# American Institute of Mathematical Sciences

November  2012, 6(4): 385-400. doi: 10.3934/amc.2012.6.385

## Decoding affine reflection group codes with trellises

 1 Communication Systems Group, Technische Universität Darmstadt, 64283 Darmstadt, Germany 2 Department of Computer Science, Ryerson University, Toronto, ON, Canada 3 Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada

Received  April 2011 Revised  June 2012 Published  November 2012

We present two decoding methods (called hybrid and lattice cosets) for affine reflection group codes (ARGC) of any dimension. The algorithms are based on viewing the affine reflection group as a semi-direct product of a crystallographic finite reflection group and its coroot lattice. The proposed lattice cosets method gives an explicit method for drawing a trellis diagram representation of ARGC. The complexities of these two decoding methods, as well as the trade-offs between them, are discussed.
Citation: Terasan Niyomsataya, Ali Miri, Monica Nevins. Decoding affine reflection group codes with trellises. Advances in Mathematics of Communications, 2012, 6 (4) : 385-400. doi: 10.3934/amc.2012.6.385
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