Essay Summary of Statement of Purpose
Statement of Purpose The elegance of communication theory is irresistible, for it incorporates the beauty of mathematics with the rapid advancing nature of communication systems. Wireless Foundations of UC Berkeley is my first choice to do groundbreaking research. I would like to begin with self-motivated research proposal for network information theory to show my enthusiasm. Research Proposal for Network Information Theory (NIT) There are several different methodologies to address network with information theory: 1. General wireless network described by probabilistic channel statistics.
The capacity regions of many single-hop networks, such as broadcast channel (BC), relay channel (RC) and interference channel (IC), have been open for many years. But this is not the end of the world. We still need to explore suboptimal coding schemes and extend them to multi-hop networks to improve current technologies. In “Noisy Network Coding”, Lim, Kim, El Gamal, Chung 1)apply compress-forward coding scheme to multi-hop network; 2)decode the compression index without Wyner-Ziv binning; 3)simultaneous decode over long blocks, which successfully extended the achievability of compress-forward coding scheme to general networks.
I think the price for such a general model is complexity. For example, noise and interference superpose at the receiver. Prof. Tse said that we lack weapon in arsenal to solve general model and suggested deterministic approach in 2007. 1. Gaussian network with deterministic approach. Avestimehr, Diggavi and Tse proposed the deterministic channel model to capture the key properties of wireless networks i. e. channel strength, broadcast and superposition. I think the approach originates from interference channel(IC) where El Gamal-Costa IC approximated Gaussian IC.
This novel methodology has lots of followers. 1. Wired network with entropy region. Besides wireless network, wired network is of practical importance. It has been proved that capacity can be obtained via optimization on entropy region with topology constrain. Entropy region has very good natures, such as it is a cone. Theorists playing with this model, including Yeung, Hassibi and Effros also proposed network coding and solved the problem for multi-user multicast erasure network. One interesting fact is that the proofs of network coding and deterministic approach are similar in style.
In spite of the great effort from information theory community, there are still defects in NIT: 1) Delay and burstiness have not been jointly modeled yet, which are regarded as the principle barrier in “Information Theory and Communication Networks: An Unconsummated Union”; 2) Capacity regions are either achieved for high signal noise ratio within a constant or via asymptotic bound and vanishing error, making it difficult to guide network architectures. Yury Polyanskiy made progress in non-asymptotic bound for point-to-point channel recently; 3) Coding and decoding complexity is far beyond current computation power, i. . codes of NIT lack structure. As a student, I am excited about the fact that combination of IT and network has not been completed, since it means great potential for network information theory. I would like to devote myself to this important problem with the following plan: 1. Begin with research in interference channel(IC). IC is not only a fundamental model of single-hop network, but also the ultimate limit of many wireless systems. I am currently simulating the error exponent of interference between IEEE 802. 11 and Long Term Evolution to obtain firsthand material. 1.
Try to model the network and find more practical schemes by interning in a network company. I think Shannon’s experience with real communication systems during World War ? contributed to the creation of an abstract model of communication. Contemporary networks are quite similar to communication systems developed in the pre-Shannon years, both based on heuristics, empirical knowledge and partial dependence on related theories. I am determined to do theoretic research in Wireless Foundations Interest and enthusiasm: My freshman and sophomore years were devoted to finding my true interest.
I tried academic and non-academic pursuits like pure mathematics and physics, microwave engineering, and mountain climbing etc. The elegance of communication theory finally presented an answer to my dedicated search. From then on, enthusiasm for this subject has always been driven me to success. I ranked 1st/240 in my junior year. Prof. El Gamal covered point-to-point information theory in just one week while I managed to follow him through watching class videos, reading lecture notes and discussing with TAs.
Solid mathematics and programming background: By applying Sukhatme’s Theorem which de-correlates exponential order statistics, I proposed an optimal power allocation on selected antennas with Alamouti scheme (paper on writing); I got top marks in many mathematics courses which are of greater difficulty than my peers took; I won the Meritorious Award of Mathematical Contest in Modeling (MCM/ICM). Aware of the complex programming tasks for PhD, I completed a large amount of highly-complex, time-consuming programming in my summer research. Moreover, I required myself to optimize the accuracy of codes in first version.
Wireless Foundations is my first choice: I would like to join in Professor Tse’s work on network information theory with focus on interference channel and network. It will be an honor to be advised by Professor Ramchandran on information theory and networks. Professor Anantharam’s research interests, including coding theory, theory of point processes and information theory, are all appealing to me. I am also interested in Professor Wainwright’s works on high-dimensional statistics. I believe UC Berkeley will be the right stage to realize my dream.