Spatially “Mt. Fuji” Coupled LDPC Codes

Yuta NAKAHARA; Shota SAITO; Toshiyasu MATSUSHIMA

doi:10.1587/transfun.E100.A.2594

Spatially “Mt. Fuji” Coupled LDPC Codes

Yuta NAKAHARA, Shota SAITO, Toshiyasu MATSUSHIMA

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A new type of spatially coupled low density parity check (SCLDPC) code is proposed. This code has two benefits. (1) This code requires less number of iterations to correct the erasures occurring through the binary erasure channel in the waterfall region than that of the usual SCLDPC code. (2) This code has lower error floor than that of the usual SCLDPC code. Proposed code is constructed as a coupled chain of the underlying LDPC codes whose code lengths exponentially increase as the position where the codes exist is close to the middle of the chain. We call our code spatially “Mt. Fuji” coupled LDPC (SFCLDPC) code because the shape of the graph representing the code lengths of underlying LDPC codes at each position looks like Mt. Fuji. By this structure, when the proposed SFCLDPC code and the original SCLDPC code are constructed with the same code rate and the same code length, L (the number of the underlying LDPC codes) of the proposed SFCLDPC code becomes smaller and M (the code lengths of the underlying LDPC codes) of the proposed SFCLDPC code becomes larger than those of the SCLDPC code. These properties of L and M enables the above reduction of the number of iterations and the bit error rate in the error floor region, which are confirmed by the density evolution and computer simulations.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.12 pp.2594-2606

Publication Date: 2017/12/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2594

Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Coding Theory and Techniques

Authors

Yuta NAKAHARA
  Waseda University
Shota SAITO
  Waseda University
Toshiyasu MATSUSHIMA
  Waseda University

Keyword

density evolution, LDPC codes, spatially coupled codes

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Yuta NAKAHARA, Shota SAITO, Toshiyasu MATSUSHIMA, "Spatially “Mt. Fuji” Coupled LDPC Codes" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 12, pp. 2594-2606, December 2017, doi: 10.1587/transfun.E100.A.2594.
Abstract: A new type of spatially coupled low density parity check (SCLDPC) code is proposed. This code has two benefits. (1) This code requires less number of iterations to correct the erasures occurring through the binary erasure channel in the waterfall region than that of the usual SCLDPC code. (2) This code has lower error floor than that of the usual SCLDPC code. Proposed code is constructed as a coupled chain of the underlying LDPC codes whose code lengths exponentially increase as the position where the codes exist is close to the middle of the chain. We call our code spatially “Mt. Fuji” coupled LDPC (SFCLDPC) code because the shape of the graph representing the code lengths of underlying LDPC codes at each position looks like Mt. Fuji. By this structure, when the proposed SFCLDPC code and the original SCLDPC code are constructed with the same code rate and the same code length, L (the number of the underlying LDPC codes) of the proposed SFCLDPC code becomes smaller and M (the code lengths of the underlying LDPC codes) of the proposed SFCLDPC code becomes larger than those of the SCLDPC code. These properties of L and M enables the above reduction of the number of iterations and the bit error rate in the error floor region, which are confirmed by the density evolution and computer simulations.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2594/_p

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@ARTICLE{e100-a_12_2594,
author={Yuta NAKAHARA, Shota SAITO, Toshiyasu MATSUSHIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Spatially “Mt. Fuji” Coupled LDPC Codes},
year={2017},
volume={E100-A},
number={12},
pages={2594-2606},
abstract={A new type of spatially coupled low density parity check (SCLDPC) code is proposed. This code has two benefits. (1) This code requires less number of iterations to correct the erasures occurring through the binary erasure channel in the waterfall region than that of the usual SCLDPC code. (2) This code has lower error floor than that of the usual SCLDPC code. Proposed code is constructed as a coupled chain of the underlying LDPC codes whose code lengths exponentially increase as the position where the codes exist is close to the middle of the chain. We call our code spatially “Mt. Fuji” coupled LDPC (SFCLDPC) code because the shape of the graph representing the code lengths of underlying LDPC codes at each position looks like Mt. Fuji. By this structure, when the proposed SFCLDPC code and the original SCLDPC code are constructed with the same code rate and the same code length, L (the number of the underlying LDPC codes) of the proposed SFCLDPC code becomes smaller and M (the code lengths of the underlying LDPC codes) of the proposed SFCLDPC code becomes larger than those of the SCLDPC code. These properties of L and M enables the above reduction of the number of iterations and the bit error rate in the error floor region, which are confirmed by the density evolution and computer simulations.},
keywords={},
doi={10.1587/transfun.E100.A.2594},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - Spatially “Mt. Fuji” Coupled LDPC Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2594
EP - 2606
AU - Yuta NAKAHARA
AU - Shota SAITO
AU - Toshiyasu MATSUSHIMA
PY - 2017
DO - 10.1587/transfun.E100.A.2594
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2017
AB - A new type of spatially coupled low density parity check (SCLDPC) code is proposed. This code has two benefits. (1) This code requires less number of iterations to correct the erasures occurring through the binary erasure channel in the waterfall region than that of the usual SCLDPC code. (2) This code has lower error floor than that of the usual SCLDPC code. Proposed code is constructed as a coupled chain of the underlying LDPC codes whose code lengths exponentially increase as the position where the codes exist is close to the middle of the chain. We call our code spatially “Mt. Fuji” coupled LDPC (SFCLDPC) code because the shape of the graph representing the code lengths of underlying LDPC codes at each position looks like Mt. Fuji. By this structure, when the proposed SFCLDPC code and the original SCLDPC code are constructed with the same code rate and the same code length, L (the number of the underlying LDPC codes) of the proposed SFCLDPC code becomes smaller and M (the code lengths of the underlying LDPC codes) of the proposed SFCLDPC code becomes larger than those of the SCLDPC code. These properties of L and M enables the above reduction of the number of iterations and the bit error rate in the error floor region, which are confirmed by the density evolution and computer simulations.
ER -