using PEG algorithm, but the error correction performance in waterfall region is compromised since a stopping set with small size will form the codeword with small Hamming weight over AWGN [2]. In this paper, we propose a novel algorithm to construct LDPC Codes. In our algorithm, we construct LDPC Code to avoid small girth and small stopping set by detecting the complete associated matrix of check node (defined in this paper) that converted from bipartite graph of LDPC Code based on the graph theory. Simulation shows that the LDPC code constructed by our algorithm has lower error floor than randomly constructed LDPC Code. The performance improvement of our algorithm is 0.1dB at BER of 10-3compared with PEG algorithm.
There exist many different algorithms to construct good low-density parity-check (LDPC) codes. To maximize the girth of the bipartite graph, which represents the LDPC code, the progressive edge-growth (PEG) algorithm was introduced. This construction methods leads for irregular LDPC codes to a lower error floor, but also to a performance loss in the waterfall region compared with randomly constructed LDPC codes. In this paper, we describe a modification of the PEG algorithm that improves the performance in the waterfall region. Furthermore, this modified PEG algorithm yields codes with lower error floors and a slightly better performance in the waterfall region than randomly constructed 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 was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.
In this paper, we present a construction method based on the progressive edge-growth (PEG) algorithm to design irregular low-density parity-check (LDPC) codes without small stopping sets. We show how to choose the connections in the PEG algorithm when having multiple choices to connect a variable node with a check node. Since preventing small stopping sets also prevents a low minimum distance, our construction method also leads to LDPC codes with a higher minimum distance. Furthermore, we show by simulation that our construction method improves the performance over the binary erasure channel and over the additive white Gaussian noise channel for a low erasure probability and a high signal-to-noise ratio, respectively.
In this paper, a method for constructing Low-Density Parity-Check (LDPC) codes of good performance in terms of Bit Error Rate (BER) using a computer search algorithm is presented. First, LDPC codes and encoding along with its Tanner graph representation is described. Then, a detailed description of the proposed construction algorithm is given. A Modified Shortest-Path (MSP) Algorithm of lower complexity is applied to obtain a code graph of the desired structure. The proposed algorithm works directly on the parity-check matrix of the LDPC code. The parity-check matrix of the code is constructed column by column subject to the bit-degree and girth constraints. Using the proposed algorithm, both regular and irregular LDPC codes have been constructed. Furthermore, not only have the girth been improved but also the rate of LDPC codes. Finally, by simulation results the constructed codes were shown to perform well over an additive white Gaussian noise (AWGN) channel.