Analysis of Decoding Error Probability of Spatially “Mt. Fuji” Coupled LDPC Codes in Waterfall Region of the BEC
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.12 pp.1337-1346
- Publication Date
- 2020/12/01
- Publicized
- 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
Authors
Yuta NAKAHARA
Waseda University
Toshiyasu MATSUSHIMA
Waseda University
Keyword
Latest Issue
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Yuta NAKAHARA, Toshiyasu MATSUSHIMA, "Analysis of Decoding Error Probability of Spatially “Mt. Fuji” Coupled LDPC Codes in Waterfall Region of the BEC" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 12, pp. 1337-1346, December 2020, doi: 10.1587/transfun.2020TAP0010.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020TAP0010/_p
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@ARTICLE{e103-a_12_1337,
author={Yuta NAKAHARA, Toshiyasu MATSUSHIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Analysis of Decoding Error Probability of Spatially “Mt. Fuji” Coupled LDPC Codes in Waterfall Region of the BEC},
year={2020},
volume={E103-A},
number={12},
pages={1337-1346},
abstract={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.},
keywords={},
doi={10.1587/transfun.2020TAP0010},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Analysis of Decoding Error Probability of Spatially “Mt. Fuji” Coupled LDPC Codes in Waterfall Region of the BEC
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1337
EP - 1346
AU - Yuta NAKAHARA
AU - Toshiyasu MATSUSHIMA
PY - 2020
DO - 10.1587/transfun.2020TAP0010
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2020
AB - 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.
ER -
English
