Non-Random Coding Error Exponent for Lattices

Abstract

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, an error-exponent is derived for specific lattice sequences (of increasing dimension) over the AWGN channel. Measuring the sequence's gap to capacity, using the new exponent, is demonstrated.