Interference and X Networks with Noisy Cooperation and Feedback

The Gaussian $K$-user interference and $M\times K$ X channels are investigated with no instantaneous channel state information (CSI) at transmitters. First, it is assumed that the CSI is fed back to all nodes after a finite delay (delayed CSIT), and furthermore, the transmitters operate in full-duplex mode, i.e., they can transmit and receive simultaneously. Achievable results are obtained on the degrees of freedom (DoF) of these channels under the above assumption. It is observed that, in contrast with no CSIT and full CSIT models, when CSIT is delayed, the achievable DoFs for both channels with full-duplex transmitter cooperation are greater than the best available achievable results on their DoF without transmitter cooperation. Our results are the first to show that the full-duplex transmitter cooperation can potentially improve the channel DoF with delayed CSIT. Then, $K$-user interference and $K\times K$ X channels are considered with output feedback, wherein the channel output of each receiver is causally fed back to its corresponding transmitter. Our achievable results with output feedback demonstrate strict DoF improvements over those with the full-duplex delayed CSIT when $K>5$ in the $K$-user interference channel and $K>2$ in the $K\times K$ X channel. Next, the combination of delayed CSIT and output feedback, known as Shannon feedback, is studied and strictly higher DoFs compared to the output feedback model are achieved in the $K$-user interference channel when K=5 or $K>6$, and in the $K\times K$ X channel when $K>2$. Although being strictly greater than 1 and increasing with size of the networks, the achievable DoFs in all the models studied in this paper approach limiting values not greater than 2.Comment: 53 pages, 15 figures; Submitted to IEEE Transactions on Information Theory, May 2012. To be presented in part in ISIT 2012, Cambridge, MA, US

Secure GDoF of the Z-channel with Finite Precision CSIT: How Robust are Structured Codes?

Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages for secure communication in an interference network, e.g., structured jamming signals based on lattice codes may allow a receiver to decode the sum of the jamming signal and the signal being jammed, even though they cannot be separately resolved due to secrecy constraints, subtract the aggregate jammed signal, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself -- a Z interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF region of the Z interference channel is obtained as a byproduct of the analysis.Comment: 34 pages, 10 figure

Online edge caching and wireless delivery in fog-aided networks

Multimedia content is the significant fraction of transferred data over the wireless medium in the modern cellular and wireless communication networks. To improve the quality of experience perceived by users, one promising solution is to push the most popular contents as close as to users, also known as the edge of network. Storing content at the edge nodes (ENs) or base stations (BSs) is called caching . In Fog Radio Access Network (F-RAN), each EN is equipped with a cache as well as a fronthaul connection to the content server. Among the new design problems raised by the outlined scenarios, two key issues are addressed in this dissertation: 1) How to utilize cache and fronthaul resources while taking into account the wireless channel impairments; 2) How to incorporate the time-variability of popular set in the performance evaluation of F-RAN. These aspects are investigated by using information-theoretic models, obtaining fundamental insights that have been corroborated by various illustrative examples. To address point 1), two scenarios are investigated. First, a single-cell scenario with two transmitters is considered. A fog-aided small-cell BS as one of the transmitters and a cloud-aided macro-cell BS as the second transmitter collaborate with each other to send the requested content over a partially connected wireless channel. The intended and interference channels are modeled by erasure channels. Assuming a static set of popular contents, offline caching maps the library of files to cached contents stored at small-cell BS such that the cache capacity requirement is met. The delivery time per bit (DTB) is adopted as a measure of the coding latency, that is, the duration of the transmission block, required for reliable delivery. It is proved that optimal DTB is a linear decreasing function of cache capacity as well as inversely proportional with capacity of fronthaul link. In the second scenario, the same single-cell model is used with the only caveat that the set of popular files is time-varying. In this case, online caching maps the library of files to cached contents at small-cell BS. Thanks to availability of popular set at macro-BS, the DTB is finite and has upper and lower bounds which are functions of system resources i.e., cache and fronthaul link capacities. As for point 2), the model is comprised of an arbitrary number of ENs and users connected through an interference-limited wireless channel at high-SNR regime. All equally important ENs are benefited from cache capacity as well as fronthaul connection to the content server. The time-variability of popular set necessitates online caching to enable ENs keep track of changes in the popular set. The analysis is centered on the characterization of the long-term Normalized Delivery Time (NDT), which captures the temporal dependence of the coding latencies accrued across multiple time slots in the high-SNR regime. Online edge caching and delivery schemes based on reactive and proactive caching principles are investigated for both serial and pipelined transmission modes across fronthaul and edge segments. The outcome of analytical results provides a controversial view of contemporary research on the edge caching. It is proved that with a time-varying set of popular files, the capacity of fronthaul link between ENs and content server set a fundamental limit on the system performance. This is due to the fact that the original information source is content server and the only way to retrieve information is via fronthaul links. While edge caching can provide some gains in term of reduced latency, the gain diminishes as a result of the fact that the cached content is prone to be outdated with time-varying popularity

Degrees of freedom of wireless interference network

Wireless communication systems are different from the wired systems mainly in three aspects: fading, broadcast, and superposition. Wireless communication networks, and multi-user communication networks in general, have not been well understood from the information-theoretic perspective: the capacity limits of many multi-user networks are not known. For example, the capacity region of a two-user single-antenna interference channel is still not known, though recent result can bound the region up to a constant value. Characterizing the capacity limits of multi-user multiple-input multiple-output (MIMO) interference network is usually even more difficult than the single antenna setup. To alleviate the difficulty in studying such networks, the concept of degrees of freedom (DoF) has been adopted, which captures the first order behavior of the capacities or capacity regions. One important technique developed recently for quantifying the DoF of multi-user networks is the so-called interference alignment. The purpose of interference alignment is to design the transmit signals structurally so that the interference signals from multiple interferers are aligned to reduce the signal dimensions occupied by interference. In this thesis, we mainly study two problems related to DoF and interference alignment: 1) DoF region of MIMO full interference channel (FIC) and Z interference channel (ZIC) with reconfigurable antennas, and 2) the DoF region of an interference network with general message demands. For the first problem, we derive the outer bound on the DoF region and show that it is achievable via time-sharing or beamforming except for one special case. As to this particular special case, we develop a systematic way of constructing the DoF-achieving nulling and beamforming matrices. Our results reveal the potential benefit of using the reconfigurable antenna in MIMO FIC and ZIC. In addition, the achievability scheme has an interesting space-frequency interpretation. For the second problem, we derive the DoF region of a single antenna interference network with general message demands, which includes the multiple unicasts and multiple multicasts as special cases. We perform interference alignment using multiple base vectors and align the interference at each receiver to its largest interferer. Furthermore, we show that the DoF region is determined by a subset of receivers, and the DoF region can be achieved by considering a smaller number of interference alignment constraints so as to reduce the number of time expansion. Finally, as a related research topic, we also include a result on the average throughput of a MIMO interference channel with single-user detector at receivers and without channel state information at transmitters. We present a piecewise linear approximation of the channel throughput under weak, moderate and strong interference regimes. Based on that we determine the optimal number of streams that a transmitter should use for different interference levels