Ph.D. 2003, Stanford University

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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.

There are three research projects I am pursuing in the area of nonlinear optimization of communication systems. One concerns the information theoretic limits of data transmission and compression, another generalizes network utility maximization, and the third advocates a new paradigm of quantifying the X-ities metrics in addition to the traditional performance metrics.

**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.