Multilevel Coding Schemes for Compute-and-Forward With Flexible Decoding

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute-and-forward paradigm, we present a multilevel coding scheme that permits reliable computation (or, decoding) of a class of functions at the relay. The function to be computed (or decoded) is then chosen depending on the channel realization. We define such a class of functions which can be decoded at the relay using the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using 4-ary and 8-ary modulation schemes. Numerical results demonstrate that the flexibility afforded by our proposed scheme results in substantially higher rates than those achievable by always using a fixed function or considering only linear functions over higher order fields.