著者

ARIMURA Mitsuharu KOGA Hiroki IWATA Ken-ichi

出版者

電子情報通信学会

雑誌

IEICE transactions on fundamentals of electronics, communications and computer sciences (ISSN:09168508)

巻号頁・発行日

vol.E96.A, no.12, pp.2443-2446, 2013-12

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In this letter, we first introduce a stronger notion of the optimistic achievable coding rate and discuss a coding theorem. Next, we give a necessary and sufficient condition under which the coding rates of all the optimal FF codes asymptotically converge to a constant.

著者

ARIMURA Mitsuharu KOGA Hiroki IWATA Ken-ichi

出版者

電子情報通信学会

雑誌

IEICE transactions on fundamentals of electronics, communications and computer sciences (ISSN:09168508)

巻号頁・発行日

vol.E96.A, no.12, pp.2332-2342, 2013-12

被引用文献数

1

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In this paper we consider fixed-to-fixed length (FF) coding of a general source X with vanishing error probability and define two kinds of optimalities with respect to the coding rate and the redundancy, where the redundancy is defined as the difference between the coding rate and the symbolwise ideal codeword length. We first show that the infimum achievable redundancy coincides with the asymptotic width W(X) of the entropy spectrum. Next, we consider the two sets $\mCH(\bX)$ and $\mCW(\bX)$ and investigate relationships between them, where $\mCH(\bX)$ and $\mCW(\bX)$ denote the sets of all the optimal FF codes with respect to the coding rate and the redundancy, respectively. We give two necessary and sufficient conditions corresponding to $\mCH(\bX) \subseteq \mCW(\bX)$ and $\mCW(\bX) \subseteq \mCH(\bX)$, respectively. We can also show the existence of an FF code that is optimal with respect to both the redundancy and the coding rate.

著者

KOGA Hiroki

出版者

電子情報通信学会

雑誌

IEICE transactions on fundamentals of electronics, communications and computer sciences (ISSN:09168508)

巻号頁・発行日

vol.E95.A, no.12, pp.2100-2106, 2012-12

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This paper is concerned with coding theorems in the optimistic sense for separate coding of two correlated general sources X1 and X2. We investigate the achievable rate region Rtopt(X1,X2) such that the decoding error probability caused by two encoders and one decoder can be arbitrarily small infinitely often under a certain rate constraint. We give an inner and an outer bounds of Rtopt(X1,X2), where the outer bound is described by using new information-theoretic quantities. We also give two simple sufficient conditions under which the inner bound coincides with the outer bound.

著者

Iwamoto Mitsugu Koga Hiroki Yamamoto Hirosuke

出版者

IEEE

雑誌

IEEE transactions on information theory (ISSN:00189448)

巻号頁・発行日

vol.58, no.9, pp.6194-6206, 2012-09

被引用文献数

1

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Coding theorems on a $(2,2)$-threshold scheme with an opponent are discussed in an asymptotic setup, where the opponent tries to impersonate one of the two participants. A situation is considered where $n$ secrets $S^{n}$ from a memoryless source is blockwisely encoded to two shares and the two shares are decoded to $S^{n}$ with permitting negligible decoding error. We introduce correlation level of the two shares and characterize the minimum attainable rates of the shares and a uniform random number for realizing a $(2, 2)$-threshold scheme that is secure against the impersonation attack by the opponent. It is shown that if the correlation level between the two shares equals to $ell geq 0$, the minimum attainable rates coincide with $H(S)+ell $, where $H(S)$ denotes the entropy of the source, and the maximum attainable exponent of the success probability of the impersonation attack equals to $ell $. It is also shown that a simple scheme using an ordinary $(2,2)$-threshold scheme attains all the bounds as well.

著者

Koga Hiroki

出版者

電子情報通信学会

雑誌

IEICE transactions on fundamentals of electronics, communications and computer sciences (ISSN:09168508)

巻号頁・発行日

vol.E94.A, no.11, pp.2073-2082, 2011-11

被引用文献数

2 3

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In information-spectrum methods proposed by Han and Verdú, quantities defined by using the limit superior (or inferior) in probability play crucial roles in many problems in information theory. In this paper, we introduce two nonconventional quantities defined in probabilistic ways. After clarifying basic properties of these quantities, we show that the two quantities have operational meaning in the eps-coding problem of a general source in the ordinary and optimistic senses. The two quantities can be used not only for obtaining variations of the strong converse theorem but also establishing upper and lower bounds on the width of the entropy-spectrum. We also show that the two quantities are expressed in terms of the smooth Rényi entropy of order zero.