On the Equivalence of TCM Encoders
Paper in proceedings, 2012

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.

Labelings

Search spaces

Asymptotically optimal

Gray codes

Convolutional encoders

Ungerboeck

Exhaustive search

Trellis coded modulation

Constellation sizes

Joint designs

Author

Alex Alvarado

University of Cambridge

Alexandre Graell i Amat

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Fredrik Brännström

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Erik Agrell

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

2012 IEEE International Symposium on Information Theory, ISIT 2012. Cambridge, MA, 1 - 6 July 2012

2401-2405 6283945

Areas of Advance

Information and Communication Technology

Subject Categories

Telecommunications

DOI

10.1109/ISIT.2012.6283945

ISBN

978-146732579-0

More information

Latest update

5/2/2018 7