2026
R. Smarandache, D. G. M. Mitchell, and A. Gómez-Fonseca, Structural Analysis of Generalized Quasi-Cyclic LDPC Codes: Rank, Design, and Generator Matrices, IEEE Transactions on Information Theory, Vol. 72 (1), pp. 253–267.
RS
University of Notre Dame
Roxana Smarandache
Professor of Mathematics and Professor of Electrical Engineering
- Mathematics: Department of Mathematics
- Electrical Engineering: Department of Electrical Engineering
- Office: 268 Hurley, University of Notre Dame, Notre Dame, IN 46556
- Phone: (574) 631-4862
- Email: rsmarand (at) nd.edu
About
Roxana Smarandache received the B.Sc. degree in Mathematics (with a thesis in Number Theory) from the University of Bucharest in 1996 and a 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 a professor in both the Department of Mathematics and the Department of Electrical Engineering at the University of Notre Dame.
Highlights & News
2024
R. Smarandache, A. Gómez-Fonseca, and D. G. M. Mitchell, Generalized Quasi-Cyclic LDPC Codes: Design and Efficient Encoding, IEEE International Symposium on Information Theory (ISIT), pp. 434–439.
2023
A. Gómez-Fonseca, R. Smarandache, and D. G. M. Mitchell, An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes, IEEE Journal on Selected Areas in Information Theory, Vol. 4, pp. 499–513.
2023
A. Gómez-Fonseca, R. Smarandache, and D. G. M. Mitchell, On the Tanner Cycle Distribution of QC-LDPC Codes from Polynomial Parity-Check Matrices, IEEE International Symposium on Information Theory (ISIT), pp. 2356–2361.
2023
A. Gómez-Fonseca, R. Smarandache, and D. G. M. Mitchell, A Low Complexity PEG-like Algorithm to Construct Quasi-Cyclic LDPC Codes, International Symposium on Topics in Coding (ISTC), pp. 1–5.
2022
R. Smarandache and D. G. M. Mitchell, A Unifying Framework to Construct QC-LDPC Tanner Graphs of Desired Girth, IEEE Transactions on Information Theory, Vol. 68 (9), pp. 5802–5822.
2022
R. Smarandache, A. Gómez-Fonseca, and D. G. M. Mitchell, Using Minors to Construct Generator Matrices for Quasi-Cyclic LDPC Codes, IEEE International Symposium on Information Theory (ISIT), pp. 548–553.
2021
R. Smarandache and D. G. M. Mitchell, Necessary and Sufficient Girth Conditions for Tanner Graphs of Quasi-Cyclic LDPC Codes, IEEE International Symposium on Information Theory (ISIT), pp. 380–385.
2021
A. Gómez-Fonseca, R. Smarandache, and D. G. M. Mitchell, Necessary and Sufficient Girth Conditions for LDPC Tanner Graphs with Denser Protographs, International Symposium on Topics in Coding (ISTC), pp. 1–5.
2020
S. Mo, L. Chen, D. J. Costello, Jr., D. G. M. Mitchell, R. Smarandache, and J. Qiu, Designing Protograph-Based Quasi-Cyclic Spatially Coupled LDPC Codes With Large Girth, IEEE Transactions on Communications, Vol. 68 (9), pp. 5326–5337.
2018
C. Zhou, D. G. M. Mitchell, and R. Smarandache, Free Pseudodistance Growth Rates for Spatially Coupled LDPC Codes over the BEC, IEEE Information Theory Workshop (ITW), pp. 1–5.
2017
L. Chen, S. Mo, D. J. Costello, Jr., D. G. M. Mitchell, and R. Smarandache, A Protograph-Based Design of Quasi-Cyclic Spatially Coupled LDPC Codes, IEEE International Symposium on Information Theory (ISIT), pp. 1683–1687.
2014–2017
Editorial board, IEEE Transactions on Information Theory.
2013–2017
NSF Grant DMS-1313221, The mathematics of pseudocodewords (PI).
2012–2016
NSF CIF Award, Spatially Coupled Sparse Codes on Graphs: Theory, Practice, and Extensions (PI; collaborative research with EE, Notre Dame, UCLA, and New Mexico).
2016
D. Napp and R. Smarandache, Constructing strongly-MDS convolutional codes with maximum distance profile, Advances in Mathematics of Communications, Vol. 10, no. 2, pp. 275–290.
2014
D. G. M. Mitchell, R. Smarandache, and D. J. Costello, Jr., Quasi-Cyclic LDPC Codes Based on Pre-lifted Protographs, IEEE Transactions on Information Theory, Vol. 60 (10), pp. 5856–5874.
2014
D. J. Costello, Jr., L. Dolecek, T. E. Fuja, J. Kliewer, D. G. M. Mitchell, and R. Smarandache, Spatially Coupled Sparse Codes on Graphs — Theory and Practice, IEEE Communications Magazine, Vol. 52 (7), pp. 168–176.
2013–2014
Editorial board, Advances in Mathematics of Communications .
2013
M. Haenggi and R. Smarandache, Diversity Polynomials for the Analysis of Temporal Correlations in Wireless Networks, IEEE Transactions on Wireless Communications, Vol. 12 (11), pp. 5940–5951.
2008–2012
NSF CCF Award, New Directions in Graph-Based Code Design (PI; collaborative research with EE, Notre Dame).
