Spatially-Coupled MacKay-Neal codes and Hsu-Anastasopoulos codes

Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the capacity-achieving spatially coupled LDPC codes is that one needs to increase the column and row weight of parity-check matrices of the underlying LDPC codes. It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes achieve the capacity of memoryless binary-input symmetric-output channels under MAP decoding with bounded column and row weight of the parity-check matrices. The HA codes and the MN codes are dual each other. In this paper, we study spatial coupling of MN codes and HA codes. The BP thresholds of the MN and HA codes are 0. While the MAP thresholds reach the Shannon limit. We observe "threshold saturation" such that the BP thresholds of the coupled MN and HA codes approach the Shannon limit of the BEC.