SUNMONTUEWEDTHUFRISAT
Events for November 14, 2006
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Interface between Information Theory and Estimation Theory: THEORY AND APPLICATIONS
Tue, Nov 14, 2006 @ 11:00 AM - 12:00 PM
Ming Hsieh Department of Electrical and Computer Engineering
Conferences, Lectures, & Seminars
SPEAKER: Prof. Antonia Tulino, University of NaplesABSTRACT: For signals observed in Gaussian noise, there are several interesting intersections between information theory and linear and nonlinear minimum mean-square error (MMSE) estimation.A recently unveiled fundamental relationship between the input-output mutual information and the MMSE achievable by the optimal estimator of the input is now emerging as a powerful new tool that provides with explicit expressions for the sought derivative of the mutual information. This relationship holds for arbitrarily distributed scalar and vector signals, as well as for discrete-input discrete-output channels.Using this new tool, we have been able to analytically solve some of the long-standing constrained optimization problems in information theory. One example of such optimization problems is the problem often encountered in transmitter design of allocating a certain amount of power among a bank of parallel noninteracting channels. Examples abound, both in the wireline and the wireless domains are:* Multicarrier transmission. Signalling takes place over a number of distinct frequency bands, each of which constitutes a parallel channel. These bands may be nonoverlapping or, as in OFDM (orthogonal frequency division multiplexing), overlapping but with spectral shapes designed to ensure orthogonality. A prime application in the wireline world is the DMT (discrete multitone) technique employed in digital subscriber lines.* Multiantenna communication. If multiple transmit and receive antennas are employed and the transmitter knows the transfer coefficients between the antennas, the left singular vectors of the resulting matrix can be used for signaling and the right singular vectors for reception. The outcome is a set of parallel noninteracting channels.* Power control for fading channels. When the gain of an individual frequency-flat channel varies over time, it can be seen as a collection of parallel channels where each such channel encompasses a group of symbols over which the fading coefficients are identical.* Dispersive channels. For linear dispersive channels or parallel channels with correlated noises, a power-preserving orthonormal linear transformation at transmitter and receiver turns the channel into one with parallel branches with uncorrelated noises and possibly different signal-to-noise ratios.Another example of problems that use this fundamental link between information theory and estimation theory we have been able to analytically solve is the monotonic Decrease of the Non-Gaussianness of the Sum of independent Random Variables. Although long suspected that the non-Gaussianness decreases at each convolution, it was not shown until 2004 (in the equivalent version of increasing differential entropy) by Artstein, Ball, Barthe and Naor by means of a tour-de-force in functional analysis. Using the relationship between non-Gaussianness and MMSE in Gaussian channels, we will give a simplified proof of the above result dealing with the more general setting of non-identically distributed random variables.Bio:
Antonia Maria Tulino was born in Napoli, Italy, on September 12, 1971. She received the Dr. Engr. degree (summa cum laude) from the Universita degli Studi di Napoli Federico II, Napoli, Italy, in 1995 and the Ph.D. degree in electronic engineering from the Seconda Universita degli Studi di Napoli, Napoli, Italy, in 1999. In 1999, she was a Research Scientist at the Center for Wireless Communications (CWC), Oulu, Finland. From January 2000 to February 2001, she was a post-doctoral visitor with Princeton University, Princeton, NJ. From February 2001 to November 2002, she was an Assistant Professor with the Dipartmento di Ingegneria delle Telecomunicazioni, Universita degli Studi del Sannio, Benevento, Italy. From November 2002 she has been an Associate Professor with the Dipartmento di Ingegneria Elettronica e delle Telecomunicazioni, Universita degli Studi di Napoli "Federico II", Napoli, Italy. She is periodically appointed as a visiting research staff member in the Department of Electrical Engineering, Princeton University. Her current research interests are in the areas of statistical signal processing, information theory, and random matrix theory.Host: Prof. Giuseppe Caire, caire@usc.eduLocation: Hughes Aircraft Electrical Engineering Center (EEB) - 248
