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In this paper, new probability estimates are derived for ideal lattice codesfrom totally real number fields using ideal class Dedekind zeta functions. Incontrast to previous work on the subject, it is not assumed that the ideal inquestion is principal. In particular, it is shown that the correspondinginverse norm sum depends not only on the regulator and discriminant of thenumber field, but also on the values of the ideal class Dedekind zetafunctions. Along the way, we derive an estimate of the number of elements in agiven ideal with a certain algebraic norm within a finite hypercube. We provideseveral examples which measure the accuracy and predictive ability of ourtheorems.

Probability Estimates for Fading and Wiretap Channels from Ideal Class Zeta Functions