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.

We pose a network-wide scheduling problem for cellular wireless networks in which users are capable of being served by several schedulers on the downlink, though not jointly. We present a distributed algorithm, with limited communication across servers, that solves this problem optimally, in that it gives the network-wide proportional fair solution. An idealized version is presented first, in which all users are capable of being served by all schedulers and in which all the decision-making takes place among the schedulers alone. A practical version is also presented, in which users play a role in choosing their servers and servers decide how to allocate resources to the users that choose them. The practical version can achieve the same optimum as the idealized one and gives gains up to 60% in typical network deployments. This version can be implemented on any wireless technology to achieve optimal network scheduling. We have focused particularly on LTE, HSPA and 1xEV-DO and the first commercial deployment will soon occur on the 1xEV-DO system, based on the 3GPP2 standard, under the rubric of `Smart Networks.

This paper presents outerbounds for the two-user Gaussian fading broadcast channel. These outerbounds are based on Costa's entropy power inequality (Costa-EPI) and are formulated mathematically as a feasibility problem. For classes of the two-user Gaussian fading broadcast channel where the outerbound is found to have a feasible solution, we find conditions under which a suitable inner and outer bound meet. For all such cases, this paper provides a partial characterization of the capacity region of the Gaussian two-user fading broadcast channel.

Determining the capacity of networks has been a long-standing issue of interest in the literature. Although for multi-source multi-sink networks it is known that using network coding is advantageous over traditional routing, finding the best coding strategy is not trivial in general. Among different classes of codes that could be potentially used in a network, linear codes due to their simplicity are of particular interest. Although linear codes are proven to be sub-optimal in general, in some cases such as the multicast scenario they achieve the cut-set bound. Since determining the capacity of a network is closely related to the characterization of the entropy region of all its random variables, if one is interested in finding the best linear solution for a network, one should find the region of all linear representable entropy vectors of that network. With this approach, we study the scalar linear solutions over arbitrary network problems with two sources. We explicitly calculate this region for small number of variables and suggest a method for larger networks through finding the best scalar linear solution to a storage problem as an example of practical interest.

This paper extends the literature on interference alignment to more certain classes of deterministic channels which incorporate non-linear input-output relationships. It is found that the concept of alignment extends naturally to these deterministic interference channels, and in many cases, the achieved degrees of freedom (DoF) can be shown to be optimal. A key contribution of the paper is the connection it builds between interference alignment and number theory.

This paper studies the K > 2 user cognitive radio network. In this paper, there are one licensed transmit-receive pair and K - 1 cognitive transmit-receive pairs wishing to communicate simultaneously. For the case of a class of ¿very strong¿ interference channels, this paper shows that all users can simultaneously communicate as if all cross-channels in the interference network were absent.

In this paper, we investigate upper and lower bounds on the capacity of two-user fading broadcast channels where one of the users has a constant (non-fading) channel. We use the Costa entropy power inequality (EPI) along with an optimization framework to derive upper bounds on the sum-capacity and superposition coding to obtain lower bounds on the sum-rate for this channel. For this fading broadcast channel where one channel is constant, we find that the upper and lower bounds meet under special cases, and in general, we show that the achievable sum-rate comes within a constant of the outer bound.

This paper studies a symmetricKuser Gaussian interference channel withKtransmitters andKreceivers. A "very strong" interference regime is derived for this channel setup. A "very strong" interference regime is one where the capacity region of the interference channel is the same as the capacity region of the channel with no interference. In this regime, the interference can be perfectly canceled by all the receivers without incurring any rate penalties. A "very strong" interference condition for an example symmetricKuser deterministic interference channel is also presented.