---
abstract: 'The paper studies a class of three user Gaussian interference channels. A new layered lattice coding scheme is introduced as a transmission strategy. The use of lattice codes allows for an “alignment" of the interference observed at each receiver. The layered lattice coding is shown to achieve more than one degree of freedom for a class of interference channels and also achieves rates which are better than the rates obtained using the Han-Kobayashi coding scheme.'
author:
- 'Sriram Sridharan, Amin Jafarian, Sriram Vishwanath, Syed A. Jafar and Shlomo Shamai (Shitz) [^1][^2][^3]'
nocite:
- '[@Benzel1979; @HanKobayashi1981; @Sato1981; @GamalCosta1982; @Costa1985; @EtkinTseWang2007; @ShangKramerChen2007; @AnnapureddyVeeravalli]'
- '[@AnnapureddyVeeravalli]'
- '[@CadambeJafarWirelessXNetworks; @CadambeJafarWirelessNetworks]'
- '[@Poltyrev]'
- '[@ZamirShamaiErez; @ErezShamaiZamir; @NamElGamal; @KrithivasanPradhan; @NazerGastparAllerton2007]'
title: A Layered Lattice Coding Scheme for a Class of Three User Gaussian Interference Channels
---

Introduction
============

Determining the capacity region of the Gaussian interference channel (IC) has been a long standing open problem. Several achievable regions and outer bounds have been obtained over the last three decades [@Carleial1978]–[@MotahariKhandani]. Recently, it has been shown in [@EtkinTseWang2007] that the Han-Kobayashi achievable region [@HanKobayashi1981] achieves the capacity region of the two user Gaussian IC to within one bit. However, this result does not extend to 