Achievable Rates for $K$-User Gaussian Interference Channels

The aim of this paper is to study the achievable rates for a K-user Gaussian interference channel (G-IFC) for any signal-to-noise ratio using a combination of lattice and algebraic codes. Lattice codes are first used to transform the 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. This 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 nontrivial rates for the original G-IFC.

[1]  Michael Gastpar,et al.  Compute-and-Forward: Harnessing Interference Through Structured Codes , 2009, IEEE Transactions on Information Theory.

[2]  Gerhard Kramer,et al.  A New Outer Bound and the Noisy-Interference Sum–Rate Capacity for Gaussian Interference Channels , 2007, IEEE Transactions on Information Theory.

[3]  Simon Litsyn,et al.  Lattices which are good for (almost) everything , 2005, IEEE Transactions on Information Theory.

[4]  Amir K. Khandani,et al.  On the Degrees of Freedom of the 3-user Gaussian interference channel: The symmetric case , 2009, 2009 IEEE International Symposium on Information Theory.

[5]  M. Gastpar,et al.  The case for structured random codes: Beyond linear models , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[6]  Gerhard Kramer,et al.  Outer bounds on the capacity of Gaussian interference channels , 2004, IEEE Transactions on Information Theory.

[7]  Shlomo Shamai,et al.  A layered lattice coding scheme for a class of three user Gaussian interference channels , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[8]  Aria Nosratinia,et al.  The multiplexing gain of wireless networks , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[9]  Amir K. Khandani,et al.  Real Interference Alignment , 2010, ArXiv.

[10]  Rudolf Ahlswede,et al.  Multi-way communication channels , 1973 .

[11]  Venugopal V. Veeravalli,et al.  Gaussian Interference Networks: Sum Capacity in the Low-Interference Regime and New Outer Bounds on the Capacity Region , 2008, IEEE Transactions on Information Theory.

[12]  Te Sun Han,et al.  A new achievable rate region for the interference channel , 1981, IEEE Trans. Inf. Theory.

[13]  Abhay Parekh,et al.  The Approximate Capacity of the Many-to-One and One-to-Many Gaussian Interference Channels , 2008, IEEE Transactions on Information Theory.

[14]  Sriram Vishwanath,et al.  Gaussian interference networks: Lattice alignment , 2010, 2010 IEEE Information Theory Workshop on Information Theory (ITW 2010, Cairo).

[15]  Hiroshi Sato,et al.  The capacity of the Gaussian interference channel under strong interference , 1981, IEEE Trans. Inf. Theory.

[16]  Syed Ali Jafar,et al.  Interference Alignment and Degrees of Freedom of the $K$-User Interference Channel , 2008, IEEE Transactions on Information Theory.

[17]  Sriram Vishwanath,et al.  Capacity of Symmetric K-User Gaussian Very Strong Interference Channels , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[18]  Erik Ordentlich,et al.  The Degrees-of-Freedom of the $K$-User Gaussian Interference Channel Is Discontinuous at Rational Channel Coefficients , 2009, IEEE Transactions on Information Theory.

[19]  Erik Ordentlich,et al.  On the Degrees-of-Freedom of the K-user Gaussian interference channel , 2009, 2009 IEEE International Symposium on Information Theory.

[20]  Amir K. Khandani,et al.  Capacity bounds for the Gaussian Interference Channel , 2008, 2008 IEEE International Symposium on Information Theory.

[21]  S. Vishwanath,et al.  Algebraic lattice alignment for K-user interference channels , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[22]  Claude E. Shannon,et al.  Two-way Communication Channels , 1961 .

[23]  Hua Wang,et al.  Gaussian Interference Channel Capacity to Within One Bit , 2007, IEEE Transactions on Information Theory.

[24]  W. Fischer,et al.  Sphere Packings, Lattices and Groups , 1990 .

[25]  Uri Erez,et al.  Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding , 2004, IEEE Transactions on Information Theory.

[26]  Terence Tao,et al.  Additive combinatorics , 2007, Cambridge studies in advanced mathematics.

[27]  Hans-Andrea Loeliger,et al.  Averaging bounds for lattices and linear codes , 1997, IEEE Trans. Inf. Theory.

[28]  Shlomo Shamai,et al.  Interference alignment on the deterministic channel and application to fully connected AWGN interference networks , 2008, 2008 IEEE Information Theory Workshop.

[29]  Aydano B. Carleial,et al.  A case where interference does not reduce capacity (Corresp.) , 1975, IEEE Trans. Inf. Theory.