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IEEE International Symposium on Information Theory (ISIT)

Quasi-Cyclic LDPC Codes for Correcting Multiple Phased Bursts of Erasures

Xin Wei Xiao, Bane V. Vasic, Shu Lin, Khaled Abdel-Ghaffar, W.E. Ryan

Published Jul 1, 2019• 5 citations
Publisher

Abstract

This paper presents designs and constructions of two classes of binary quasi-cyclic LDPC codes for correcting multiple random phased-bursts of erasures over the binary erasure channel. The erasure correction of codes in both classes is characterized by the cycle and adjacency structure of their Tanner graphs. Erasure correction of these codes is a very simple process which requires only modulo-2 additions. The codes in the second class are capable of correcting locally and globally distributed phased-bursts of erasures with a two-phase iterative erasure-correction process.

DOI
10.1109/isit.2019.8849853

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This paper presents designs and constructions of two classes of binary quasi-cyclic LDPC codes for correcting multiple random phased-bursts of erasures over the binary erasure channel. The erasure correction of codes in both classes is characterized by the cycle and adjacency structure of their Tanner graphs. Erasure correction of these codes is a very simple process which requires only modulo-2 additions. The codes in the second class are capable of correcting locally and globally distributed phased-bursts of erasures with a two-phase iterative erasure-correction process.
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The performance of iterative decoding of low density parity check (LDPC) codes over binary erasure channels can be completely characterized by the study of stopping sets. Therefore, the burst erasure correction capability of a given LDPC code can be readily quantified by searching for stopping sets within consecutive bit nodes. In this work we study the optimal permutation of the bit nodes that will result in the maximum possible burst erasure correction capability for a given LDPC code. Noting that this is essentially a combinatorial optimization problem that is highly likely to be NP-hard, we adopt a simulated annealing based approach for finding the optimal permutation. We present bounds based on stopping sets that limit the burst erasure correction capability. As part of our results, we provide interleavers that greatly improve the burst erasure correction capability of protograph quasi-cyclic LDPC codes used in the WiMax standard.