Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) is a bandwidth ef- ficient transmission, where the bit error rate is reduced through the iterative information exchange between the inner demapper and the outer decoder. The choice of the symbol mapping is the crucial design parameter. This paper indicates that the Harmonic Mean of the Minimum Squared Euclidean (HMMSE) distance is the best criterion for the mapping design. Based on the design criterion of the HMMSE distance, a new search algorithm to find the optimized labeling maps for BICM-ID system is proposed. Numerical results and performance comparison show that the new labeling search method has a low complexity and outperforms other labeling schemes using other design criterion in BICM-ID system, therefore it is an optimized labeling method.
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