On Optimal TCM Encoders
Artikel i vetenskaplig tidskrift, 2013

An asymptotically optimal trellis-coded modulation (TCM) encoder requires the joint design of the encoder and the binary labeling of the constellation. Since analytical approaches are unknown, the only available solution is to perform an exhaustive search over the encoder and the labeling. For large constellation sizes and/or many encoder states, however, an exhaustive search is unfeasible. Traditional TCM designs overcome this problem by using a labeling that follows the set-partitioning principle and by performing an exhaustive search over the encoders. 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 $8$-ary constellations, the number of different binary labelings that must be tested is reduced from $8!=40320$ to $240$. For the particular case of an $8$-ary pulse amplitude modulation constellation, this number is further reduced to $120$ and for $8$-ary phase shift keying to only $30$. An algorithm to generate one labeling in each class is also introduced. Asymptotically optimal TCM encoders are tabulated which are up to $0.3$~dB better than the previously best known encoders.

performance bounds

Viterbi decoding


convolutional encoder

bit-interleaved coded modulation

Binary reflected Gray code

coded modulation

trellis-coded modulation


Alex Alvarado

University of Cambridge

Alexandre Graell i Amat

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk

Fredrik Brännström

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk

Erik Agrell

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk

IEEE Transactions on Communications

0090-6778 (ISSN) 15580857 (eISSN)

Vol. 61 6 2178 - 2189 6510021

Komprimerad avkänning med hjälp av kodningsteori

Vetenskapsrådet (VR) (2011-5961), 2012-01-01 -- 2015-12-31.

Analys och Design av MIMO-BICM

Vetenskapsrådet (VR) (2011-5950), 2012-01-01 -- 2015-12-31.






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