On the asymptotic performance of bit-wise decoders for coded modulation

Two decoder structures for coded modulation over the Gaussian channel are studied: 1) the maximum likelihood symbol-wise decoder and 2) the (suboptimal) bit-wise decoder based on the bit-interleaved coded modulation paradigm. We consider a 16-ary quadrature amplitude constellation labeled with a Gray labeling. It is shown that the asymptotic loss in terms of pairwise error probability, for any two codewords caused by the bit-wise decoder, is bounded by 1.25 dB. The analysis also shows that the asymptotic loss is zero for a wide range of linear codes, including all rate-1/2 convolutional codes.