On the Burst Erasure Capability of Spatially Coupled LDPC Ensembles

Spatially-Coupled LDPC (SC-LDPC) ensembles achieve the capacity of binary memoryless channels, asymptotically, under belief-propagation decoding. In this work, we are interested in the finite-length performance of these ensembles on binary channels with memory. We study the average performance of random regular SC-LDPC ensembles on the single block erasure channel and provide tight approximations for the block erasure probability. Further, we show the effect of expurgation by analyzing the minimal stopping sets. Finally, we show how the proposed analysis tools can be used to construct an ensemble that can always completely recover from a burst affecting a spatial position.