Non-random coding error bounds for lattices

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, error-exponent and channel-dispersion expressions are derived for specific lattice sequences (of increasing dimension) over the AWGN channel. Measuring a sequence's gap to capacity, using the new asymptotics, is demonstrated. Additional finite dimension results, encountered along the way, are presented.