**
Communication, Control**
**
and Signal Processing Seminar****
**

**Abstracts
of talks**

*Fall 2011*

** 09/22 Woomyoung Park (UMD)****,
Multilevel polarization for nonbinary codes and parallel channels **

ABSTRACT: We study polarization for nonbinary channels with input alphabet of
size q = 2^r; r = 2,3,... Using Arikan’s successive
cancellation decoding, we prove that the virtual channels that arise in the
process of polarization converge to q-ary channels with capacity 1, 2,...,r bits, and that the total transmission rate approaches
the symmetric capacity of the channel. The multilevel polarization arising in
this transmission represents a new phenomenon which is
well suited to the description of dependent parallel channels that are subject
to fading according to the order of their indices.

This is a joint work with Alexander Barg.

**10/06, 10/13 Prakash
Narayan (UMD), Multiuser secrecy, data compression and transmission, I,II**

ABSTRACT: Secrecy generation for multiuser ``source"
and ``channel" models will be considered, and connections drawn to
associated multiuser compression and transmission problems (without secrecy constraints).
Open problems (especially those that flummoxed us) will be described. This talk
is based on joint work with Imre Csiszar, and the contents are taken from the
three attached papers.

References: ic-pn2004.pdf,
ic-pn2008.pdf,
ic-pn2011.pdf

10/20 **
Alexander Barg (UMD) Statistical RIP and sparse recovery**

ABSTRACT: We consider recovery of
sparse signals from noisy linear observations. A well-known sufficient condition
for stable and robust recovery is the Restricted Isometry Property of the
sampling operator. The known constructions of RIP matrices stop short of
achieving the optimal sketch dimension.

We propose a relaxation of the RIP condition that permits shorter sketches and
prove error bounds for some popular estimators. We also briefly discuss a
construction of matrices that satisfy the relaxed conditions.

Joint work with Arya Mazumdar.

** Wei-Hsuan
Yu (UMD) Introduction to frame theory**

ABSTRACT: Frames are interesting
because they provide decompositions in applications where bases could be a
liability. Tight frames are valuable to ensure fast

convergence of such decomposition. Normalized frames guarantee control of the
frame elements. Finite frames avoid the subtle and omnipresent approximation
problems associated with the truncation of infinite frames. In this talk, I will
present the theory of finite normalized tight frames (FNTFs). The main theorem
is the characterization of all FNTFs in terms of the minima of a potential
energy function, which was designed to measure the total orthogonality of a
Bessel sequence. Examples of FNTFs abound, e.g., in R 3 the vertices of the
Platonic solids and of a soccer ball are FNTFs.

** Radu Balan (UMD)
**ABSTRACT: In this talk we present an algorithm for
signal reconstruction from absolute value of frame coefficients. Then we compare
its performance to the Cramer-Rao Lower Bound (CRLB) at high signal-to-noise
ratio. To fix notations, assume {f_i; 1<= i <= m} is a spanning set (hence
frame) in R^n. Given noisy measurements d_i=|<x,f_i>|^2+\nu_i, 1<= i<= m, the
problem is to recover x\in R^n up to a global sign. In this talk the
reconstruction algorithm solves a regularized

least squares criterion of the form I(x) = \sum_{i=1}^m ||<x,f_i>|^2-d_i|^2 + \lambda ||x||^2 This criterion is modified in the following way: 1) the vector x is

replaced by a nxr matrix L; 2) the criterion is augmented to allow an iterative procedure. Once the matrix L has been obtained, an estimate for x is obtained through an SDV factorization.