Analysis of Error Floors for Non-binary LDPC Codes over General Linear Group through <I>q</I>-Ary Memoryless Symmetric Channels

Takayuki NOZAKI; Kenta KASAI; Kohichi SAKANIWA

doi:10.1587/transfun.E95.A.2113

Analysis of Error Floors for Non-binary LDPC Codes over General Linear Group through q-Ary Memoryless Symmetric Channels

Takayuki NOZAKI, Kenta KASAI, Kohichi SAKANIWA

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In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over general linear groups with those for non-binary LDPC codes over finite fields transmitted through the q-ary memoryless symmetric channels under belief propagation decoding. To analyze non-binary LDPC codes defined over both the general linear group GL(m, F₂) and the finite field F_2^m, we investigate non-binary LDPC codes defined over GL(m₃, F_2^m₄). We propose a method to lower the error floors for non-binary LDPC codes. In this analysis, we see that the non-binary LDPC codes constructed by our proposed method defined over general linear group have the same decoding performance in the error floors as those defined over finite field. The non-binary LDPC codes defined over general linear group have more choices of the labels on the edges which satisfy the condition for the optimization.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.12 pp.2113-2121

Publication Date: 2012/12/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E95.A.2113

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

Category: Coding Theory

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Takayuki NOZAKI, Kenta KASAI, Kohichi SAKANIWA, "Analysis of Error Floors for Non-binary LDPC Codes over General Linear Group through q-Ary Memoryless Symmetric Channels" in IEICE TRANSACTIONS on Fundamentals, vol. E95-A, no. 12, pp. 2113-2121, December 2012, doi: 10.1587/transfun.E95.A.2113.
Abstract: In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over general linear groups with those for non-binary LDPC codes over finite fields transmitted through the q-ary memoryless symmetric channels under belief propagation decoding. To analyze non-binary LDPC codes defined over both the general linear group GL(m, F₂) and the finite field F_2^m, we investigate non-binary LDPC codes defined over GL(m₃, F_2^m₄). We propose a method to lower the error floors for non-binary LDPC codes. In this analysis, we see that the non-binary LDPC codes constructed by our proposed method defined over general linear group have the same decoding performance in the error floors as those defined over finite field. The non-binary LDPC codes defined over general linear group have more choices of the labels on the edges which satisfy the condition for the optimization.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.2113/_p

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@ARTICLE{e95-a_12_2113,
author={Takayuki NOZAKI, Kenta KASAI, Kohichi SAKANIWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Analysis of Error Floors for Non-binary LDPC Codes over General Linear Group through q-Ary Memoryless Symmetric Channels},
year={2012},
volume={E95-A},
number={12},
pages={2113-2121},
abstract={In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over general linear groups with those for non-binary LDPC codes over finite fields transmitted through the q-ary memoryless symmetric channels under belief propagation decoding. To analyze non-binary LDPC codes defined over both the general linear group GL(m, F₂) and the finite field F_2^m, we investigate non-binary LDPC codes defined over GL(m₃, F_2^m₄). We propose a method to lower the error floors for non-binary LDPC codes. In this analysis, we see that the non-binary LDPC codes constructed by our proposed method defined over general linear group have the same decoding performance in the error floors as those defined over finite field. The non-binary LDPC codes defined over general linear group have more choices of the labels on the edges which satisfy the condition for the optimization.},
keywords={},
doi={10.1587/transfun.E95.A.2113},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - Analysis of Error Floors for Non-binary LDPC Codes over General Linear Group through q-Ary Memoryless Symmetric Channels
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2113
EP - 2121
AU - Takayuki NOZAKI
AU - Kenta KASAI
AU - Kohichi SAKANIWA
PY - 2012
DO - 10.1587/transfun.E95.A.2113
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2012
AB - In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over general linear groups with those for non-binary LDPC codes over finite fields transmitted through the q-ary memoryless symmetric channels under belief propagation decoding. To analyze non-binary LDPC codes defined over both the general linear group GL(m, F₂) and the finite field F_2^m, we investigate non-binary LDPC codes defined over GL(m₃, F_2^m₄). We propose a method to lower the error floors for non-binary LDPC codes. In this analysis, we see that the non-binary LDPC codes constructed by our proposed method defined over general linear group have the same decoding performance in the error floors as those defined over finite field. The non-binary LDPC codes defined over general linear group have more choices of the labels on the edges which satisfy the condition for the optimization.
ER -