Abstract

Optimal trellis-coded modulation (TCM) schemes are obtained by jointly designing the convolutional encoder and the binary labeling of the constellation. Unfortunately this approach is infeasible for large encoder memories or constellation sizes. Traditional TCM designs circumvent this problem by using a labeling that follows the set-partitioning principle and by performing an exhaustive search over the encoders. Therefore, traditional TCM schemes are not necessarily optimal. In this paper, we study binary labelings for TCM and show how they can be grouped into classes, which considerably reduces the search space in a joint design. For the particular case of 8-ary modulation the search space is reduced from 40320 to 240. Using this classification, we formally prove that for any channel it is always possible to design a TCM system based on the binary-reflected Gray code with identical performance to the one proposed by Ungerboeck in 1982. Moreover, the classification is used to tabulate asymptotically optimal TCM schemes.

Fredrik Brännström is an Assistant Professor at the Department of Signals and Systems, Chalmers University of Technology, Gothenburg, Sweden. He received his Ph.D. degree in communication theory from the Department of Computer Engineering, Chalmers University of Technology, Gothenburg, Sweden, in 2004. From 2004 to 2006, he had a Postdoctoral position in the Communication Systems Group at the Department of Signals and Systems, Chalmers University of Technology. From 2006 to 2010 he was a Senior Algorithm Engineer and Principal Design Engineer at Quantenna Communications, Fremont, CA. At Quantenna he was part of the system team that developed the PHY layer for the world’s first WiFi 802.11n chip with 4×4 MIMO and LDPC codes operating at 600 Mbps. His research interests in communication theory and information theory include coding, modulation, and efficient iterative processing.