Bits-to-symbol mappings for superposition coding based HARQ systems

We consider the mapping of bits-to-superimposed constellation symbols in terms of the achievable rate on the channel for the HARQ system using superposition coding as proposed in [2]. We show that using a Gray mapping of bits-to-superimposed constellation symbols has better performance than the conventional natural mapping that results from superposition in signal space, for all the values of the superposition ratio. We also show through link-level simulations that the predicted gains in terms of achievable rate can be realized in practice using LDPC codes. Furthermore, we show that the optimal superposition ratio for the Gray mapping case results in conventional higher order constellation symbols after the superposition operation.