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 $mCH(X)$ and $mCW(X)$ and investigate relationships between them, where $mCH(X)$ and $mCW(X)$ 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 $mCH(X) subseteq mCW(X)$ and $mCW(X) subseteq mCH(X)$, respectively. We can also show the existence of an FF code that is optimal with respect to both the redundancy and the coding rate.

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 Ropt (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 Ropt (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.

In information-spectrum methods proposed by Han and Verdu, 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 ε-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 Renyi entropy of order zero.

This paper establishes a new unified method for fixed-length source coding problems of general sources. Specifically, we introduce an alternative definition of the smooth Renyi entropy of order zero, and show a unified approach to present the fixed-length coding rate in terms of this information quantity. Our definition of the smooth Renyi entropy has a clear operational meaning, and hence is easy to calculate for finite block lengths. Further, we represent various ε-source coding rate and the strong converse property for general sources in terms of the smooth Renyi entropy, and compare them with the results obtained by Han and Renner et al.

This paper analyzes a generalized secret-key authentication system from a viewpoint of the information-spectrum methods. In the generalized secret-key authentication system, for each n 1 a legitimate sender transmits a cryptogram Wn to a legitimate receiver sharing a key En in the presence of an opponent who tries to cheat the legitimate receiver. A generalized version of the Simmons' bounds on the success probabilities of the impersonation attack and a certain kind of substitution attack are obtained.