We study the performance of algebraic codes for multi-terminal communications.This thesis consists of three parts: In the rst part, we analyze the performance ofgroup codes for communications systems. We observe that although group codes arenot optimal for point-to-point scenarios, they can improve the achievable rate regionfor several multi-terminal communications settings such as the Distributed SourceCoding and Interference Channels. The gains in the rates are particularly signicantwhen the structure of the source/channel is matched to the structure of the underlyinggroup. In the second part, we study the continuous alphabet version of group/linearcodes, namely lattice codes. We show that similarly to group codes, lattice codescan improve the achievable rate region for multi-terminal problems. In the third partof the thesis, we present coding schemes based on polar codes to practically achievethe performance limits derived in the two earlier parts. We also present polar codingschemes to achieve the known achievable rate regions for multi-terminal communicationsproblems such as the Distributed Source Coding, the Multiple DescriptionCoding, Broadcast Channels, Interference Channels and Multiple Access Channels.
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