This paper proves that a family of number field lattice codes simultaneously
achieves a constant gap to capacity in Rayleigh fast fading and Gaussian
channels.
The key property in the proof is the existence of infinite towers of Hilbert
class fields with bounded root discriminant. The gap to capacity of the
proposed families is determined by the root discriminant.
The comparison between the Gaussian and fading case reveals that in Rayleigh
fading channels the normalized minimum product distance plays an analogous role
to the Hermite invariant in Gaussian channels.Comment: Will be submitted to ISIT. Comments, suggestions for references etc.
are warmly welcome. Edit:Appendix adde