Spatially Coupled Low-Density Parity-Check Codes on Two-Dimensional Array Erasure Channel

Gou HOSOYA  Hiroyuki YASHIMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2008-2017
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2008
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding theory and techniques
Keyword: 
spatially coupled LDPC code,  low-density parity-check code,  storage device,  density evolution,  

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Summary: 
In this study, spatially coupled low-density parity-check (SC-LDPC) codes on the two-dimensional array erasure (2DAE) channel are devised, including a method for generating new SC-LDPC codes with a restriction on the check node constraint. A density evolution analysis confirms the improvement in the threshold of the proposed two-dimensional SC-LDPC code ensembles over the one-dimensional SC-LDPC code ensembles. We show that the BP threshold of the proposed codes can approach the corresponding maximum a posteriori (MAP) threshold of the original residual graph on the 2DAE channel. Moreover, we show that the rates of the residual graph of the two-dimensional LDPC block code ensemble are smaller than those of the one-dimensional LDPC block code ensemble. In other words, a high performance can be obtained by choosing the two-dimensional SC-LDPC codes.