IEICE TRANSACTIONS on Fundamentals
Decision Feedback Scheme with Criterion LR+Th for the Ensemble of Linear Block Codes
Summary :
In decision feedback scheme, Forney's decision criterion (Forney's rule: FR) is optimal in the sense that the Neyman-Pearson's lemma is satisfied. Another prominent criterion called LR+Th was proposed by Hashimoto. Although LR+Th is suboptimal, its error exponent is shown to be asymptotically equivalent to that of FR by random coding arguments. In this paper, applying the technique of the DS2 bound, we derive an upper bound for the error probability of LR+Th for the ensemble of linear block codes. Then we can observe the new bound from two significant points of view. First, since the DS2 type bound can be expressed by the average weight distribution whose code length is finite, we can compare the error probability of FR with that of LR+Th for the fixed-length code. Second, the new bound elucidates the relation between the random coding exponents of block codes and those of linear block codes.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.1 pp.334-345
- Publication Date
- 2020/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2019EAP1045
- Type of Manuscript
- PAPER
- 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, "Decision Feedback Scheme with Criterion LR+Th for the Ensemble of Linear Block Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 1, pp. 334-345, January 2020, doi: 10.1587/transfun.2019EAP1045.
Abstract: In decision feedback scheme, Forney's decision criterion (Forney's rule: FR) is optimal in the sense that the Neyman-Pearson's lemma is satisfied. Another prominent criterion called LR+Th was proposed by Hashimoto. Although LR+Th is suboptimal, its error exponent is shown to be asymptotically equivalent to that of FR by random coding arguments. In this paper, applying the technique of the DS2 bound, we derive an upper bound for the error probability of LR+Th for the ensemble of linear block codes. Then we can observe the new bound from two significant points of view. First, since the DS2 type bound can be expressed by the average weight distribution whose code length is finite, we can compare the error probability of FR with that of LR+Th for the fixed-length code. Second, the new bound elucidates the relation between the random coding exponents of block codes and those of linear block codes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAP1045/_p
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@ARTICLE{e103-a_1_334,
author={Toshihiro NIINOMI, Hideki YAGI, Shigeichi HIRASAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Decision Feedback Scheme with Criterion LR+Th for the Ensemble of Linear Block Codes},
year={2020},
volume={E103-A},
number={1},
pages={334-345},
abstract={In decision feedback scheme, Forney's decision criterion (Forney's rule: FR) is optimal in the sense that the Neyman-Pearson's lemma is satisfied. Another prominent criterion called LR+Th was proposed by Hashimoto. Although LR+Th is suboptimal, its error exponent is shown to be asymptotically equivalent to that of FR by random coding arguments. In this paper, applying the technique of the DS2 bound, we derive an upper bound for the error probability of LR+Th for the ensemble of linear block codes. Then we can observe the new bound from two significant points of view. First, since the DS2 type bound can be expressed by the average weight distribution whose code length is finite, we can compare the error probability of FR with that of LR+Th for the fixed-length code. Second, the new bound elucidates the relation between the random coding exponents of block codes and those of linear block codes.},
keywords={},
doi={10.1587/transfun.2019EAP1045},
ISSN={1745-1337},
month={January},}
Copy
TY - JOUR
TI - Decision Feedback Scheme with Criterion LR+Th for the Ensemble of Linear Block Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 334
EP - 345
AU - Toshihiro NIINOMI
AU - Hideki YAGI
AU - Shigeichi HIRASAWA
PY - 2020
DO - 10.1587/transfun.2019EAP1045
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2020
AB - In decision feedback scheme, Forney's decision criterion (Forney's rule: FR) is optimal in the sense that the Neyman-Pearson's lemma is satisfied. Another prominent criterion called LR+Th was proposed by Hashimoto. Although LR+Th is suboptimal, its error exponent is shown to be asymptotically equivalent to that of FR by random coding arguments. In this paper, applying the technique of the DS2 bound, we derive an upper bound for the error probability of LR+Th for the ensemble of linear block codes. Then we can observe the new bound from two significant points of view. First, since the DS2 type bound can be expressed by the average weight distribution whose code length is finite, we can compare the error probability of FR with that of LR+Th for the fixed-length code. Second, the new bound elucidates the relation between the random coding exponents of block codes and those of linear block codes.
ER -
English
