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Mung Chiang

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There are two major areas of research I am currently pursuing. One is the architectures and algorithms for broadband access networks. The other is nonlinear optimization of communication systems. Together they span a wide range of intellectual emphasis, from problems driven purely by theoretical curiosity to those motivated by pressing practical needs. These research activities are often combined with curriculum development projects, and sometimes pursued jointly with industrial partners to enhance the practical impacts of theoretical innovations.

1: Broadband Access Networks. A ubiquitous and broadband access to information makes significant impacts to the economics and ways of life in our society. Currently the access network often forms the bottleneck of end-to-end communication systems. Part of my research aims at providing a technological foundation to substantially enhance the data rate, ubiquity, and quality of information access networks. A particular focus is to further revolutionize the engineering of sending data along telephone wires, and another is to maximize user utilities in wireless local area networks. Achieving these goals requires novel theoretical foundations through the mathematical tools of optimization techniques. As described later, the other part of my research is on nonlinear optimization methods and their applications to communication systems, from deriving the fundamental limits of data transmission and compression to designing resource allocation algorithms for network efficiency and robustness. The theories and methodologies developed in 2A, 2B, and 2C provide rigorous and powerful approaches to the problems in 1A and 1B.

1A: FAST Copper. The goal of the FAST Copper Project is to provide an engineering foundation for ubiquitous 100 Mbps broadband access to everyone in the U.S. with a phone line. This goal will be achieved through two threads of research: dynamic and joint optimization of resources in Frequency, Amplitude, Space, and Time (FAST) to overcome the attenuation and crosstalk bottlenecks, and the integration of communication, networking, computation, modelling, and distributed information management and control for the multi-user twisted-pair network. To facilitate the equity of broadband information access, including access from rural and less-priviledged areas, we propose to further leverage the installed copper plant, which is by far the most ubiquitous access network in the U.S. To achieve data rates significantly higher than the current levels on low-twist unshielded telephone wires demands thinking about transmission on copper wires in a new way. This project combines innovative signal processing techniques with novel system architecture and network protocols to enable an access infrastructure that is both broadband and ubiquitous. This project is pursued jointly with Sandy Fraser of Fraser Research Institute and John Cioffi of Stanford University.

1B: Utility Maximization in Wireless LAN. Wireless local area networks have very promising commercial potential to be widely deployed and used in a variety of application scenarios, but also suffer from a number of significant engineering difficulties. There is no shortage of near term ideas about how to improve the delivery of wireless Internet services. What is missing is an optimization framework that captures utility at the level of networked applications, and makes it possible to figure out whether any particular incremental change at the medium access control or physical layer is positive or negative. The primary focus of this project is to identify the global user utility optimization to which embedded diversity coding for flexible rate-reliability tradeoff, together with scheduling for medium access, is the solution. This project is pursued jointly with Rob Calderbank of Princeton University.

2: Nonlinear Optimization of Communication Systems. Linear programming and other classical optimization techniques have found important applications in communication systems for several decades, notably several important special cases of network flow problems. Over the last few years, there has been a surge in research activities that utilize the power of recently developed nonlinear (often convex, and sometimes nonconvex) optimization theory to tackle a much wider scope of work in the analysis and design of communication systems, touching every 'layer' of the layered network architecture, and resulting in intellectual and practical impacts significantly beyond the earlier established frameworks. These research activities are driven by both new demands from the areas of communications and networking and new tools emerging from optimization theory.

The phrase 'nonlinear optimization of communication systems' in fact carries three different meanings. In the most straight forward way, an analysis or design problem in a communication system may be formulated as minimizing a cost or maximizing a utility function over a set of variables confined within a constraint set. In a more subtle approach, a given network protocol may be interpreted as a distributed algorithm solving an implicit global optimization problem. In yet another approach, the underlying theory of a network control method or a communication strategy may be generalized using nonlinear optimization techniques, thus extending the scope of applicability of the theory.

