Design Criteria for Hierarchical Exclusive Code with Parameter-Invariant Decision Regions for Wireless 2-Way Relay Channel

The unavoidable parametrization of the wireless link represents a major problem of the network-coded modulation synthesis in a 2-way relay channel. Composite (hierarchical) codeword received at the relay is generally parametrized by the channel gain, forcing any processing on the relay to be dependent on channel parameters. In this paper, the authors introduce the codebook design criteria, which ensure that all permissible hierarchical codewords have decision regions invariant to the channel parameters (as seen by the relay). They utilize the criterion for parameter-invariant constellation space boundary to obtain the codebooks with channel parameter-invariant decision regions at the relay. Since the requirements on such codebooks are relatively strict, the construction of higher-order codebooks will require a slightly simplified design criteria.