In communications, the multiuser Gaussian channel model is commonly used to capture fundamental features of a wireless channel. Over the past couple of decades, study of multiuser Gaussian networks has been an active area of research for many scientists. However, due to the complexity of the Gaussian model, except for the simplest networks such as the one-to-many Gaussian broadcast channel and the many-to-one Gaussian multiple access channel, the capacity region of most Gaussian networks is still unknown. For example, even the capacity of a three node Gaussian relay network, in which a point to point communication is assisted by one helper (relay), has been open for more than 30 years.To make further progress, we present a linear finite-field deterministic channel model which is analytically simpler than the Gaussian model but still captures two key wireless channels: broadcast and superposition. The noiseless nature of this model allows us to focus on the interaction between signals transmitted from different nodes of the network rather than background noise of the links.Then, we consider a model for a wireless relay network with nodes connected by such 1 deterministic channels, and present an exact characterization of the end-to-end capacity when there is a single source and a single destination and an arbitrary number of relay nodes. This result is a natural generalization of the celebrated max-flow min-cut theorem for wireline networks. We also characterize the multicast capacity of linear finite-field deterministic relay networks when one source is multicasting the same information to multiple destinations, with the help of arbitrary number of relays.Next, we use the insights obtained from the analysis of the deterministic model and present an achievable rate for general Gaussian relay networks. We show that the achievable rate is within a constant number of bits from the information-theoretic cut-set upper bound on the capacity of these networks. This constant depends on the number of nodes in the network, but not the values of the channel gains. Therefore, we uniformly characterize the capacity of Gaussian relay networks within a constant number of bits, for all channel parameters. For example, we approximate the unknown capacity of the three node Gaussian relay channel within one bit/sec/Hz.Finally, we illustrate that the proposed deterministic approach is a general tool and can be applied to other problems in wireless network information theory. In particular we demonstrate its application to make progress in two other problems: two-way relay channel and relaying with side information.

Abstract-How can we optimally trade extra computing power to reduce the communication load in distributed computing? We answer this question by characterizing a fundamental tradeoff between computation and communication in distributed computing, i.e., the two are inversely proportional to each other.More specifically, a general distributed computing framework, motivated by commonly used structures like MapReduce, is considered, where the overall computation is decomposed into computing a set of "Map" and "Reduce" functions distributedly across multiple computing nodes. A coded scheme, named "Coded Distributed Computing" (CDC), is proposed to demonstrate that increasing the computation load of the Map functions by a factor of r (i.e., evaluating each function at r carefully chosen nodes) can create novel coding opportunities that reduce the communication load by the same factor.An information-theoretic lower bound on the communication load is also provided, which matches the communication load achieved by the CDC scheme. As a result, the optimal computation-communication tradeoff in distributed computing is exactly characterized.Finally, the coding techniques of CDC is applied to the Hadoop TeraSort benchmark to develop a novel CodedTeraSort algorithm, which is empirically demonstrated to speed up the overall job execution by 1.97× -3.39×, for typical settings of interest.

Abstract-We consider a basic cache network, in which a single server is connected to multiple users via a shared bottleneck link. The server has a database of files (content). Each user has an isolated memory that can be used to cache content in a prefetching phase. In a following delivery phase, each user requests a file from the database, and the server needs to deliver users' demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of the rate-memory tradeoff for this problem, by deriving both the minimum average rate (for a uniform file popularity) and the minimum peak rate required on the bottleneck link for a given cache size available at each user. In particular, we propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among user demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without any coordination.

It is shown that in the K-user interference channel, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in dB scale), then the simple scheme of using point to point Gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise at every receiver (in short, TIN scheme) achieves all points in the capacity region to within a constant gap. The generalized degrees of freedom (GDoF) region under this condition is a polyhedron, which is shown to be fully achieved by the same scheme, without the need for time-sharing. The results are proved by first deriving a polyhedral relaxation of the GDoF region achieved by TIN, then providing a dual characterization of this polyhedral region via the use of potential functions, and finally proving the optimality of this region in the desired regime.

We consider a system, comprising a library of N files (e.g., movies) and a wireless network with KT transmitters, each equipped with a local cache of size of MT files, and KR receivers, each equipped with a local cache of size of MR files. Each receiver will ask for one of the N files in the library, which needs to be delivered. The objective is to design the cache placement (without prior knowledge of receivers' future requests) and the communication scheme to maximize the throughput of the delivery. In this setting, we show that the sum degrees-of-freedom (sum-DoF) of min, KR is achievable, and this is within a factor of 2 of the optimum, under one-shot linear schemes. This result shows that (i) the one-shot sum-DoF scales linearly with the aggregate cache size in the network (i.e., the cumulative memory available at all nodes), (ii) the transmitters' caches and receivers' caches contribute equally in the one-shot sum-DoF, and (iii) caching can offer a throughput gain that scales linearly with the size of the network.To prove the result, we propose an achievable scheme that exploits the redundancy of the content at transmitters' caches to cooperatively zero-force some outgoing interference, and availability of the unintended content at the receivers' caches to cancel (subtract) some of the incoming interference. We develop a particular pattern for cache placement that maximizes the overall gains of cache-aided transmit and receive interference cancellations. For the converse, we present an integer optimization problem which minimizes the number of communication blocks needed to deliver any set of requested files to the receivers. We then provide a lower bound on the value of this optimization problem, hence leading to an upper bound on the linear one-shot sum-DoF of the network, which is within a factor of 2 of the achievable sum-DoF.