Universal Lattice Codes for MIMO Channels

TL;DR

This paper introduces a universal lattice coding scheme for MIMO channels that leverages algebraic structures to approach capacity, effectively handling channel variations and outperforming previous methods.

Contribution

It presents a novel algebraic lattice construction that achieves near-capacity for compound and ergodic fading MIMO channels, with reduced gap to capacity.

Findings

Achieves capacity of compound MIMO channels with algebraic lattices.

Uses algebraic properties to reduce gap to capacity.

Constructs alternative codes for ergodic fading channels.

Abstract

We propose a coding scheme that achieves the capacity of the compound MIMO channel with algebraic lattices. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. These techniques, along with algebraic properties of the proposed lattices, are then used to construct a sub-optimal de-coupled coding schemes that achieves a gap to compound capacity by decoding in a lattice that does not depend of the channel realization. The gap is characterized in terms of algebraic invariants of the codes, and shown to be significantly smaller than previous schemes in the literature. We also exhibit alternative algebraic constructions that achieve the capacity of ergodic fading channels.