The Treewidth of MDS and Reed-Muller Codes

Kashyap, Navin and Thangaraj, Andrew (2012) The Treewidth of MDS and Reed-Muller Codes. In: IEEE Transactions on Information Theory, 58 (7). pp. 4837-4847.

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Abstract

The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free graphical realizations. This notion provides a useful parameterization of the maximum-likelihood decoding complexity for linear codes. In this paper, we show the surprising fact that for maximum distance separable codes and Reed-Muller codes, treewidth equals trelliswidth, which, for a code, is defined to be the least constraint complexity (or branch complexity) of any of its trellis realizations. From this, we obtain exact expressions for the treewidth of these codes, which constitute the only known explicit expressions for the treewidth of algebraic codes.

Item Type:	Journal Article
Publication:	IEEE Transactions on Information Theory
Publisher:	IEEE
Additional Information:	Copyright for this article belongs to the IEEE.
Keywords:	Maximum distance separable (MDS) codes;Reed-Muller codes; treewidth;trelliswidth
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	23 Jul 2012 12:42
Last Modified:	23 Jul 2012 12:42
URI:	http://eprints.iisc.ac.in/id/eprint/44820

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