show that the layered lattice coding scheme can achieve more than one degree of freedom for a wide class of three user ICs. The results of the paper can be extended to $K$ user ICs.

The use of structured codes for ICs has already been introduced for one-sided ICs in [@BreslerParekhTse] and more recently in [@Sridharan-Globecom] in determining capacity of very-strong ICs. Lattice coding has also been used as an effective transmission strategy in achieving the capacity of several other channels. It is used as a transmission strategy for an AWGN channel in [@deBuda]–[@Loeliger] to achieve a rate close to capacity in the high SNR regime. In [@ErezZamir2004], lattice coding is shown to achieve the capacity of the AWGN channel. Some other relevant results include [@ErezLitsynZamir]–[@NazerGastpar].

The rest of the paper is organized as follows: In Section II, we describe the system model for the three user Gaussian ICs and introduce the class of channels we analyze in this paper. In Section III, we introduce preliminaries on lattice coding and summarize some relevant results that we will use in this paper. In Section IV, we present the layered lattice coding approach for a symmetric three user Gaussian IC from a 