BICM Receivers for Trellis Codes

In this chapter, the author studies a trellis encoder and a bit‐interleaved coded modulation (BICM) receiver, i.e., the coded modulation (CM) encoder is a serial concatenation of a convolutional encoder (CENC) and a memoryless mapper. The chapter introduces the idea of BICM with “trivial interleavers” (i.e., no interleaving). The design philosophies behind trellis‐coded modulation (TCM) and BICM for the additive white Gaussian noise (AWGN) channel are quite different. On one hand, TCM is constructed coupling together a CENC and a constellation using a set‐partitioning (SP) labeling. On the other hand, BICM is typically a concatenation of a binary encoder, a bit‐level interleaver, and a mapper with constellation labeled by the binary reflected Gray code (BRGC). The chapter studies the optimal selection of CENCs for this configuration, and also the binary labelings for trellis encoders. It analyzes the performance of BICM‐T for asymptotically high signal‐to‐noise ratio (SNR).