Spatially Coupled LDPC Codes Affected by a Single Random Burst of Erasures

TL;DR

This paper investigates the decoding performance of spatially coupled LDPC codes over binary memoryless channels affected by a single burst of erasures, identifying the maximum burst length for successful decoding and analyzing the error floor.

Contribution

It introduces an analysis of BP decoding for SC-LDPC codes under burst erasures, revealing the maximum recoverable burst length and comparing performance over different channel types.

Findings

Maximum recoverable burst length is similar for BEC and BAWGN channels with same capacity.

Successful decoding is possible if burst length is below a certain threshold.

Finite-length analysis estimates the decoding failure probability (error floor).

Abstract

Spatially-Coupled LDPC (SC-LDPC) ensembles achieve the capacity of binary memoryless channels (BMS), asymptotically, under belief-propagation (BP) decoding. In this paper, we study the BP decoding of these code ensembles over a BMS channel and in the presence of a single random burst of erasures. We show that in the limit of code length, codewords can be recovered successfully if the length of the burst is smaller than some maximum recoverable burst length. We observe that the maximum recoverable burst length is practically the same if the transmission takes place over binary erasure channel or over binary additive white Gaussian channel with the same capacity. Analyzing the stopping sets, we also estimate the decoding failure probability (the error floor) when the code length is finite.