A Multivariate Weight Enumerator for Tail-biting Trellis Pseudocodewords
Departments of Mathematics, Electrical and Computer Engineering, University of Wisconsin, Madison, WI 53706, USA
- Corresponding Author:
- Nigel Boston
Departments of Mathematics
and Electrical and Computer Engineering
University of Wisconsin, Madison
WI 53706, USA
E-mail: [email protected]
Received date: July 21, 2015 Accepted date: August 03, 2015 Published date: August 31, 2015
Citation: Boston N (2015) A Multivariate Weight Enumerator for Tail-biting Trellis Pseudocodewords. J Generalized Lie Theory Appl S1:004. doi:10.4172/1736-4337.S1-004
Copyright: © 2015 Boston N. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Tail-biting-trellis representations of codes allow for iterative decoding algorithms, which are limited in effectiveness by the presence of pseudocodewords. We introduce a multivariate weight enumerator that keeps track of these pseudocodewords. This enumerator is invariant under many linear transformations, often enabling us to compute it exactly. The extended binary Golay code has a particularly nice tail-biting-trellis and a famous unsolved question is to determine its minimal AWGN pseudodistance. The new enumerator provides an inroad to this problem.