The Ergodic Capacity of Phase-Fading Interference Networks

We identify the role of equal strength interference links as bottlenecks on the ergodic sum capacity of a $K$ user phase-fading interference network, i.e., an interference network where the fading process is restricted primarily to independent and uniform phase variations while the channel magnitudes are held fixed across time. It is shown that even though there are $K(K-1)$ cross-links, only about $K/2$ disjoint and equal strength interference links suffice to determine the capacity of the network regardless of the strengths of the rest of the cross channels. This scenario is called a \emph{minimal bottleneck state}. It is shown that ergodic interference alignment is capacity optimal for a network in a minimal bottleneck state. The results are applied to large networks. It is shown that large networks are close to bottleneck states with a high probability, so that ergodic interference alignment is close to optimal for large networks. Limitations of the notion of bottleneck states are also highlighted for channels where both the phase and the magnitudes vary with time. It is shown through an example that for these channels, joint coding across different bottleneck states makes it possible to circumvent the capacity bottlenecks.Comment: 19 page

Ergodic Interference Alignment

This paper develops a new communication strategy, ergodic interference alignment, for the K-user interference channel with time-varying fading. At any particular time, each receiver will see a superposition of the transmitted signals plus noise. The standard approach to such a scenario results in each transmitter-receiver pair achieving a rate proportional to 1/K its interference-free ergodic capacity. However, given two well-chosen time indices, the channel coefficients from interfering users can be made to exactly cancel. By adding up these two observations, each receiver can obtain its desired signal without any interference. If the channel gains have independent, uniform phases, this technique allows each user to achieve at least 1/2 its interference-free ergodic capacity at any signal-to-noise ratio. Prior interference alignment techniques were only able to attain this performance as the signal-to-noise ratio tended to infinity. Extensions are given for the case where each receiver wants a message from more than one transmitter as well as the "X channel" case (with two receivers) where each transmitter has an independent message for each receiver. Finally, it is shown how to generalize this strategy beyond Gaussian channel models. For a class of finite field interference channels, this approach yields the ergodic capacity region.Comment: 16 pages, 6 figure, To appear in IEEE Transactions on Information Theor

Channel Aided Interference Alignment

Interference alignment (IA) techniques mostly attain their degrees of freedom (DoF) benefits as the number of channel extensions tends to infinity. Intuitively, the more interfering signals that need to be aligned, the larger the number of dimensions needed to align them. This requirement poses a major challenge for IA in practical systems. This work evaluates the necessary and sufficient conditions on channel structure of a fully connected interference network with time-varying fading to make perfect IA feasible within limited number of channel extensions. We propose a method based on the obtained conditions on the channel structure to achieve perfect IA. For the case of $3$ user interference channel, it is shown that only one condition on channel coefficients is required to make perfect IA feasible at all receivers. IA feasibility literature have mainly focused on network topology so far. In contrast, derived channel aiding conditions in this work can be considered as the perfect IA feasibility conditions on channel structure.Comment: 20 pages, 4 figure. arXiv admin note: text overlap with arXiv:0901.4379 by other author

Interference Mitigation in Large Random Wireless Networks

A central problem in the operation of large wireless networks is how to deal with interference -- the unwanted signals being sent by transmitters that a receiver is not interested in. This thesis looks at ways of combating such interference. In Chapters 1 and 2, we outline the necessary information and communication theory background, including the concept of capacity. We also include an overview of a new set of schemes for dealing with interference known as interference alignment, paying special attention to a channel-state-based strategy called ergodic interference alignment. In Chapter 3, we consider the operation of large regular and random networks by treating interference as background noise. We consider the local performance of a single node, and the global performance of a very large network. In Chapter 4, we use ergodic interference alignment to derive the asymptotic sum-capacity of large random dense networks. These networks are derived from a physical model of node placement where signal strength decays over the distance between transmitters and receivers. (See also arXiv:1002.0235 and arXiv:0907.5165.) In Chapter 5, we look at methods of reducing the long time delays incurred by ergodic interference alignment. We analyse the tradeoff between reducing delay and lowering the communication rate. (See also arXiv:1004.0208.) In Chapter 6, we outline a problem that is equivalent to the problem of pooled group testing for defective items. We then present some new work that uses information theoretic techniques to attack group testing. We introduce for the first time the concept of the group testing channel, which allows for modelling of a wide range of statistical error models for testing. We derive new results on the number of tests required to accurately detect defective items, including when using sequential `adaptive' tests.Comment: PhD thesis, University of Bristol, 201

