Low complexity decoding of bit-interleaved coded modulation for M-ary QAM

It has been shown by Zehavi that the performance of coded modulation can be improved over a Rayleigh fading channel by bit-wise interleaving at the encoder output, and by using an appropriate soft-decision metric for a Viterbi decoder at the receiver. Caire et al presented the details of the theory behind bit-interleaved coded modulation (BICM). In this paper we show that for Gray encoded M-ary quadrature amplitude modulation (QAM) systems, the bit metrics of BICM can be further simplified. In QAM systems, the maximum likelihood (ML) detector for BICM uses the minimum distance between the received symbol and M/2 constellation points on the complex plane as soft-decision metrics. We show that soft-decision bit metrics for the ML decoder can be further simplified to the minimum distance between the received symbol and √M/2 constellation points on the real line R1. This reduces the number of calculations needed for each bit metric substantially, and therefore reduces the complexity of the decoder without compromising the performance. Simulation results for single carrier modulation (SCM), and multi-carrier modulation (MCM) systems over additive white Gaussian noise (AWGN) and Rayleigh fading channels agree with our findings. In addition, we tie this result to the decoding methods for bit interleaved convolutional code standards used in industry.