Two kinds of problems - multiterminal hypothesis testing and one-to-many lossy source coding - are investigated in a unified way. It is demonstrated that a simple key idea, which is developed by Iriyama for one-to-one source coding systems, can be applied to multiterminal source coding systems. In particular, general bounds on the error exponents for multiterminal hypothesis testing and one-to-many lossy source coding are given.

The wiretap channel is now a fundamental model for information-theoretic security. After introduced by Wyner, Csiszár and Körner have generalized this model by adding an auxiliary random variable. Recently, Han, Endo and Sasaki have derived the exponents to evaluate the performance of wiretap channels with cost constraints on input variable plus such an auxiliary random variable. Although the constraints on two variables were expected to provide larger-valued (or tighter) exponents, some non-trivial theoretical problems had been left open. In this paper, we investigate these open problems, especially concerning the concavity property of the exponents. Furthermore, we compare the exponents derived by Han et al. with the counterparts derived by Gallager to reveal that the former approach has a significantly wider applicability in contrast with the latter one.

The multiterminal hypothesis testing problem with zero-rate constraint is considered. For this problem, an upper bound on the optimal error exponent is given by Shalaby and Papamarcou, provided that the positivity condition holds. Our contribution is to prove that Shalaby and Papamarcou's upper bound is valid under a weaker condition: (i) two remote observations have a common random variable in the sense of Gácks and Körner, and (ii) when the value of the common random variable is fixed, the conditional distribution of remaining random variables satisfies the positivity condition. Moreover, a generalization of the main result is also given.

Weissman introduced a coding problem for channels with action-dependent states. In this coding problem, there are two encoders and a decoder. An encoder outputs an action that affects the state of the channel. Then, the other encoder outputs a codeword of the message into the channel by using the channel state. The decoder receives a noisy observation of the codeword, and reconstructs the message. In this paper, we show an exponential error bound for channels with action-dependent states based on the random coding argument.

This paper investigates the performance of a combination of the affine encoder and the maximum mutual information decoder for symmetric channels, and proves that the random coding error exponent can be attained by this combination even if the conditional probability of the symmetric channel is not known to the encoder and decoder. This result clarifies that the restriction of the encoder to the class of affine encoders does not affect the asymptotic performance of the universal code for symmetric channels.

A universal coding scheme for information from i.i.d., arbitrarily varying sources, or memoryless correlated sources is constructed using LDPC matrices and shown to have an exponential upper bound of decoding error probability. As a corollary, we construct a universal code for the noisy channel model, which is not necessarily BSC. Simulation results show universality of the code with sum-product decoding, and presence of a gap between the error exponent obtained by simulation and that obtained theoretically.

This paper deals with the random number generation problem under the framework of a separate coding system for correlated memoryless sources posed and investigated by Slepian and Wolf. Two correlated data sequences with length n are separately encoded to nR1, nR2 bit messages at each location and those are sent to the information processing center where the encoder wish to generate an approximation of the sequence of independent uniformly distributed random variables with length nR3 from two received random messages. The admissible rate region is defined by the set of all the triples (R1,R2,R3) for which the approximation error goes to zero as n tends to infinity. In this paper we examine the asymptotic behavior of the approximation error inside and outside the admissible rate region. We derive an explicit lower bound of the optimal exponent for the approximation error to vanish and show that it can be attained by the universal codes. Furthermore, we derive an explicit lower bound of the optimal exponent for the approximation error to tend to 2 as n goes to infinity outside the admissible rate region.

We investigate the error exponent in the lossy source coding with a fidelity criterion. Marton (1974) established a formula of the reliability function for the stationary memoryless source with finite alphabet. In this paper, we consider a stationary memoryless source assuming that the alphabet space is a metric space and not necessarily finite nor discrete. Our aim is to prove that Marton's formula for the reliability function remains true even if the alphabet is general.

We study the reliability functions or the minimum r-achievable rates of the lossless coding for the general sources in the sense of Han-Verdu, where r means the exponent of the error probability. Han has obtained formulas for the minimum r-achievable rates of the general sources. Our aim is to give alternative expressions for the minimum r-achievable rates. Our result seems to be a natural extension of the known results for the stationary memoryless sources and Markov sources.

We are interesting in the error exponent for source coding with fidelity criterion. For each fixed distortion level Δ, the maximum attainable error exponent at rate R, as a function of R, is called the reliability function. The minimum rate achieving the given error exponent is called the minimum achievable rate. For memoryless sources with finite alphabet, Marton (1974) gave an expression of the reliability function. The aim of the paper is to derive formulas for the reliability function and the minimum achievable rate for memoryless Gaussian sources.

In 1989, Ahlswede and Dueck introduced a new formulation of Shannon theory called identification via channels. This paper presents a simple construction of codes for identification via channels when the probability of false identification is measured by its average. The proposed code achieves the identification capacity, and its construction does not require any knowledge of coding theory.