3 research outputs found
Probability Estimates for Fading and Wiretap Channels from Ideal Class Zeta Functions
In this paper, new probability estimates are derived for ideal lattice codes
from totally real number fields using ideal class Dedekind zeta functions. In
contrast to previous work on the subject, it is not assumed that the ideal in
question is principal. In particular, it is shown that the corresponding
inverse norm sum depends not only on the regulator and discriminant of the
number field, but also on the values of the ideal class Dedekind zeta
functions. Along the way, we derive an estimate of the number of elements in a
given ideal with a certain algebraic norm within a finite hypercube. We provide
several examples which measure the accuracy and predictive ability of our
theorems.Comment: 24 pages. Extends our earlier arxiv submission arxiv.1303.347