Number field lattices achieve Gaussian and Rayleigh channel capacity within a constant gap

Roope Vehkalahti (1) , Laura Luzzi (2)

1 University of Turku
2 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes

This paper shows 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 lattice codes 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.

Mots clés: Lattice coding; Gaussian channel; fast fading channels; number theory

Domaines: Théorie de l'information [cs.IT]

Roope Vehkalahti, Laura Luzzi. Number field lattices achieve Gaussian and Rayleigh channel capacity within a constant gap. IEEE International Symposium on Information Theory, Jun 2015, Hong-Kong, China. pp.436 - 440, ⟨10.1109/ISIT.2015.7282492⟩. ⟨hal-01420955⟩