TY - JOUR

T1 - Spatially "Mt. Fuji" Coupled LDPC codes

AU - Nakahara, Yuta

AU - Saito, Shota

AU - Matsushima, Toshiyasu

N1 - Funding Information:
We are very grateful to the anonymous reviewers for helpful comments. We would like to express deep appreciation to everyone of Matsushima Laboratory. This work was supported by JSPS KAKENHI Grant Numbers 16K00195, 16K00417, and 17K06446.
Publisher Copyright:
Copyright © 2017 The Institute of Electronics, Information and Communication Engineers.

PY - 2017/12

Y1 - 2017/12

N2 - 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.

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.

KW - Density evolution

KW - LDPC codes

KW - Spatially coupled codes

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U2 - 10.1587/transfun.E100.A.2594

DO - 10.1587/transfun.E100.A.2594

M3 - Article

AN - SCOPUS:85038209366

SN - 0916-8508

VL - E100A

SP - 2594

EP - 2606

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

IS - 12

ER -