Capacity of a Modulo-Sum Simple Relay Network

Abstract

This paper presents the capacity of a modulo-sum simple relay network. In previous work related to this paper, capacity was characterized for the case where the noise was transmitted to the relay. And the closed-form capacity was derived only for the noise with a Bernoulli-( distribution. However, in this paper, 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 both from the relay and source. This paper assumes 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, this paper proves that the capacity is strictly below the cut- set bound. In addition, this paper presents the proof of the converse theorem. Finally, this paper extends the capacity of the binary symmetric simple relay network to that of an m-ary modulo-sum relay network.