Parameter-Invariant Hierarchical Exclusive Alphabet Design for 2-WRC with HDF Strategy

Hierarchical eXclusive Code (HXC) for the Hierarchical Decode and Forward (HDF) strategy in the Wireless 2-Way Relay Channel (2-WRC) has the achievable rate region extended beyond the classical MAC region. Although direct HXC design is in general highly complex, a layered approach to HXC design is a feasible solution. While the outer layer code of the layered HXC can be any state-of-the-art capacity approaching code, the inner layer must be designed in such a way that the exclusive property of hierarchical symbols (received at the relay) will be provided. The simplest case of the inner HXC layer is a simple signal space channel symbol memoryless mapper called Hierarchical eXclusive Alphabet (HXA). The proper design of HXA is important, especially in the case of parametric channels, where channel parametrization (e.g. phase rotation) can violate the exclusive property of hierarchical symbols (as seen by the relay), resulting in significant capacity degradation. In this paper we introduce an example of a geometrical approach to Parameter-Invariant HXA design, and we show that the corresponding hierarchical MAC capacity region extends beyond the classical MAC region, irrespective of the channel pametrization.