Superposition coding for wireless Butterfly Network with partial Network Side-Information

Although the 2-source wireless Butterfly Network (BN) represents a natural extension of the well-known 2-Way Relay Channel (2-WRC) scenario, a direct implementation of conventional Wireless Network Coding (WNC)/Physical Layer Network Coding (PLNC) principles in this network is not straightforward. While the information necessary for decoding of the desired data from WNC-coded data at each destination is naturally available in 2-WRC, in the BN the destinations can obtain such information only by overhearing the wireless transmission from the unintended source. Since the amount of such received “Network” Side-Information (N-SI) would be limited by the quality of the corresponding source-destination link, the assumption of perfect side-information is no longer valid in BN, rising many novel research challenges for the design of WNC-based BN. In this paper we propose the Superposition Coding (SC) based scheme as a feasible strategy for relaying in BN. We will show that by a proper optimization of its parameters (rates & power allocation of underlying SC messages), SC is able to achieve the upper bound of two-way rate in BN for both the zero and perfect N-SI case and moreover, it represents a viable solution even for the case where only partial N-SI is available at both destinations.