[IEEE Trans. on Information Theory, March 1999, pp. 670-681]
Universal Bound on the Performance of Lattice Codes
Vahid Tarokh, Alexander Vardy, and Kenneth Zeger
Abstract
We present a new lower bound on the probability of symbol error
for maximum-likelihood decoding of 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 of the existing bounds that
become tight asymptotically for high SNR.
Moreover, the new lower bound is universal: it provides a limit on
the highest possible coding gain that may be achieved, for specific
symbol error probabilities, using any lattice code in $n$-dimensions.
In particular, it is shown that the effective coding gains of the densest
lattice codes are much lower than their nominal coding gains, at practical
symbol error rates of $10^{-5}$ to $10^{-7}$.
Finally, the asymptotic (as $\to\infty$) behavior of the new
bound is investigated, and shown to coincide with the Shannon limit
for Gaussian channels.