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Computer Science > Information Theory

arXiv:1102.4612 (cs)
[Submitted on 22 Feb 2011 (v1), last revised 25 Jan 2013 (this version, v3)]

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

Authors:Kenta Kasai, Kohichi Sakaniwa
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Abstract: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.
Comments: Corrected typos in degree distributions νand μof MN and HA codes
Subjects: Information Theory (cs.IT)
Cite as: arXiv:1102.4612 [cs.IT]
  (or arXiv:1102.4612v3 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1102.4612
Related DOI: https://doi.org/10.1587/transfun.E94.A.2161

Submission history

From: Kenta Kasai [view email]
[v1] Tue, 22 Feb 2011 20:57:08 UTC (249 KB)
[v2] Thu, 7 Jul 2011 17:31:13 UTC (200 KB)
[v3] Fri, 25 Jan 2013 10:36:46 UTC (200 KB)
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