Christine Kelley

Contact Information

Mailing Address:
317 Avery Hall
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE 68588-0130

FAX: 402-472-8466

Teaching Schedule

Funding

• Lead PI, Gretchen Matthews, Co-PI Christine Kelley. NSF Collaborative Research: Graphs, Codes, Transitivity, and Decoding ($664,940). July 2022-June 2025. Under review.
• Lead PI. Simons Collaboration Grant ($42,000). September 2022-August 2027. Under review.
• Lead PI, Co-PI Alexander Zupan. NSA Grant: Nebraska Conference for Undergraduate Women in Mathematics, ($50,000). January 2022 - December 2024.
• Lead PI, Co-PIs Glenn Ledder and Alex Zupan. NSF Grant for Nebraska Conference for Undergraduate Women in Mathematics, ($150,000), Jan. 2020 - Dec. 2022.
• Lead PI, Co-PIs Glenn Ledder and Alex Zupan. NSA Grant for Nebraska Conference for Undergraduate Women in Mathematics, ($50,000), Dec. 2019 - Dec 2021.
• Lead PI, Co-PIs Glenn Ledder and Alex Zupan. NSF Grant for Nebraska Conference for Undergraduate Women in Mathematics, ($50,000), Jan. 2019 - Dec 2019.
• Co-PI, NSF Grant for Nebraska Conference for Undergraduate Women in Mathematics, ($150,000), July 2016 - Dec. 2018.
• Lead PI, NSA Grant for Nebraska Conference for Undergraduate Women in Mathematics 2018. ($50,000), Dec. 2017- Dec. 2019.
• Co-PI, NSA Grant for Nebraska Conference for Undergraduate Women in Mathematics 2016, ($20,000), July 2015 - July 2016.
• Co-PI, NSA Grant for Nebraska Conference for Undergraduate Women in Mathematics 2015, ($20,000), July 2014 - July 2015.
• Co-PI, NSA Grant for Nebraska Conference for Undergraduate Women in Mathematics 2014. ($20,000), July 2013 - July 2014.
• Sole PI, NSA Young Investigator Grant, ($29,930), Spring 2011 - Fall 2013.
• Sole PI, NSF EPSCoR First Award ($20,000), 2009-2010.

Research

Curriculum Vitae

My research interests lie in coding theory, applied discrete mathematics, and applied algebra. One emphasis is on graph-based codes and algorithms, and the design and analysis of such codes using algebraic methods. Another research interest is in applying algebraic and combinatorial methods to coding applications such as flash memory storage, data streaming, and communication networks. My research has been supported by an NSA Young Investigator grant (Spring 2011-Fall 2013) and by an NSF EPSCoR First Award (2009-2010).

Below are my selected publications:

