Spatial coupling for distributed storage and diversity applications

Abstract

Low-density parity-check codes are considered for erasure channels, mainly Root-LDPC codes that include a special type of checknodes. Spatial coupling is applied on parity bits of a Root-LDPC ensemble designed for a channel with 4 block-erasure states and a maximal design rate of 3/4 attaining double diversity. The advantage of spatial coupling is shown in the erasure plane as an improvement of a threshold boundary, under independent erasures. The spatial coupling maintains the double diversity because it connects parity bits only. The drawback of this partial coupling is a weak saturation of the threshold boundary towards the capacity boundary.