Development of Fundamental Theory on Multi-User Channel Coding forHigh Speed Network

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This study aims to analyze coding rates of optimal codes and to develop methods for constructing codes that can approach the theoretical limit over multi-user communication systems. The main result is to develop an explicit construction method of codes having the following three properties over a (compound) multiple access channel: (1) they can be implemented with the complexity polynomial in the code length N, (2) they can approach the optimal coding rates asymptotically, and (3) their decoding error probability can converge to zero exponentially in N. Another important result is to give bounds on coding rates of optimal codes with a fixed code length N, which are tighter than known bounds.