Coding theorems for correlated sources with cooperative encoding

This thesis deals with multiterminal source coding problems for a general framework of coding systems, called coding systems with cooperation, where there are some linkages among encoders and decoders. Especially, the main focus of this thesis is encoder cooperation. Two types of coding systems are investigated that incorporate encoder cooperation: the Slepian-Wolf coding system with linkages (called the SWL system) and the complementary delivery coding system. The SWL system involves some mutual linkages between two encoders of the coding system investigated by Slepian and Wolf (called the SW system) that involves two separate encoders and one common decoder. Especially, some special cases are considered, where the coding rate for the mutual linkage between two encoders is negligibly small. The main results in this thesis shows that the achievable rate region of the SWL system equals that of the SW system when considering fixed-length coding, while weak variable-length coding makes the achievable rate region of the SWL system larger than that of the SW system. This implies that encoder cooperation may improve the coding rate. The complementary delivery coding system contrasts with the SW system in the sense of cooperation, which means that the complementary delivery coding system consists of a common encoder and separate decoders, while the SW system includes separate encoders and a common decoder. Especially, in the complementary delivery coding system, each decoder has access to some of encoded messages to enable the decoder to reproduce the other messages from a common codeword emitted from the common encoder. First, the minimum achievable rate for lossy coding is clarified, which implies that encoder cooperation may increase the coding rate. Next, universal coding schemes for lossless coding are proposed. Explicit constructions of universal lossless codes and the bounds of the error probabilities are clarified by using methods of types and the graph-theoretical analysis.