• A. Beemer, C.A. Kelley, An Iteration Search Algorithm for Implementing Hard Decision Decoders. In preparation to be submitted.
• C.A. Kelley, Invited book chapter on Codes over Graphs to be part of A Concise Encyclopedia of Coding Theory for CRC Press. Editors: W. Cary Huffman, Jon-Lark Kim, and Patrick Sole. Final version due Jan. 1, 2019.
• C. Mayer and C. A. Kelley. Erasure Relay Channels with Partial Erasures. In preparation to be submitted.
• A. Beemer, K. Haymaker, and C. A. Kelley. Absorbing Sets of Codes from Finite Geometries. Accepted, pending revision.
• A. Beemer and C. A. Kelley. Iterative Decoder Analysis using Multidimensional Decoding Networks. Currently under revision to be resubmitted.
• C. Mayer, K. Haymaker, and C. A. Kelley. Coding for Multilevel and Partial Erasure Channels. Advances in Mathematics of Communications. 17 pages. Feb. 2018. PDF
• A. Beemer, S. Habib, C.A. Kelley, and J. Kliewer. A General Algebraic Approach to Optimizing SC-LDPC codes. Proceedings of the 55th Annual Allerton Conference on Communication, Control, and Computing, 8 pages, double-column. Monticello, IL, October 2017. PDF
• A. Beemer, C. Mayer, and C. A. Kelley. Erasure Correction and Locality of Hypergraph Codes. Lecture Notes in Computer Science 10495, Springer. pp 21-29. August 2017. PDF
• A. Beemer and C. A. Kelley. Multidimensional Decoding Networks for Trapping Set Analysis. Lecture Notes in Computer Science 10495, Springer. pp 11-20. August 2017. PDF
• Z. Sakkaff, M. Pieroban, J. L. Catlett, N. Buan, M. Cashman, M. Cohen, and C. A. Kelley. End-to-end Molecular Communication Channels in Cell Metabolism: an Information Theoretic Study. Proceedings of the ACM International Conference on Nanoscale Computing and Communication, NanoCom 2017. 6 pages, double-column. (ACM Nanocom Best Paper Award 2017). PDF
• C. Mayer and C. A. Kelley. LT Codes for Partial Erasure Channels. In Proceedings of IEEE International Symposium on Information Theory, Aachen, Germany, 5 pages, IEEE double column format, June 2017. PDF
• M. Cashman, J. L. Catlett, M. B. Cohen, N. R. Buan, Z. Sakkaff, M. Pierobon, and C. A. Kelley. Sampling and Inference in Configurable Biological Systems: A Software Engineering Perspective. In Proceedings of International Workshop on Software Engineering for Science. 8 pages, double-column, 2017. PDF
• J. Bolkema, H. Gluessing-Luerssen, C.A. Kelley, K. Lauter, B. Malmskog, and J. Rosenthal. Variants of the McEleice Cryptosystem. Springer "Association for Women in Mathematics" Series, 19 pages, 2017. PDF
• A. Beemer and C. A. Kelley. Avoiding trapping sets of SC-LDPC codes with respect to the windowed-decoder. In Proceedings of the IEEE International Symposium on Information Theory and its Applications, Monterey, CA, 5-pages, double-column, October 2016. PDF
• M. Cashman, J. L. Catlett, M. B. Cohen, N. R. Buan, Z. Sakkaff, M. Pierobon, and C. A. Kelley. Sampling and inference in configurable biological systems: A software engineering perspective. In proceedings of International workshop on software engineering for science, 2017. 8-pages, double-column format. PDF
• K. Haymaker, C. A. Kelley. Structured bit-interleaved LDPC codes for MLC flash memory. IEEE Journal on Selected Areas of Communications (JSAC), Special Issue on Communication Methodologies for the Next-Generation Storage Systems, 10 pages (double-column), May 2014. PDF
• K. Haymaker, C. A. Kelley. Covering codes for multi-level flash memories. Proceedings of the IEEE Asilomar Conference on Signals, Systems, and Computers in November 2012 (Special Session on Coding for Next-Generation Storage). PDF
• C. A. Kelley. Algebraic design and implementation of protograph codes using non-commuting permutation matrices. IEEE Transactions on Communications, vol.61, no. 3, pp. 910-918, March 2013. PDF
• K. Haymaker, C. A. Kelley. Geometric WOM codes and coding strategies for multi-level flash memories. Special Issue on Coding Theory and Applications, Designs, Codes, and Cryptography, Springer, May 2012. Available at ArXiv.
• C. Kelley, J. Kliewer. Algebraic constructions of graph-based nested codes from protographs. Proceedings of the 2010 IEEE International Symposium on Information Theory, Austin, TX, USA, June 2010. PDF
• C. Kelley. Minimum distance and pseudodistance lower bounds for generalized LDPC codes. International Journal of Information and Coding Theory, Special Issue on Algebraic and Combinatorial Coding Theory: in Honour of the retirement of Vera Pless, Spring 2010. PDF
• C. Kelley. On codes designed via algebraic lifts of graphs. Proceedings of the 2008 Allerton Conference on Control, Communications, and Computing, Sept. 22-26, 2008, Allerton, Illinois, USA. PDF
• C. Kelley and D. Sridhara. Pseudocodewords of Tanner Graphs. IEEE Transactions on Information Theory, vol. 53, no. 11, pp. 4013-4038, Nov. 2007. PDF
• C. Kelley and D. Sridhara. Eigenvalue bounds on the pseudocodeword weight of expander codes. Journal of Advances in Mathematics of Communications, vol. 1, no. 3, pp. 287-307, Aug. 2007. PDF
• C. Kelley, D. Sridhara, and J. Rosenthal. Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights. IEEE Transactions on Information Theory, vol. 53, no. 4, pp. 1460-1478, April 2007. PDF
• C. Kelley, D. Sridhara, and J. Rosenthal. Pseudocodeword weights for non-binary LDPC codes. Proceedings of the 2006 IEEE Internation Symposium on Information Theory, July 9-14, 2006, Seattle, USA. PDF
• C. Kelley, D. Sridhara, J. Xu, and J. Rosenthal. Pseudocodeword Weights and Stopping Sets. Proceedings of the 2004 IEEE International Symposium on Information Theory, p. 150, Chicago, June 27-July 3, 2004. PDF

Other publications:

