Analysis on wiretap lattice codes and probability bounds from Dedekind zeta functions

When employing lattice codes based on algebraic number fields in wiretap channel coding, certain norm sums pop up in the expression of the probability of correct decision for Eve the Eavesdropper. These norm sums closely resemble the Dedekind zeta function. The aim in this paper is to derive bounds for Eve´s probability of correct decision in Rayleigh fading channels by using zeta functions and provide some numerical analysis on the behavior of the norm sums. It is then pointed out that, not surprisingly, similar sums occur in e.g. the expression of the pairwise error probability (PEP), when using similar number field lattice codes. Hence, same tools can be - and have been - used to derive bounds for the PEP and diversity-multiplexing gain tradeoff (DMT) as well.