The recent developments of this nonlinear optimization framework have three distinctive characteristics. First, they integrate various protocol layers into a coherent framework, and provide a unified framework on disparate problems and algorithms in wired and wireless communication and networking. Second, the watershed between efficiently solvable problems and intractable ones is being recognized as 'convexity' instead of 'linearity'. Third, some of these theoretical advances are already being put into the practice of communication systems design in the industry.

2A: Optimization Methods in Information Theory. Nonlinear optimization techniques provide new tools to study the fundamental limits of data transmission and compression in information theory, in terms of new proof technqiues to prove channel capacity and rate distortion results, a deeper understanding of the duality and symmetry structures of these limits, and numerical methods to efficiently evaluate or bound important information theoretic quantities. We have used Geometric Programming for all these purposes in the single-user, memoryless case, and are investigating the multi-user case and systems with memory.

2B: Generalized Network Utility Maximization. Network utility maximization has provided an increasingly powerful framework for resource allocation in the Internet TCP/IP suite and various layers in wireless networks over the last few years. Compared to the traditional network linear flow problems, this framework utilizes many of the advances in nonlinear optimization and distributed algorithms. We have extended network utility maximization for wireless power control with QoS constraints and nonlinear objectives, for joint optimization of power control and rate allocation in several different cases in wireless cellular networks, for balancing the transport and physical layers in wireless ad hoc networks, and for non-selfish social utilities in sensor networks. We are investigating further extensions for Internet rate allocation among inelastic traffic from real-time applications and for the equilibrium and dynamic properties of heterogeneous TCP congestion control protocols. In general, we try to establish the approach of 'layering as optimization decomposition', where different functional modules in a communication system correspond to different decomposed subproblems of a generalized network utility maximization problem, and the layering interfaces correspond to some primal or dual variables.

2C: Quantifying Network X-ities. Architectures and algorithms in communication systems are not established only to enhance the efficiency of performance metrics in terms of throughput, latency, distortion, or energy efficiency, but also to enhance robustness in terms of important X-ities: evolvability, scalability, verifiability, manageability, deployability, survivability, adaptability ... Compared with standard performance metrics, these X-ities are much less well-understood, often without any theoretical foundations, quantitative frameworks, or even units of measurement. Yet X-ities are crucial if we are to analyze current network designs and optimize future ones properly. We have recently obtained initial results on quantifying some aspects of evolvability, and are continuing the development of a software called Evolvable Network Design END Tool. We are also investigating various specific cases where evolvability and scalability can be quantified, so that the important 'utilities' of a network in terms of X-ities can be optimized, and the optimal tradeoff between traditional performance metrics and X-ities metrics can be characterized.

Other Earlier Work. In addition to the recent results on the above topics, some of our other earlier work is summarized below.

Channel capacity and rate distortion with state information. Data transmission and compression with state information model various communication scenarios. We showed that the known results in eight special cases in fact all belong to a common form, and can be extended to the general case of two-sided state information. In the case of channels with state information at the transmitter, we formulated a new problem of tradeoff between sending pure information and helping receiver's state estimation. For additive Gaussian noise channels, we completed characterized the optimal tradeoff region between channel capacity and estimation error, with a converse proof and an achievability scheme by power allocation between two extreme signalling strategies.

Geometric programming for communication systems. Geometric programming is a class of nonlinear optimization invented in 1960s and studied primarily for mechanical and chemical engineering problems in 1970s. As part of the recent revival of large scale, distributed algorithms and new applications of GP for electrical engineering problems, we showed how GP can be used to solve basic information theory problems, simple queuing system optimization, many network resource allocation problems such as wireless power control, congestion control for wired network rate allocation, and cross-layer design in ad hoc networks. We also obtained the reasons why GP are so applicable to communication systems: for stochastic models this is because many large deviations bounds can be obtained by GP, and for deterministic models this is because proportional allocation, and robust and stable economic equilibrium can be obtained by GP.

Convex optimization of resource allocation. We also showed how to turn other difficult nonlinear resource allocation problems into, or approximate them by, convex optimization with highly efficient and sometimes distributed solution methods for global optimality. Examples range from packet switch architecture to ultra-wideband receiver design.