Asymptotically optimal trellis coded modulation systems

Other conference contribution, 2012

An asymptotically optimal trellis-coded modulation (TCM) system requires the joint design of the encoder and the binary labeling of the constellation. This problem can only be solved via exhaustive searches over the encoder and the labeling which is unfeasible for large constellation sizes. In this paper, we study binary labelings for TCM and show how they can be grouped in (modified Hadamard) classes, which considerably reduces the search space. Using this classification, we formally prove that it is always possible to design a TCM system based on the binary-reflected Gray code (among many other labelings) with identical performance to the one proposed by Ungerboeck in 1982.