  The aim of this paper is to study the achievable rates for a $K$ user
Gaussian interference channels for any SNR using a combination of lattice and
algebraic codes. Lattice codes are first used to transform the Gaussian
interference channel (G-IFC) into a discrete input-output noiseless channel,
and subsequently algebraic codes are developed to achieve good rates over this
new alphabet. In this context, a quantity called efficiency is introduced which
reflects the effectiveness of the algebraic coding strategy. The paper first
addresses the problem of finding high efficiency algebraic codes. A combination
of these codes with Construction-A lattices is then used to achieve non trivial
rates for the original Gaussian interference channel.
