Coding and decoding for multiuser communication systems

Coding and decoding for multiuser communication systems are investigated. In this dissertation, we consider two channel models in multiuser communication systems: multiple-access adder channel (MAAC) and two-way relay channel (TWRC). For MAAC, we propose a coding scheme of (k + 1)-ary error-correcting signature codes. It is used to detect the status of users in MAAC, even in the presence of channel noise. The main coding scheme is presented that given a signature matrix A and a difference matrix D = D+−D− a priori, we obtain a larger signature matrix by replacing each element in Hadamard matrix with A, or D, or D− depending on the values of elements and their locations in Hadamard matrix. The set of rows of the proposed matrix gives an errorcorrecting signature code. Introducing the difference matrix makes it possible to construct the error-correcting signature code whose sum rate is increased with an increase in the order of Hadamard matrix. We give binary and non-binary signature codes. They are the best error-correcting signature codes for MAAC, in the sense that they have highest sum rates known.

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