Audiences: Everyone Is Invited
Contact: Mayumi Thrasher
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Codes for Optical CDMA
Tue, Nov 14, 2006 @ 03:30 PM - 04:30 PM
Ming Hsieh Department of Electrical and Computer Engineering
Conferences, Lectures, & Seminars
SPEAKER: Mr. Reza Omrani, Communication Sciences Institute, University of Southern CaliforniaABSTRACT: There has been a recent upsurge of interest in applying code division multiple access (CDMA) techniques to optical networks. This interest is in part due to the increase in security afforded by OCDMA as measured for instance, by the increased effort needed to intercept an OCDMA signal, and in part due to the flexibility and simplicity of network control afforded by optical-CDMA (OCDMA). There are two main approaches to code design for OCDMA systems. The first approach uses direct sequence encoding, which employs {0,1} sequences with good correlation properties as code sequences, and the data sequence modulates the code sequence simply by switching it on or off. These may be termed as 1-D optical orthogonal codes (OOC) since the code sequences are only associated with the time dimension. It has recently been recognized that in order to bring down the required chip rate to within practical limits, it is desirable that 2-D {0,1} codes be used in which the code sequence consist of a 2-D pattern in which the second dimension corresponds to wavelength.The second OCDMA approach is via phase encoding in which the code sequences are collections of complex numbers of unit magnitude with each entry associated to a carrier of different wavelength. The phase of an element in the λ-th sequence corresponds to the phase of the λ-th carrier. The focus of our work is on efficient code design for OCDMA systems under both direct sequence and phase encoding approaches.We first introduce some new bounds on the size of 1-D and 2-D OOCs. Subsequently, the focus is on explicit constructions for 2-D wavelength-time OOCs. We introduce four major constructions for wavelength-time OOCs which include a method to map 1-D OOCs to 2-D OOCs, a method based on Reed-Solomon Codes, a method which concatenates a constant weight code with a Reed-Solomon based 2-D OOC and finally a function-plot method in which the values of an appropriately-chosen function are used to derive the 2-D codes. The functions used in function plot construction include polynomial functions and rational functions.A major drawback of OCDMA systems is their low spectral efficiency. In this work we explore a modulation scheme for OCDMA systems which has the potential for increasing the spectral efficiency manyfold. We term this scheme code-cycle modulation (CCM). Under this modulation scheme, different cyclic shifts of the code sequence assigned to each user are used to transmit M-ary information. While this means of modulation was known earlier in the literature, most prior modulation schemes needed M different receiver units to recover the data resulting in increased complexity and power. In this work we provide a novel receiver architecture with significantly reduced power requirements and complexity.Following this, we turn our attention to phase-encoded OCDMA. We first derive a mathematical model for the output of this system and based on this model we introduce a metric to design code sequences for asynchronous transmission. Then, a connection between the phase-encoding sequence design problem and the PMEPR (peak to mean envelope power ratio) problem which arises in OFDM transmission is established. We construct a family of phase sequences which are based on the theory of generalized bent functions and with properties desirable for asynchronous phase encoding OCDMA systems.BIO: Reza Omrani received his B.S. degree from the University of Tehran, Tehran, Iran, and his M.S. degree from the University of Southern California (USC), Los Angeles, both in electrical engineering, in 1999 and 2002, respectively. He did his PhD dissertation under the supervision of Professor P. Vijay Kumar at the Communication Sciences Institute, Department of Electrical Engineering-Systems, USC. His research interests include low-density parity-check (LDPC) codes, network coding, combinatorics and signal design for good correlation properties.Host: Michael J. Neely, mjneely@usc.edu
Location: Hughes Aircraft Electrical Engineering Center (EEB) - 248
Audiences: Everyone Is Invited
Contact: Mayumi Thrasher
