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IEEE Communications Letters

Eliminating small stopping sets in irregular low-density parity-check codes

Xiaopeng Jiao, Jianjun Mu, Jing Song, Lihua Zhou

Published Jun 1, 2009• 23 citations
Publisher

Abstract

We present a novel scheme to eliminate small stopping sets in irregular low-density parity-check (LDPC) codes. By adding several new check nodes and having their edges connected to small stopping sets in the original code, the improved code decreases the number of small stopping sets efficiently. Simulation results show that the proposed scheme decreases the frame error rate (FER) significantly in the error floor region, whereas having almost the same rate as the original code.

DOI
10.1109/lcomm.2009.090009

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We present a novel scheme to eliminate small stopping sets in irregular low-density parity-check (LDPC) codes. By adding several new check nodes and having their edges connected to small stopping sets in the original code, the improved code decreases the number of small stopping sets efficiently. Simulation results show that the proposed scheme decreases the frame error rate (FER) significantly in the error floor region, whereas having almost the same rate as the original code.
Abstract: Small stopping sets have been proved to be harmful to the error floor performance of a finite-length irregular low-density parity-check (LDPC) code over the binary erasure channel (BEC). On the additive white gaussian noise (AWGN) channel, small stopping sets are expected to have a similar effect. This paper proposes an algorithm that iteratively removes the small-stopping-set-inducing patterns from the graph of a randomly generated irregular LDPC code by means of node exchange, aiming at enlarging the average size of stopping sets in this code. Computer simulation results show that the short-length LDPC codes after our processing achieve a considerable performance improvement in the low-BER region compared to the randomly generated codes. Key words: Error floor, irregular LDPC codes, iterative processing, small stopping set 1
Trapping sets have been identified as one of the main factors causing error floors of low-density parity-check (LDPC) codes at high SNR values. By adding several new rows to the original parity-check matrix, a novel method is proposed to eliminate small trapping sets in the LDPC code's Tanner graph. Based on this parity-check matrix extension, we design new codes with low error floors from the original irregular LDPC codes. Simulation results show that the proposed method can lower the error floors of irregular LDPC codes significantly at high SNR values over AWGN channels.
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.
This paper proposes a novel scheme for bit recovery of Low-Density Parity-Check (LDPC) Codes. Firstly, the most erroneous and the most reliable bits are located by searching the codeword bits. Subsequently, new check nodes are added to connect them, thus the negative effects of the most erroneous bits along with the corresponding trapping sets are avoided. Eventually, the BER performance is dramatically improved in the error-floor region according to the simulated results. This idea could be a more concise and simple alternative to weaken the effects of trapping sets in LDPC applications.
We present a construction algorithm for short block length irregular low-density parity-check (LDPC) codes. Based on a novel interpretation of stopping sets in terms of the parity-check matrix, we present an approximate trellis-based search algorithm that detects many stopping sets. Growing the parity check matrix by a combination of random generation and the trellis-based search, we obtain codes that possess error floors orders of magnitude below randomly constructed codes and significantly better than other comparable constructions.