Analysis of decoding error probability of spatially "Mt. Fuji" coupled LDPC codes inwaterfall region of the BEC

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Abstract

A spatially "Mt. Fuji"coupled (SFC) low-density paritycheck (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.

Original languageEnglish
Pages (from-to)1337-1346
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE103A
Issue number12
DOIs
Publication statusPublished - 2020 Dec

Keywords

  • Covariance evolution
  • Expected graph evolution
  • Finite-length code performance
  • Spatially coupled codes

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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