Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design

9.3 Equivalent Labelings for Trellis Encoders

Conventionally, CM designs based on CENCs either optimize the encoder for a constellation labeled by a SP labeling (TCM), or simply connect an encoder designed for binary transmission with the BRGC (BICM). Of course, none of these approaches is optimal. Instead, a joint optimization over the labeling universe (see Section 2.5.2) and the CENC universe (see Section 2.6.1) should be performed. This problem is very difficult, even for the simplest cases. As an example, we consider the design of a trellis encoder based on an CENC with and an -ary constellation. In this case, the labeling universe includes different binary labelings and the CENC universe (discarding catastrophic encoders) includes about encoders.⁵ An exhaustive search for this ...