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

Kenta KASAI  Kohichi SAKANIWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.11   pp.2161-2168
Publication Date: 2011/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.2161
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
spatial coupling,  LDPC code,  iterative decoding,  

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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 codes each other. The aim of this paper is to present an empirical evidence that spatially-coupled MN (resp. HA) codes with bounded column and row weight achieve the capacity of the BEC. To this end, we introduce a spatial coupling scheme of MN (resp. HA) codes. By density evolution analysis, we will show that the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close to the Shannon limit.