Layered Design of Hierarchical Exclusive Codebook and Its Capacity Regions for HDF Strategy in Parametric Wireless 2-WRC

This paper addresses a hierarchical decode-and-forward (HDF) strategy in the wireless two-way relay channel (2-WRC). This strategy uses a Hierarchical eXclusive Code (HXC) that allows full decoding of the hierarchical symbols at the relay. The HXC represents two data sources only through the exclusive law and requires side information on the complementary data at the destination (which naturally holds for the 2-WRC). The HDF strategy has the advantage over classical medium-access control (MAC) stage relaying with joint decoding in that its rate region extends beyond the classical MAC region. We present a layered design of the HXC codebook, which uses an arbitrary outer state-of-the-art capacity-approaching code [e.g., low density parity check (LDPC)] and an inner layer with an exclusive symbol alphabet. We provide basic theorems, showing that this scheme forms an HXC, and we also evaluate its alphabet-constrained rate regions. The rate regions depend on the relative channel phase parameters. Some channel rotation leads to catastrophic violation of the exclusive law. However, these values appear only in a limited range of phases and have only a mild impact on the mean capacity for some component symbol constellations.