Optimal 8PSK mappings for BICM-ID over quasi-static fading channels

In this paper, we investigate the optimal mapping scheme for 8PSK for an iterative demapping and decoding system over quasi-static fading channels. We show that there are only 86 unique 8PSK mappings and conjecture that only 70 8PSK mappings will have unique error performance characteristics. We obtain an analytical expression for the demapper extrinsic information transfer (EXIT) functions using a binary erasure channel (BEC) to model a-priori information and use this to help select the mapping that converges earliest to a bit error rate (BER) value of 10^-5. Finally, we present the performance of the optimal mapping scheme and compare its performance with mappings that have the lowest bit error floor, earliest convergence threshold and best non-iterative performance over an additive white Gaussian noise (AWGN) channel.