2007–2011
NSF DMS Award, Pseudo-Codeword Analysis and Design of Quasi-Cyclic and Convolutional Codes (PI).
Teaching
- EE 30210-02 — Random Phenomena in Electrical EngineeringSpring 2026
- MATH 10310 — Calculus A, section 02Fall 2025
- MATH 10310 — Calculus A, section 03Fall 2025
- EE 60665 — Mathematical Methods for Electrical EngineersSpring 2025
- MATH 30310 — Undergraduate Coding TheoryFall 2024
- EE 30363 — Random Phenomena in Electrical EngineeringSpring 2024
- MATH 10150-03 — Principles of CalculusFall 2023
- MATH 10150-04 — Principles of CalculusFall 2023
- MATH 30310 — Undergraduate Coding TheoryFall 2019
- MATH 20580-03 — Introduction to linear algebra and differential equations (course chair)Fall 2019
- EE 30363 — Random Phenomena in Electrical EngineeringSpring 2019
- MATH 30310 — Undergraduate Coding TheoryFall 2018
- EE 30363 — Random Phenomena in Electrical EngineeringSpring 2018
- MATH 20580-04 — Introduction to linear algebra and differential equationsSpring 2018
- MATH 30310 — Undergraduate Coding TheoryFall 2017
- EE 30363 — Random Phenomena in Electrical EngineeringSpring 2017
- EE 30363 — Random Phenomena in Electrical EngineeringSpring 2016
- MATH 10360-06 — Calculus BSpring 2016
- MATH 30310 — Undergraduate Coding TheoryFall 2015
- EE 30363 — Random Phenomena in Electrical EngineeringSpring 2014
- MATH 30310 — Undergraduate Coding TheoryFall 2013
- MATH 10550 — Calculus IFall 2013
- MATH 87500 — Coding TheorySpring 2013
- EE 80654 — Coding TheoryFall 2012
- MATH 10260 — Elements of Calculus IISpring 2006
- MATH 40210 — Basic CombinatoricsFall 2005
- MATH 10250 — Elements of Calculus IFall 2005
Undergraduate Students
- Weike Fang — Fall 2022— ``Hamming and cyclic codes"
- Dane Krzyskowski — Fall 2012
- Hannah Porter — 2015-2016 and summers of 2014, 2015— ``Computing the permanent of a matrix"
- Katherine Sanders — 2016-2017— ``Breaking the Code: An analysis of cryptography and its applications to present society"
Graduate Students
- Yasmin Aguillon — 2023-2025, MS degree
- Luis Benitez Norat — 2021-2023, MS degree
- Anthony Gomez Fonseca— 2019-2025, PH.D. — ``Efficient Algorithms for the Construction of QC-LDPC Codes from Girth and Cycle Analysis"— now postdoc at University of South Florida
- Cunlu Zhou — 2013-2019, PH.D. —`` Entropy, Optimization and Coding Theory"— followed by postdoc at U. of Toronto then tenure track at the University of Sherbrooke
- Derric Chien — Dec. 2015-2016, MS degree— now high-school teacher in California.
Postdocs
- Henry Chimal-Dzul — 2022-2024— now at UT San Antonio
Research
The research program centers on coding theory and its intersections with combinatorics, graph theory, network coding, index coding, and coding for storage.
Current topics / graduate projects
Quantum Coding
Bethe permanents
Properties of Bethe-permanents of matrices and approximation of permanents.
Interference and the diversity polynomial
LDPC codes: algebraic and combinatorial approaches
Spatially coupled LDPC codes
Design and decoding issues.
Pseudocodewords, trapping sets, and absorbing sets for LDPC codes
Designing codes with predictable low error floors.
Convolutional codes with large distance
Constructions over large finite fields and decoding over the erasure channel.
Linear programming and compressed sensing
Pseudocodewords and connections to compressed sensing.
Algebraic combinatorics and graph theory
Distance bounds from eigenvalues of the adjacency matrix.
Research problems
The theory of error-correcting codes offers a large number of research problems in applied mathematics and theoretical engineering, appealing both to mathematicians interested in applications and to theoretically minded engineers.
What is coding theory?
Coding theory is an applied mathematical field that uses classical and modern algebraic techniques involving finite fields, discrete mathematics, group theory, polynomial algebra, combinatorics, probability, algebraic geometry, and number theory to solve applied problems in telecommunications.
It deals with the design of error-correcting codes: sets of vectors of a specified length chosen according to algebraic or probabilistic rules to enable reliable transmission of information across noisy channels.
Error-correcting codes are integral to communication and storage systems, including:
- CD, DVD, Blu-ray players, and computer hard drives, which use Reed–Solomon codes for error protection.
- Deep-space communications, which depend crucially on LDPC codes.
- Fiber-optic transmission systems, which rely on error-control coding.
Collaborators
- Daniel J. Costello, Jr.
- Lara Dolecek
- A. G. Dimakis
- M. Flanagan
- Thomas E. Fuja
- Heide Gluesing-Luerssen
- Anthony Gomez-Fonseca
- Marcus Greferath
- Martin Haenggi
- Ryan Hutchinson
- Michael Lentmaier
- Negar Kiyavash
- Joerg Kliewer
- David G. M. Mitchell
- Mohsen Moradi
- Diego Napp
- Vahid Nourozi
- Ali E. Pusane
- Joachim Rosenthal
- Jochen Trumpf
- Pascal Vontobel
- Dejan Vukobratovic
- Cunlu Zhou