Systematic Design of Hierarchical Network Code Mapper for Butterfly Network Relaying

A majority of the research results on Wireless Network Coding (WNC) considers only a basic 2-Way Relay Channel (2-WRC) system scenario, where the Complementary Side Information (C-SI) is naturally available at both destinations. Although an extension of the WNC principles from the 2-WRC system to the butterfly network could seem relatively straightforward, several new unconventional phenomena of the WNC arise (and need to be considered). First of all, the unreliable transmission of the C-SI can be overcome by an increased cardinality of the relay output. This opens a question how a suitable Hierarchical Network Code (HNC) mapper could be designed for a given quality of the C-SI link (and source alphabet cardinality). In this paper we focus on this problem. We introduce a systematic approach to the design of a set of HNC mappers, respecting the amount of available C-SI. Observed capacity gains of this (extended cardinality) relaying pave the way for an adaptive butterfly network, where the achievable throughput can be maximized by a suitable choice of the HNC map at the relay.