Minimum Cost Distributed Source Coding Over a Network

This paper considers the problem of transmitting multiple compressible sources over a network at minimum cost. The aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be transmitted so that the cost of the transmission is minimal. We consider networks with capacity constraints and linear cost functions. The problem is complicated by the fact that the description of the feasible rate region of distributed source coding problems typically has a number of constraints that is exponential in the number of sources. This renders general purpose solvers inefficient. We present a framework in which these problems can be solved efficiently by exploiting the structure of the feasible rate regions coupled with dual decomposition and optimization techniques such as the subgradient method and the proximal bundle method

Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach

The classical theoretical framework for communication networks is based on the simplifying assumption that each message to be sent is known to a single transmitter and intended for a single receiver. Modern communication protocols reflect this framework by treating the physical layer as a network of individual links. However, this wireline view of wireless communications fails to account for the heterogeneous nature of network demands, consisting of both unicast and multicast services, and can fail to leverage the inherent broadcast advantage of the wireless medium. This thesis extends the classical framework of a private-message interface to the physical layer to one with both private and common messages. A key difficulty, in both the description and analysis of a communication model with general messages sets, is that there are combinatorially many message possibilities. With order-theoretic language and tools from combinatorial optimization and graphical models, we develop a general framework for characterizing the fundamental limits of information transfer over large many-to-one (multiple access) and one-to-many (broadcast) communication channels with general message sets. In particular, achievable regions are proposed for arbitrary such channels. For the multiple-access channel, the achievable region is optimal, and the order-theoretic perspective both unifies and extends previous results. For the broadcast channel, the region is specialized to an inner bound to the Degree of Freedom region, a setting where it is provably optimal in select cases. This thesis provides fresh insights into the long-standing random coding technique of superposition coding to arrive at these results. Governing constraints on reliable communication through superposition coding are shown to be polymatroidal over a lattice of subsets that may not be the boolean lattice of all subsets. Permissible input distributions for superposition coding are concisely characterized through directed graphical models of conditional dependencies. The two-user interference channel is also addressed, where the state-of-the art is extended from the case with two private messages to one with an additional common message

Achievable schemes for cost/performance trade-offs in networks

A common pattern in communication networks (both wired and wireless) is the collection of distributed state information from various network elements. This network state is needed for both analytics and operator policy and its collection consumes network resources, both to measure the relevant state and to transmit the measurements back to the data sink. The design of simple achievable schemes are considered with the goal of minimizing the overhead from data collection and/or trading off performance for overhead. Where possible, these schemes are compared with the optimal trade-off curve. The optimal transmission of distributed correlated discrete memoryless sources across a network with capacity constraints is considered first. Previously unreported properties of jointly optimal compression rates and transmission schemes are established. Additionally, an explicit relationship between the conditional independence relationships of the distributed sources and the number of vertices for the Slepian-Wolf rate region is given. Motivated by recent work applying rate-distortion theory to computing the optimal performance-overhead trade-off, the use of distributed scalar quantization is investigated for lossy encoding of state, where a central estimation officer (CEO) wishes to compute an extremization function of a collection of sources. The superiority of a simple heterogeneous (across users) quantizer design over the optimal homogeneous quantizer design is proven. Interactive communication enables an alternative framework where communicating parties can send messages back-and-forth over multiple rounds. This back-and-forth messaging can reduce the rate required to compute an extremum/extrema of the sources at the cost of increased delay. Again scalar quantization followed by entropy encoding is considered as an achievable scheme for a collection of distributed users talking to a CEO in the context of interactive communication. The design of optimal quantizers is formulated as the solution of a minimum cost dynamic program. It is established that, asymptotically, the costs for the CEO to compute the different extremization functions are equal. The existence of a simpler search space, which is asymptotically sufficient for minimizing the cost of computing the selected extremization functions, is proven.Ph.D., Electrical Engineering -- Drexel University, 201

Submodularity and Its Applications in Wireless Communications

This monograph studies the submodularity in wireless communications and how to use it to enhance or improve the design of the optimization algorithms. The work is done in three different systems. In a cross-layer adaptive modulation problem, we prove the submodularity of the dynamic programming (DP), which contributes to the monotonicity of the optimal transmission policy. The monotonicity is utilized in a policy iteration algorithm to relieve the curse of dimensionality of DP. In addition, we show that the monotonic optimal policy can be determined by a multivariate minimization problem, which can be solved by a discrete simultaneous perturbation stochastic approximation (DSPSA) algorithm. We show that the DSPSA is able to converge to the optimal policy in real time. For the adaptive modulation problem in a network-coded two-way relay channel, a two-player game model is proposed. We prove the supermodularity of this game, which ensures the existence of pure strategy Nash equilibria (PSNEs). We apply the Cournot tatonnement and show that it converges to the extremal, the largest and smallest, PSNEs within a finite number of iterations. We derive the sufficient conditions for the extremal PSNEs to be symmetric and monotonic in the channel signal-to-noise (SNR) ratio. Based on the submodularity of the entropy function, we study the communication for omniscience (CO) problem: how to let all users obtain all the information in a multiple random source via communications. In particular, we consider the minimum sum-rate problem: how to attain omniscience by the minimum total number of communications. The results cover both asymptotic and non-asymptotic models where the transmission rates are real and integral, respectively. We reveal the submodularity of the minimum sum-rate problem and propose polynomial time algorithms for solving it. We discuss the significance and applications of the fundamental partition, the one that gives rise to the minimum sum-rate in the asymptotic model. We also show how to achieve the omniscience in a successive manner