Superposition Coding to Support Multiple Streams, Priorities, and Channel Capacities in the Context of GMSK

Abstract—It is well known in information theory that superposition coding is an optimal technique for providing a single transmission that both provides a high data rate when channel conditions are good and still provides some information when the channel conditions are poor (perhaps due to jamming). Typical superposition coding schemes for the additive white Gaussian noise channel combine signals after the modulator. For modulation schemes such as GMSK, this standard form of (additive) superposition is not acceptable because it does not maintain a constant envelope. This paper introduces a new approach in which newly designed nonlinear codes allow superposition to take place before the GMSK modulation. These codes are demonstrated to operate very close to the boundary of the achievable rate region for the broadcast binary symmetric channel which would result from GMSK transmission with hard decoding. The results also suggest that similarly optimal performance might be obtainable in the soft decoding regime. I