Band Splitting Permutations for Spatially Coupled LDPC Codes Achieving Asymptotically Optimal Burst Erasure Immunity

Hiroki MORI  Tadashi WADAYAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.2   pp.663-669
Publication Date: 2017/02/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Coding Theory
spatially coupled LDPC codes,  burst erasure,  stopping sets,  belief propagation,  

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It is well known that spatially coupled (SC) codes with erasure-BP decoding have powerful error correcting capability over memoryless erasure channels. However, the decoding performance of SC-codes significantly degrades when they are used over burst erasure channels. In this paper, we propose band splitting permutations (BSP) suitable for (l,r,L) SC-codes. The BSP splits a diagonal band in a base matrix into multiple bands in order to enhance the span of the stopping sets in the base matrix. As theoretical performance guarantees, lower and upper bounds on the maximal burst correctable length of the permuted (l,r,L) SC-codes are presented. Those bounds indicate that the maximal correctable burst ratio of the permuted SC-codes is given by λmax≃1/k where k=r/l. This implies the asymptotic optimality of the permuted SC-codes in terms of burst erasure correction.