Analysis of Decoding Error Probability of Spatially “Mt. Fuji” Coupled LDPC Codes in Waterfall Region of the BEC

Yuta NAKAHARA  Toshiyasu MATSUSHIMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.12   pp.1337-1346
Publication Date: 2020/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020TAP0010
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
Keyword: 
spatially coupled codes,  expected graph evolution,  covariance evolution,  finite-length code performance,  

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Summary: 
A spatially “Mt. Fuji” coupled (SFC) low-density parity-check (LDPC) ensemble is a modified version of the spatially coupled (SC) LDPC ensemble. Its decoding error probability in the waterfall region has been studied only in an experimental manner. In this paper, we theoretically analyze it over the binary erasure channel by modifying the expected graph evolution (EGE) and covariance evolution (CE) that have been used to analyze the original SC-LDPC ensemble. In particular, we derive the initial condition modified for the SFC-LDPC ensemble. Then, unlike the SC-LDPC ensemble, the SFC-LDPC ensemble has a local minimum on the solution of the EGE and CE. Considering the property of it, we theoretically expect the waterfall curve of the SFC-LDPC ensemble is steeper than that of the SC-LDPC ensemble. In addition, we also confirm it by numerical experiments.