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In this paper, new probability bounds are derived for algebraic latticecodes. This is done by using the Dedekind zeta functions of the algebraicnumber fields involved in the lattice constructions. In particular, it is shownhow to upper bound the error performance of a finite constellation on aRayleigh fading channel and the probability of an eavesdropper's correctdecision in a wiretap channel. As a byproduct, an estimate of the number ofelements with a certain algebraic norm within a finite hyper-cube is derived.While this type of estimates have been, to some extent, considered in algebraicnumber theory before, they are now brought into novel practice in the contextof fading channel communications. Hence, the interest here is insmall-dimensional lattices and finite constellations rather than in theasymptotic behavior.

Nonasymptotic Probability Bounds for Fading Channels Exploiting Dedekind Zeta Functions