On Precoding for Constant K-User MIMO Gaussian Interference Channel with Finite Constellation Inputs

This paper considers linear precoding for constant channel-coefficient $K$-User MIMO Gaussian Interference Channel (MIMO GIC) where each transmitter-$i$ (Tx-$i$), requires to send $d_i$ independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution, to receiver-$i$ (Rx-$i$) for $i=1,2,\cdots,K$. We define the maximum rate achieved by Tx-$i$ using any linear precoder, when the interference channel-coefficients are zero, as the signal to noise ratio (SNR) tends to infinity to be the Constellation Constrained Saturation Capacity (CCSC) for Tx-$i$. We derive a high SNR approximation for the rate achieved by Tx-$i$ when interference is treated as noise and this rate is given by the mutual information between Tx-$i$ and Rx-$i$, denoted as $I[X_i;Y_i]$. A set of necessary and sufficient conditions on the precoders under which $I[X_i;Y_i]$ tends to CCSC for Tx-$i$ is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Further, we propose gradient-ascent based algorithms to optimize the sum-rate achieved by precoding with finite constellation inputs and treating interference as noise. Simulation study using the proposed algorithms for a 3-user MIMO GIC with two antennas at each node with $d_i=1$ for all $i$, and with BPSK and QPSK inputs, show more than 0.1 bits/sec/Hz gain in the ergodic sum-rate over that yielded by precoders obtained from some known IA algorithms, at moderate SNRs.Comment: 15 pages, 9 figure

Degrees of Freedom of Time Correlated MISO Broadcast Channel with Delayed CSIT

We consider the time correlated multiple-input single-output (MISO) broadcast channel where the transmitter has imperfect knowledge on the current channel state, in addition to delayed channel state information. By representing the quality of the current channel state information as P^-{\alpha} for the signal-to-noise ratio P and some constant {\alpha} \geq 0, we characterize the optimal degree of freedom region for this more general two-user MISO broadcast correlated channel. The essential ingredients of the proposed scheme lie in the quantization and multicasting of the overheard interferences, while broadcasting new private messages. Our proposed scheme smoothly bridges between the scheme recently proposed by Maddah-Ali and Tse with no current state information and a simple zero-forcing beamforming with perfect current state information.Comment: revised and final version, to appear in IEEE transactions on Information Theor

Delay-rate tradeoff in ergodic interference alignment

Ergodic interference alignment, as introduced by Nazer et al (NGJV), is a technique that allows high-rate communication in n-user interference networks with fast fading. It works by splitting communication across a pair of fading matrices. However, it comes with the overhead of a long time delay until matchable matrices occur: the delay is q^n^2 for field size q. In this paper, we outline two new families of schemes, called JAP and JAP-B, that reduce the expected delay, sometimes at the cost of a reduction in rate from the NGJV scheme. In particular, we give examples of good schemes for networks with few users, and show that in large n-user networks, the delay scales like q^T, where T is quadratic in n for a constant per-user rate and T is constant for a constant sum-rate. We also show that half the single-user rate can be achieved while reducing NGJV's delay from q^n^2 to q^(n-1)(n-2). This extended version includes complete proofs and more details of good schemes for small n.Comment: Extended version of a paper presented at the 2012 International Symposium on Information Theory. 7 pages, 1 figur