Universal bound on the performance of lattice codes

We present a lower bound on the probability of symbol error for maximum-likelihood decoding of lattices and lattice codes on a Gaussian channel. The bound is tight for error probabilities and signal-to-noise ratios of practical interest, as opposed to most existing bounds that become tight asymptotically for high signal-to-noise ratios. The bound is also universal; it provides a limit on the highest possible coding gain that may be achieved, at specific symbol error probabilities, using any lattice or lattice code in n dimensions. In particular, it is shown that the effective coding gains of the densest known lattices are much lower than their nominal coding gains. The asymptotic (as n→∞) behavior of the new bound is shown to coincide with the Shannon (1948) limit for Gaussian channels