Analysis of Symbol Mapping for Bit-Interleaved Coded Modulation with Iterative Decoding

Symbol mapping is very crucial for the performance of bit-interleaved coded modulation with iterative decoding (BICM-ED). In this paper, an analysis method of the performances of symbol mappings is proposed. This method is via analysis based on harmonic mean of the minimum Euclidean distance and distance spectrum of Euclidean distances for mappings. Harmonic mean centered on the average of Euclidean, while distance spectrum presents the matter of distribution of Euclidean distances in detail. The performance over fading channels depends on the average (harmonic mean) of the minimum Euclidean distance, which could be reduced by using feedback. Distance spectrum of Euclidean distances illustrates that the key role in improvement is derived from the decreasing of weight at the minimum Euclidean distance. Through analysis and comparisons with several different symbol mappings in terms of both harmonic mean of the minimum Euclidean distance and distance spectrum of Euclidean distances, simulation results in Rayleigh fading channels show that the two agents determine the asymptotic gain after feedback and BER performance at high E_b / N_o range.