Spatially Coupled LDPC Ensembles on Burst Erasure Channels

Spatially-Coupled LDPC (SC-LDPC) ensembles have gained significant interest since they were shown to universally achieve the capacity of binary memoryless channels under low-complexity belief-propagation decoding. In this work, we focus on the performance of these ensembles over binary erasure channels affected additionally by bursts. We assume that the burst can erase either a complete spatial position, modeling node failures in distributed storage, or can span across multiple spatial positions. We study the expected performance of random regular SC-LDPC ensembles on single-burst-erasure channels and provide tight lower bounds for the block erasure probability (PB) at finite block length and bounds on the coupling parameter for being asymptotically able to recover the burst. Subsequently, we show the effect of introducing additional random erasures to these channels. Finally, we show that expurgation can bring substantial improvements in the block error rate by analyzing the minimal stopping sets of some expurgated code ensembles. Our study shows that for a fixed asymptotic code rate, the combination of increasing the variable node degree and expurgating the ensemble can improve the block error probability by several orders of magnitude. All the results are verified using Monte-Carlo simulations.