On the suitability of gray bit mappings to outer channel codes in iteratively decoded BICM

Deliberately designed bits-to-symbols mappings were introduced to provide significant coding gains compared to the simple Gray mapping for iteratively-decoded BICM on both AWGN and fading channels. The performance of these powerful mappings has always been illustrated in conjunction with relatively weak outer channel codes like convolutional codes with up to 16 states. However, when a powerful outer code like a parallel concatenated turbo code is employed, a simple Gray mapping becomes significantly superior in performance. The aim of this letter is to give a simple and straightforward interpretation of this discrepancy in behavior based on the extrinsic information transfer chart of the iterative receivers in both cases. Parts of the presented results are scattered in the literature but this letter presents a unified look on the mapping suitability problem and answers positively the question of: ¿if a turbo code is used as an outer code in a BICM transmission, is Gray-mapping more suitable than other more complex candidates?¿.