Construction criteria and existence results for approximately universal linear space-time codes with reduced decoding complexity

This work presents new eigenvalue bounds, necessary conditions and existence results for approximately universal linear (lattice) codes that can be drawn from lattices of reduced dimension, and can thus incur reduced decoding complexity. Currently for the n times n_r MIMO channel, all known n times T approximately universal codes, except for the Alamouti code for n = 2,n_r = 1, draw from lattices of dimension equal to or larger than nT, irrespective of n_r. Motivated by the case where n_r < n, the work describes construction criteria for lattice codes that maintain their approximate universality even when they are drawn from lattices of reduced dimensionality.