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Upper Bounds on the Error Probability for the Ensemble of Linear Block Codes with Mismatched Decoding
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Summary :
In channel decoding, a decoder with suboptimal metrics may be used because of the uncertainty of the channel statistics or the limitations of the decoder. In this case, the decoding metric is different from the actual channel metric, and thus it is called mismatched decoding. In this paper, applying the technique of the DS2 bound, we derive an upper bound on the error probability of mismatched decoding over a regular channel for the ensemble of linear block codes, which was defined by Hof, Sason and Shamai. Assuming the ensemble of random linear block codes defined by Gallager, we show that the obtained bound is not looser than the conventional bound. We also give a numerical example for the ensemble of LDPC codes also introduced by Gallager, which shows that our proposed bound is tighter than the conventional bound. Furthermore, we obtain a single letter error exponent for linear block codes.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.3 pp.363-371
- Publication Date
- 2022/03/01
- Publicized
- 2021/10/08
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021TAP0001
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory
Authors
Toshihiro NIINOMI
Tokyo City University
Hideki YAGI
the University of Electro-Communications
Shigeichi HIRASAWA
Waseda University
Keyword
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Toshihiro NIINOMI, Hideki YAGI, Shigeichi HIRASAWA, "Upper Bounds on the Error Probability for the Ensemble of Linear Block Codes with Mismatched Decoding" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 3, pp. 363-371, March 2022, doi: 10.1587/transfun.2021TAP0001.
Abstract: In channel decoding, a decoder with suboptimal metrics may be used because of the uncertainty of the channel statistics or the limitations of the decoder. In this case, the decoding metric is different from the actual channel metric, and thus it is called mismatched decoding. In this paper, applying the technique of the DS2 bound, we derive an upper bound on the error probability of mismatched decoding over a regular channel for the ensemble of linear block codes, which was defined by Hof, Sason and Shamai. Assuming the ensemble of random linear block codes defined by Gallager, we show that the obtained bound is not looser than the conventional bound. We also give a numerical example for the ensemble of LDPC codes also introduced by Gallager, which shows that our proposed bound is tighter than the conventional bound. Furthermore, we obtain a single letter error exponent for linear block codes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021TAP0001/_p
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@ARTICLE{e105-a_3_363,
author={Toshihiro NIINOMI, Hideki YAGI, Shigeichi HIRASAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Upper Bounds on the Error Probability for the Ensemble of Linear Block Codes with Mismatched Decoding},
year={2022},
volume={E105-A},
number={3},
pages={363-371},
abstract={In channel decoding, a decoder with suboptimal metrics may be used because of the uncertainty of the channel statistics or the limitations of the decoder. In this case, the decoding metric is different from the actual channel metric, and thus it is called mismatched decoding. In this paper, applying the technique of the DS2 bound, we derive an upper bound on the error probability of mismatched decoding over a regular channel for the ensemble of linear block codes, which was defined by Hof, Sason and Shamai. Assuming the ensemble of random linear block codes defined by Gallager, we show that the obtained bound is not looser than the conventional bound. We also give a numerical example for the ensemble of LDPC codes also introduced by Gallager, which shows that our proposed bound is tighter than the conventional bound. Furthermore, we obtain a single letter error exponent for linear block codes.},
keywords={},
doi={10.1587/transfun.2021TAP0001},
ISSN={1745-1337},
month={March},}
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TY - JOUR
TI - Upper Bounds on the Error Probability for the Ensemble of Linear Block Codes with Mismatched Decoding
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 363
EP - 371
AU - Toshihiro NIINOMI
AU - Hideki YAGI
AU - Shigeichi HIRASAWA
PY - 2022
DO - 10.1587/transfun.2021TAP0001
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2022
AB - In channel decoding, a decoder with suboptimal metrics may be used because of the uncertainty of the channel statistics or the limitations of the decoder. In this case, the decoding metric is different from the actual channel metric, and thus it is called mismatched decoding. In this paper, applying the technique of the DS2 bound, we derive an upper bound on the error probability of mismatched decoding over a regular channel for the ensemble of linear block codes, which was defined by Hof, Sason and Shamai. Assuming the ensemble of random linear block codes defined by Gallager, we show that the obtained bound is not looser than the conventional bound. We also give a numerical example for the ensemble of LDPC codes also introduced by Gallager, which shows that our proposed bound is tighter than the conventional bound. Furthermore, we obtain a single letter error exponent for linear block codes.
ER -
English
