Analysis and design of symbol mappers for iteratively decoded BICM

Iterative decoding and demodulation of bit-interleaved coded modulation (BICM) is investigated. The union bound on the error probability of BICM with maximum-likelihood (NIL) decoding is derived with the assumption of a uniform interleaver. Based on the union bound, it is shown that an interleaving gain is achievable for BICM at high signal-to-noise ratio (SNR). The design rules on the symbol mapper for optimal asymptotic performance at high SNR are derived and a new symbol mapper, called the maximum squared Euclidean weight (MSEW) symbol mapper, is proposed with examples given for 8-PSK and 16-QAM. The MSEW mapper is shown by means of an extrinsic information transfer (EXIT) chart to provide the best error-floor performance for BICM at high SNR. At low SNR, a mapper doping technique is proposed that combines the MSEW mapper with Gray mapper to provide a good match to a given outer code. Simulation results are also presented to confirm our analysis.