Channel capacities of parallel and serial modulo-sum relay networks

This paper presents channel capacities of parallel and serial modulo-sum relay networks. A parallel relay network consists of one source, multiple relays in parallel, and one destination node. A serial relay network consists of one source, multiple relays in serial, and one destination node. Each relay employs a quantize-and-forward (QAF) strategy. Each node including source, multiple relays, and destination, employs its own codebook for its own encoding and or decoding. Every node has information of the other nodes codebooks. And every addition in any channel is a modulo-sum. First, this paper presents the capacities for the binary modulo-sum symmetric parallel, and serial relay networks, assuming that the channels are discrete and memoryless. Second, this paper claims that the capacities obtained are strictly below the cut-set bounds except the trivial cases. Third, this paper extends the capacities obtained for the binary modulo-sum relay networks to the m-ary modulo-sum relay networks. Finally, this paper presents the closed form capacities for a worst direct channel which is a binary modulo-sum symmetric channel with a crossover probability of 1/2.