On BICM receivers for TCM transmission

Recent results have shown that the performance of bit-interleaved coded modulation (BICM) using convolutional codes in nonfading channels can be significantly improved when the interleaver takes a trivial form (BICM-T), i.e., when it does not interleave the bits at all. In this paper, we give a formal explanation for these results and show that BICM-T is, in fact, the combination of a TCM transmitter and a BICM receiver. To predict the performance of BICM-T, a new type of distance spectrum for convolutional codes is introduced, analytical bounds based on this spectrum are developed, and asymptotic approximations are presented. It is shown that the free Hamming distance of the code is not the relevant optimization criterion for BICM-T. Asymptotically optimal convolutional codes for different constraint lengths are tabulated and BICM-T is shown to offer asymptotic gains of about 2 dB over traditional BICM designs based on random interleavers. The asymptotic gains over uncoded transmission are found to be the same as those obtained by Ungerboeck's one-dimensional trellis-coded modulation (1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be as good as 1D-TCM.