Equivalence of Two Exponent Functions for Discrete Memoryless Channels with Input Cost at Rates above the Capacity
Summary :
In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Recently the author determined the optimal exponent on the correct probability of decoding have the form similar to that of Dueck and Körner determined. In this paper we give a rigorous proof of the equivalence of the above exponet function of Dueck and Körner to a exponent function which can be regarded as an extention of Arimoto's bound to the case with the cost constraint on the channel input.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.12 pp.2199-2204
- Publication Date
- 2018/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E101.A.2199
- Type of Manuscript
- Special Section LETTER (Special Section on Information Theory and Its Applications)
- Category
- Shannon theory
Authors
Yasutada OOHAMA
The University of Electro-Communications
Keyword
Latest Issue
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Yasutada OOHAMA, "Equivalence of Two Exponent Functions for Discrete Memoryless Channels with Input Cost at Rates above the Capacity" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 12, pp. 2199-2204, December 2018, doi: 10.1587/transfun.E101.A.2199.
Abstract: In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Recently the author determined the optimal exponent on the correct probability of decoding have the form similar to that of Dueck and Körner determined. In this paper we give a rigorous proof of the equivalence of the above exponet function of Dueck and Körner to a exponent function which can be regarded as an extention of Arimoto's bound to the case with the cost constraint on the channel input.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2199/_p
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@ARTICLE{e101-a_12_2199,
author={Yasutada OOHAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Equivalence of Two Exponent Functions for Discrete Memoryless Channels with Input Cost at Rates above the Capacity},
year={2018},
volume={E101-A},
number={12},
pages={2199-2204},
abstract={In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Recently the author determined the optimal exponent on the correct probability of decoding have the form similar to that of Dueck and Körner determined. In this paper we give a rigorous proof of the equivalence of the above exponet function of Dueck and Körner to a exponent function which can be regarded as an extention of Arimoto's bound to the case with the cost constraint on the channel input.},
keywords={},
doi={10.1587/transfun.E101.A.2199},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Equivalence of Two Exponent Functions for Discrete Memoryless Channels with Input Cost at Rates above the Capacity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2199
EP - 2204
AU - Yasutada OOHAMA
PY - 2018
DO - 10.1587/transfun.E101.A.2199
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2018
AB - In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Recently the author determined the optimal exponent on the correct probability of decoding have the form similar to that of Dueck and Körner determined. In this paper we give a rigorous proof of the equivalence of the above exponet function of Dueck and Körner to a exponent function which can be regarded as an extention of Arimoto's bound to the case with the cost constraint on the channel input.
ER -
English
