Universal bound on the performance of lattice codes

We present a lower bound on the probability of symbol error for maximum-lik elihood decoding of lattices and lattice codes on a Gaussian channel. The b ound is tight for error probabilities and signal-to-noise ratios of practic al interest, as opposed to most existing bounds that become tight asymptoti cally for high signal-to-noise ratios. The bound is also universal; it prov ides a limit on the highest possible coding gain that may be achieved, at s pecific symbol error probabilities, using any lattice or lattice code in n dimensions. In particular, it is shown that the effective coding gains of t he densest known lattices are much lower than their nominal coding gains, T he asymptotic (as n --> infinity) behavior of the new bound is shown to coi ncide with the Shannon limit for Gaussian channels.