Theoretical Limits and Practical Methods in Classical and Quantum Communications

Alexei Ashikhmin
Communications and Statistical Sciences Department
Bell Labs, Alcatel-LucentAbstract: The talk is in three parts covering some areas of my recent research. Information-theoretic and Coding Bounds
I will present a general method, called the polynomial method, for deriving information-theoretic and coding bounds. The method is based on results from harmonic analysis and the theory of orthogonal polynomials. Following this, I will show that an application of this method leads to an improvement of the Shannon, Gallager, and Berlekamp (1967) bound on the reliability function of the Gaussian channel. This was the first improvement of the bound to be made after a period of 30 years. Further applications of this method lead to derivations of the best currently known bounds on the minimum distance of quantum codes, probability of undetected error, and other parameters. The method of EXIT functions
EXIT functions are a powerful tool for the design and analysis of iteratively decodable codes, such as TURBO and Low Density Parity Check (LDPC) codes. In this part of the talk, I will give a formal definition of EXIT functions, consider applications of EXIT functions to the design of capacity achieving LDPC codes and capacity achieving communication schemes for multiple input-multiple output (MIMO) ergodic channel. Quantum Error Correction
It is well known that quantum computers have the potential to make radical improvements in performance over classical computational devices. Unfortunately, quantum computers are inherently vulnerable to environmental and control errors, which thus makes quantum error correction a very important subject. This part of the talk begins with a brief introduction into the theory of quantum computation and quantum error correction (no knowledge of quantum mechanics is required). Following this, I will present my recent results on the fidelity of a quantum automatic repeat request (ARQ) protocol. The talk concludes with a brief summary of other results I have obtained in the area of quantum error correction. Biography: Alexei Ashikhmin is a member of technical staff in the Communications and Statistical Sciences Department, Bell Labs, Alcatel-Lucent. He received his Ph.D. degree in Electrical Engineering from the Institute of Information Transmission Problems, Russian Academy of Science, Moscow, in 1994. In 1996 he was a visiting researcher of the Mathematics and Computer Science Department, Delft University of Technology, The Netherlands. From 1997 to 1999, he was a Postdoctoral Fellow at Modeling, Algorithms, and Informatics Group of Los Alamos National Laboratory. Since 1999 he has been with Bell Laboratories.His research interests include classical and quantum information theory and communication theory. From 2003 to 2006 Dr. Ashikhmin served as an Associate Editor of IEEE Transactions on Information Theory. In 2002, Dr. Ashikhmin received Bell Laboratories President's Gold Award for breakthrough research in wireless communications. In 2005 Dr. Ashikhmin was honored by the IEEE Communications S.O. Rice Prize Paper Award for work on LDPC codes for information transmission with multiple antennas. Host: Michael Neely, mjneely@usc.edu, EEB 520, x03505

Location: Hughes Aircraft Electrical Engineering Center (EEB) - 248

Audiences: Everyone Is Invited

Contact: Gerrielyn Ramos