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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 1-2/2019

08-02-2018 | Original Research

Effect of one redundant parity-check equation on the stopping distance

Authors: Zahra Ferdosi, Farhad Rahmati, Mohammad H. Tadayon

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2019

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Abstract

In this paper, we attempt to correct remaining erasures in the case of an iterative decoding failure. Stopping set plays the most important role in the code’s performance over binary erasure channel (BEC) under iterative decoding. The elimination of the stopping sets is one of the techniques that can be applied on the parity-check matrix of the codes for improving their performance in the low BER region. Although the problem is well-studied and many solutions are already known, a new low-complexity algorithm would be an important contribution. We present a modified decoding algorithm for array LDPC codes C(m, q) over BEC with the column weight m and row weight q where \(m<q\). Our proposed technique provides a step towards improving the decoding results and is compatible with practical implementation constraints. Our results substantiate theoretical analysis for array LDPC codes.
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Footnotes
1
The problem of creating a list of possible stopping sets can be related to the coloring problems in graph theory. Vasić et al. [14] proposed the trapping set ontology, which is a hierarchy of trapping sets that exploits the topological relations, and can he utilized for code construction or decoder design. As known in [15], a stopping set is legitimately a trapping set when the underlying channel model is the BEC and the belief propagation decoder is employed.
 
2
Every non-zero rows in the sub-matrix corresponding to a stopping set of size t is known as an unsatisfied row if the associated equation is not satisfied during the iterative decoding process.
 
3
Without loss of generality we start with the first erasure, however, it is possible to start with any arbitrary erased bit.
 
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Metadata
Title
Effect of one redundant parity-check equation on the stopping distance
Authors
Zahra Ferdosi
Farhad Rahmati
Mohammad H. Tadayon
Publication date
08-02-2018
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2019
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-018-1170-3

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