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Bit-interleaved coded modulation with iterative decoding (BICM-ID) is investigated for bandwidth efficient transmissions, where the error performance can be improved by employing a suitable symbol mapping. In this paper, we introduce a low-complexity irregular mapping optimization for BICM-ID with irregular doping and 8-ary phase-shift keying (8PSK) modulation over both additive white Gaussian noise (AWGN) and Rayleigh fading channels, for the purpose of achieving near-capacity performances. The Euclidean distance spectrum and the extrinsic information transfer (EXIT) chart analysis are aided for the proposed optimization to provide design guidelines of mappings. The bit error rate (BER) results demonstrate that the BICM-ID system with the proposed optimal irregular mapping and doping outperforms the other typical symbol mappings, and yields a gain of about 0.1 and 0.5 dB for AWGN and Rayleigh fading channels, respectively. Moreover, it is only about 0.5 and 0.73 dB away from the discrete-input continuous-output memoryless channel (DCMC) capacity limits of AWGN and Rayleigh fading channels, respectively, at the BER of 10 −4 and for the spectral efficiency of 2 bits/channel use.

Iterative decoding is an effective technique to approach the channel capacity for very large block sizes with enough iterations. However, due to the limitation of bandwidth and delay, small blocks of data are much more commonly applied in practical communications, and low iteration counts are usually preferred for both decoding complexity and delay consideration. In such cases, the design rules of near capacity decoding-which is generally asymptotic with respect to the block size-may cause inferior performance. To overcome this problem for 8-phase shift keying (8PSK) modulated variable length codes (VLCs), an irregular mapping scheme for the transmission system of bit-interleaved coded modulation with iterative decoding (BICM-ID) is studied in this paper. A submapping searching algorithm and an irregular mapping optimization algorithm are proposed aiming at maximizing the extrinsic mutual information after a target number of iterations. Simulation results show that for small data block size with a low iteration count, our scheme has advantages with respect to the existing near capacity systems optimized by the asymptotic tools.

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