Multilevel Coding Schemes for Compute-and-Forward

We investigate techniques for designing modulation/coding schemes for the wireless two-way relaying channel. The relay is assumed to have perfect channel state information, but the transmitters are assumed to have no channel state information. We consider physical layer network coding based on multilevel coding techniques. Our multilevel coding framework is inspired by the compute-and-forward relaying protocol. Indeed, we show that the framework developed here naturally facilitates decoding of linear combinations of codewords for forwarding by the relay node. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using the QPSK constellation with gray labeling. We focus our discussion on the rates at which the relay may reliably decode linear combinations of codewords transmitted from the end nodes.