Exhaustive message splitting for partial decode-forward in single-source single-destination relay networks

We introduce exhaustive message splitting for partial decode-forward in a single-source single-destination relay network with N relays, in which every relay subset has a private message to decode. We apply this idea to a three-relay network and propose a partial decode-forward scheme based on block Markov encoding with exhaustive message splitting and derive its achievable rate. A directed graph of the superposition codebook structure is provided to assist the understanding of the code hierarchy. We also apply the scheme to a Gaussian network and show that our scheme generalizes network decode-forward in [1] and the private message scheme in [2].