Capacity of a Modulo-Sum Arbitrary SISO Relay Network

This paper shows how to obtain the capacity of modular additive noise of an arbitrary single-input- single-output (SISO) relay network. The arbitrary SISO relay network is a network where the relays are interconnected with each other in various combinations. Its capacity is obtained by using a quantize-and-forward (QAF) strategy at each relay node. This paper considers all channels as discrete memoryless channels. In order to obtain the capacity of an arbitrary SISO relay network, this paper simplifies the network in terms of a parallel and serial relay network and finds the capacity. First, the capacity expression for a parallel relay network is obtained. In a parallel relay network, the source is transmitted to all relays; then each relay, using a QAF strategy, forwards the source to the destination. Second, the capacity expression for a serial relay network where the relays are interconnected serially is obtained. Finally, after expressing the capacities for parallel and serial relay networks, this paper explains how to obtain the capacity for any arbitrary SISO relay network.