IEICE TRANSACTIONS on Fundamentals
A Note on the ε-Overflow Probability of Lossless Codes
Summary :
In this letter, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the ε-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of ε-achievability for some restricted sources given ε.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.12 pp.2965-2970
- Publication Date
- 2007/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e90-a.12.2965
- Type of Manuscript
- LETTER
- Category
- Information Theory
Authors
Keyword
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Ryo NOMURA, Toshiyasu MATSUSHIMA, Shigeichi HIRASAWA, "A Note on the ε-Overflow Probability of Lossless Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E90-A, no. 12, pp. 2965-2970, December 2007, doi: 10.1093/ietfec/e90-a.12.2965.
Abstract: In this letter, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the ε-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of ε-achievability for some restricted sources given ε.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.12.2965/_p
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@ARTICLE{e90-a_12_2965,
author={Ryo NOMURA, Toshiyasu MATSUSHIMA, Shigeichi HIRASAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Note on the ε-Overflow Probability of Lossless Codes},
year={2007},
volume={E90-A},
number={12},
pages={2965-2970},
abstract={In this letter, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the ε-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of ε-achievability for some restricted sources given ε.},
keywords={},
doi={10.1093/ietfec/e90-a.12.2965},
ISSN={1745-1337},
month={December},}
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TY - JOUR
TI - A Note on the ε-Overflow Probability of Lossless Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2965
EP - 2970
AU - Ryo NOMURA
AU - Toshiyasu MATSUSHIMA
AU - Shigeichi HIRASAWA
PY - 2007
DO - 10.1093/ietfec/e90-a.12.2965
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2007
AB - In this letter, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the ε-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of ε-achievability for some restricted sources given ε.
ER -
English
