Non-Random Coding Error Exponent for Lattices
Information Theory
2013-01-03 v5 math.IT
Abstract
An upper bound on the error probability of specific lattices, based on their distance-spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers. In many ways, the new bound greatly resembles the Shulman-Feder bound for linear codes. Based on the new bound, an error-exponent is derived for specific lattice sequences (of increasing dimension) over the AWGN channel. Measuring the sequence's gap to capacity, using the new exponent, is demonstrated.
Cite
@article{arxiv.1201.6022,
title = {Non-Random Coding Error Exponent for Lattices},
author = {Yuval Domb and Meir Feder},
journal= {arXiv preprint arXiv:1201.6022},
year = {2013}
}
Comments
A subset of this work was submitted to the IEEE International Symposium on Information Theory (ISIT) 2012