• J. Cummings, C. A. Kelley. On the independence and domination numbers of replacement product graphs. Involve: A Journal of Mathematics. PDF
• K. Haymaker, C. A. Kelley. Coding strategies for reliable storage in multi-level flash memories. Proceedings of the International Castle Meeting on Coding Theory and Applications (3ICMCTA), Cardona, Spain, September 2011.
• C. Kelley and J. Walker. LDPC codes from voltage graphs. Proceedings of the 2008 IEEE International Symposium on Information Theory, July 6-11, 2008, Toronto, Canada. PDF
• J. Rosenthal, C. Kelley, D. Sridhara. Systems theoretic questions in coding theory. Proceedings in Applied Mathematics and Mechanics, ICIAM, 3 pages (electronic), Zurich, Switzerland, Oct. 2007.
• C. Kelley, D. Sridhara, and J. Rosenthal. Zig-zag and replacement product graphs and LDPC codes. Journal of Advances in Mathematics of Communications, Nov. 2008. PDF
• C. Kelley and D. Sridhara. On the pseudocodeword weight and parity-check matrix redundancy of linear codes. Proceedings of the 2007 IEEE Information Theory Workshop, Sept. 2-6, 2007, Lake Tahoe, USA. PDF
• D. Sridhara and C. Kelley. LDPC Coding for the Three Terminal Erasure Relay Channel. Proceedings of the 2006 IEEE International Symposium on Information Theory, July 9-14, 2006, Seattle, USA. PDF
• C. Kelley, D. Sridhara, and J. Rosenthal. Tree-Based Construction of LDPC Codes. Proceedings of the 2005 IEEE International Symposium on Information Theory, Adelaide, Australia, Sept. 4-9, 2005. PDF
• C. Kelley and D. Sridhara. Structure of Pseudocodewords in Tanner Graphs. Proceedings of the 2004 International Symposium on Information Theory and its Applications, (CDROM), Parma, Italy, Oct 8-10, 2004.
• C. Kelley, J. Rosenthal, and D. Sridhara. Some New Algebraic Constructions of Codes from Graphs which are Good Expanders. Proceedings of the 2003 Allerton Conference on Communication, Control, and Computing, Monticello, IL, October 2003. PDF
• E. Byrne, C. Kelley, C. Monico, and J. Rosenthal. Non-linear codes for belief propagation. Proceedings of the 2003 IEEE International Symposium on Information Theory, p. 43, Yokohama, Japan, June 2003.
• D. Pickard, L. Lovatt, M. Novelli, P. Ripley, C. Kelley, I. Bigio, and S. Brown. Diagnosis of dysplasia in Barrett's oesophagus with in-situ elastic-scattering spectroscopy. Optical Biopsy and Tissue Optics, SPIE vol. 4161, Nov. 2000.
• I. Bigio, S. Brown, G. Briggs, C. Kelley, S. Lakhani, D. Pickard, P. Ripley, I. Rose, and C. Saunders. Diagnosis of breast cancer using elastic-scattering spectroscopy: preliminary clinical results. Journal of Biomedical Optics, opt. 5, vol. 5, April 2000.
• P. Ripley, I. Rose, C. Kelley, I. Bigio, D. Pickard, G. Briggs, L. Locatt, S. Brown. A comparison of artificial intelligence techniques for spectral classification in the diagnosis of human pathologies based upon optical biopsy. Optical Society of America Biomedical Topical Meeting, Miami, FL, April 2000.

Ph.D. Students

• Kirsten Morris. Expected Ph.D. 2025. Currently a Graduate STEM Diversity Fellow.
• Dan Welchons. Expected Ph.D. 2024.
• Meraiah Martinez. Expected Ph.D. 2024.
• Emily McMillon. Expected Ph.D. 2022. Doctoral Dissertation: Theory and design of graph-based codes for improved iterative and window decoding. Received the G.C. Young and W.H. Young research award, the Linda Bors Fellowship for scholarship, and a NASA Nebraska space grant.
• Allison Beemer, Ph.D. May 2018. Doctoral dissertation: Design and Analysis of Graph-Based Codes using Algebraic Lifts and Decoding Networks. Currently an Assistant Professor of Mathematics at University of Wisconsin Eau-Claire. Allison received the G.C. Young and W. H. Young Research Award in Nov. 2016.
• Carolyn Mayer, Ph.D. May 2018. Doctoral dissertation: On Coding for Partial Erasure Channels. Currently a postdoctoral fellow at Sandia Labs. Carolyn received the Bill Leavitt Emeritus Faculty Research Award in Nov. 2016.
• John Murphree, September 2017-May 2018. Currently working a full-time position with the government.
• Kathryn Haymaker, Ph.D. May 2014. Doctoral dissertation: Algebraic and combinatorial coding techniques for flash memories. Now an Associate Professor at Villanova University and winner of the G. C. Young and W. H. Young Research Award. Katie was supported by a University of Nebraska Presidential Fellowship for the 2012-2013 year.

Undergraduate Students

• Katie McKeon, graduated May 2013 with Highest Distinction. Katie is now a Ph.D. student at Rutgers University. I co-advised her 2012-2013 Honors Thesis on Products of Voltage Graphs.
• Amy Been Bennett, graduated May 2013 with distinction. Amy is a Ph.D. student at the University of Arizona. I oversaw her 2012-2013 Honors Thesis on Pythagorean Triples over the Quaternions.
• Jessica Burow, graduated Dec. 2012. I supervised her Fall 2012 Undergraduate Creative Activities and Research Experience (UCARE) project on graph theory and social network analysis.
• Jonathan Jay Cummings, graduated May 2011 with Highest Distinction. He is now faculty at Sacramento State University. I supervised his 2010-2011 UCARE project on invariants of graph products, and also his Honors Thesis, On Invariants of Replacement Product Graphs.