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.

We consider the distributed source coding system of two correlated Gaussian Vector sources Yl=t(Yl1, Yl2),l=1,2 which are noisy observations of correlated Gaussian scalar source X0. We assume that for each (l,k)∈{1,2}, Ylk is an observation of the source X0, having the form Ylk=X0+Nlk, where Nlk is a Gaussian random variable independent of X0. We further assume that Nlk, (l,k)∈{1,2}2 are independent. In this system two correlated Gaussian observations are separately compressed by two encoders and sent to the information processing center. We study the remote source coding problem where the decoder at the center attempts to reconstruct the remote source X0. The determination problem of the rate distortion region for this communication system can be regarded as an extension of the Gaussian CEO problem to the case of vector observations. For each vector observation we can obtain an estimation on X0 from this observation. Those estimations are sufficient statistics on X0. Using those sufficient statistics, we determine the rate distortion region by showing that it coincides with the rate distortion region of the CEO problem where the scalar observations of X0 are equal to the estimations computed from the vector observations. We further extend the result to the case of L terminal and general vector observations.

This paper clarifies the adequacy of the linear channel coding approach for the source coding with partial side information at the decoder. A sufficient condition for an ensemble of linear codes which achieves the Wyner's bound is given. Our result reveals that, by combining a good lossy code, an LDPC code ensemble gives a good code for source coding with partial side information at the decoder.

This paper deals with a universal coding problem for a certain kind of multiterminal source coding system that we call the complementary delivery coding system. In this system, messages from two correlated sources are jointly encoded, and each decoder has access to one of the two messages to enable it to reproduce the other message. Both fixed-to-fixed length and fixed-to-variable length lossless coding schemes are considered. Explicit constructions of universal codes and bounds of the error probabilities are clarified via type-theoretical and graph-theoretical analyses.

We propose source coding algorithms that use the randomness of a past sequence. The proposed algorithms solve the problems of multi-terminal source coding, rate-distortion source coding, and source coding with partial side information at the decoder. We analyze the encoding rate and the decoding error rate in terms of almost-sure convergence.