Roxana Smarandache

 

 





Smarandache





 

Associate Professor,  Dept. of Mathematics
Associate Professor, Dept. of Electrical Engineering
122 Hayes-Healy
University of Notre Dame
Notre Dame, IN 46556
Tel: (574) 631-4862 (Voice)
E-Mail: rsmarand (at) nd.edu

 

Short Bio:


Roxana Smarandache received the B.Sc. degree in Mathematics
(with a thesis in Number Theory) from the University of Bucharest in 1996 and Ph.D. in Mathematics  from the University of Notre Dame in 2001 under advisor Joachim Rosenthal, with a thesis on coding theory: " Maximum distance separable convolutional codes".   

She is now a professor in both the Dept. of Mathematics and the Dept. of Electrical Engineering of the University of Notre Dame.





News:


  2013-2016


 

NSF Grant DMS-1313221, The mathematics of pseudocodewords,  (PI, 2013-2017).

2012-2015


NSF CIF-Award on Spatially Coupled Sparse Codes on Graphs: Theory, Practice, and Extensions (PI, 2012-2016; collaborative research with EE, Notre Dame, UCLA, New  Mexico).

2008-2011


NSF CCF-Award on New Directions in Graph-Based Code Design (PI, 2008-2012; collaborative research with EE, Notre Dame).

2007-2010


NSF DMS-Award on Pseudo-Codeword Analysis and Design of Quasi-Cyclic and Convolutional Codes (PI, 2007-2011).

2014-2017

Editorial board for the IEEE Transactions in Information Theory

2013-2014
Editorial board  for the Advances in Mathematics of Communications (AMC) journal.
2016


Constructing strongly-MDS convolutional codes with maximum distance profile. D. Napp and R. Smarandache, Advances in Mathematics of Communications AMC, Vol. 10, no. 2, pp. 275-290, 2016.
2014
Quasi-Cyclic LDPC Codes Based on Pre-lifted ProtographsD. G. M. Mitchell, R. Smarandache, and D. J. Costello, Jr., IEEE Trans. Inform. Theory, Vol. 60 (10), pp. 5856-5874, 2014.
2014
Spatially Coupled Sparse Codes on Graphs - Theory and Practice.  D. J. Costello, Jr., L. Dolecek, T. E. Fuja, J. Kliewer, D. G. M. Mitchell, and R. Smarandache, IEEE Communications Magazine, Vol. 52 (7), pp. 168-176, 2014.
2013
Diversity Polynomials for the Analysis of Temporal Correlations in Wireless Networks.  M. Haenggi and R. Smarandache, IEEE Trans. on Wireless Comm., Vol. 12 (11), pp. 5940-5951, 2013.

 


Teaching:


EE 30363 Random Phenomena in Electrical Engineering (Spring 2016)

MATH 10360-06 Calculus B (Spring 2016)
MATH 30310 Undergraduate Coding Theory  (Fall 2015)

EE 30363 Random Phenomena in Electrical Engineering (Spring 2014) 
MATH 30310 Undergraduate Coding Theory  (Fall 2013)

MATH 10550 Calculus I (Fall 2013)

MATH 87500 Coding Theory (Spring 2013)

EE 80654 Coding Theory (Fall 2012)

MATH 10260 Elements of Calculus II (Spring 2006)

MATH 40210 Basic Combinatorics (Fall 2005)
MATH 10250 Elements of Calculus I (Fall 2005)


Publications


CV

 


Research Projects: 

Dr. Smarandache's research topics are mainly related to coding theory.





The research projects are within or at the intersection of these fields:


Coding Theory

Combinatorics

Graph Theory
Network coding, index coding, coding for storage




  
 

Current topics/graduate projects and links to some papers:


Properties of Bethe-permanents of matrices: approximating permanents of matrices (permanents are like determinants but the addition is without the alternating sign)
[pdf][pdf]
Interference and the diversity polynomial
[pdf]
LDPC codes: algebraic and combinatorial approaches [pdf] [pdf]
Spatially coupled LDPC codes: design and decoding issues [pdf] [pdf]
Pseudocodewords, trapping sets  and absorbing sets for
LDPC codes: designing codes with predictable low error floor[pdf]
[pdf] [pdf
Convolutional codes with large distance (over large finite fields): constructions 
[pdf] [pdf][pdf][pdf] [pdf] [pdf] [pdf] and decoding over the erasure channel[pdf].
Linear programming: pseudocodewords and connection to compressed sensing
[pdf]
Algebraic combinatorics and graph theory: distance bounds from eigenvalues of the adjacency matrix
[pdf]



Research problems:


The theory of error correcting codes offers a large number of exciting research problems in
applied mathematics and theoretical engineering, which makes this area appealing to both mathematicians who would like to see their ideas and research being actually applied and theoretically minded engineers.



What is coding theory:

T
he field of coding theory is an applied mathematical field that makes use of classical and modern algebraic techniques involving finite fields, discrete mathematics,  group theory, polynomial algebra, combinatorics, probability, algebraic geometry, or number theory (depending on the research directions) to solve applied problems in telecommunications. 

It deals with the design of error-correcting codes, which are sets of vectors of a certain given length chosen according to some desired algebraic or probabilistic rules to allow for the reliable transmission of information across noisy channels.

Error-correcting codes are an integral component of all communication systems currently in operation:

  • CD, DVD, Blu-ray players and computer hard drives are protected from errors by Reed-Solomon codes (these are sets of all polynomials having roots some consecutive powers of a primitive element of a given field);
  • communication with deep-space missions depends crucially on LDPC codes (these are kernels of a very sparse binary matrices), and  
  • transmission over fiber-optic cables would not be possible without a number of codes (discussed in any coding course). 









 



 

Collaborators:
Daniel J. Costello, Jr.Lara DolecekA. G. Dimakis, M. Flanagan, Thomas E. FujaHeide Gluesing-LuerssenMartin Haenggi,  Ryan HutchinsonMichael LentmaierJoerg Kliewer, David Mitchell, Ali E. PusaneJoachim Rosenthal,  Pascal Vontobel.