Multi-stage decoding of multi-level modulation codes

Various types of multi-stage decoding for multi-level modulation codes are investigated. It is shown that if the component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. Particularly, it is shown that the difference in performance between the suboptimum multi-stage soft-decision maximum likelihood decoding of a modulation code and the single-stage optimum soft-decision decoding of the code is very small, only a fraction of dB loss in signal to noise ratio at a bit error rate (BER) of 10(exp -6).