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 c09-math-0445 (see Section 2.5.2) and the CENC universe c09-math-0446 (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 c09-math-0447 CENC with c09-math-0448 and an c09-math-0449-ary constellation. In this case, the labeling universe includes c09-math-0450 different binary labelings and the CENC universe (discarding catastrophic encoders) includes about c09-math-0451 encoders.5 An exhaustive search for this ...

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