Capacity of a modulo-sum simple relay network

Abstract

This thesis proposes the capacity of a modulo-sum simple relay network. In previous work related to relay channels, capacity was characterized in the case where noise was transmitted to the relay, and the closed-form capacity was derived only for the noise with a Bernoulli-( distribution. However, in this work, the source is transmitted to the relay, and a more general case of noise with an arbitrary Bernoulli-( distribution, , is considered. The relay observes a corrupted version of the source, uses a quantize-and-forward strategy, and transmits the encoded codeword through a separate dedicated channel to the destination. The destination receives the codeword from both the relay and source. For the relay channel, it is assumed that the channel is discrete and memoryless. After deriving the achievable capacity theorem (i.e., the forward theorem) for the binary symmetric simple relay network, it is proven that the capacity is strictly below the cut-set bound. In addition, this thesis presents the proof of the converse theorem. Finally, the capacity of the binary symmetric simple relay network is extended to that of an m-ary modulo-sum relay network.