Universal Bound on the Performanceof Lattice

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 speciic symbol error probabilities, using any lattice or lattice code in n-dimensions. In particular, it is shown that the eeective coding gains of the densest known lattices are much lower than their nominal coding gains, at practical symbol error rates of 10 ?5 to 10 ?7. The asymptotic (as n ! 1) behavior of the new bound is shown to coincide with the Shannon limit for Gaussian channels.