Expander codes
Joint with Gilles Zémor:
·
Error exponents of expander codes, IEEE Trans. Inform. Theory,
June 2002.
·
Error exponents of expander codes under linear-time decoding,
SIAM J. Discrete Math., 2004.
·
Concatenated codes: serial and parallel, IEEE Trans. Inform. Theory,
May 2005
·
Distance properties of expander codes, IEEE Trans. Inform. Theory,
Jan. 2006,
arXiv.org:cs.IT/0409010
·
Multilevel expander codes,
in "Algebraic Coding Theory and Information Theory,"
American Math. Soc. 2005, pp. 69-83. (vol. 68, AMS-DIMACS series).
arXiv.org:cs.IT/0502079
Error bounds
·
Random codes: minimum distances and
error exponents, with G. D. Forney, Jr. IEEE Trans. Inform.
Theory 48 , 9, 2002, 2568-2573
·
Improved bounds for the erasure/list scheme,
IEEE Trans. Inform. Theory 2005.
arXiv.org:cs.IT/0407010
·
Distance distribution of binary codes and the error probability
of decoding, with A. McGregor, IEEE Trans. Inform. Theory, Dec. 2005.
arXiv.org:cs.IT/0407011
·
A new upper bound on the reliability function of the Gaussian
channel, with A. Ashikhmin and S. Litsyn,
IEEE Trans. Inform. Theory, 1999.
Quantum codes
·
A quantum decoding algorithm of the
simplex code, with S. Zhou, Allerton conference, about 1998.
·
A low-rate bound on the reliability of a quantum
discrete memoryless channel,
IEEE Trans. Inform. Theory, Dec. 2002.
·
Quantum error detection I,
IEEE Trans. Inform. Theory, May 2000.
Extremal problems
·
Estimates of the distance distribution of codes
and designs, with A. Ashikhmin and S. Litsyn,
IEEE Trans. Inform. Theory, March 2001, 1050-1061.
·
Extremal problems of coding theory,
in book: H. Niederreiter, Editor, "Coding Theory and Cryprography,"
World Scientific, 2002, pp. 1-48.
(Notes of lectures at the Institute for Math. Sciences of the
University of Singapore, Sept. 01)
·
Bounds on packings of spheres in the Grassmann manifolds,
with D. Yu. Nogin, IEEE Trans. Inform. Theory, Sept. 2002.
· Spectral approach
to linear programming bounds on codes, with D. Yu. Nogin,
Problems of Information Transmission, 12, 2,
2006, 77-89, arXiv.org:cs.IT/0512025
· A bound on Grassmannian codes, with D. Yu. Nogin,
Journal of Combinatorial Theory Ser. A 113, 8, 2006, 1629-1635 (Van Lint memorial issue).
cs.IT/0512024
· Codes in spherical caps, with Oleg Musin,
Advances in Math. of Communications 2007. arXiv.org:math.MG/0606734
· Bounds on ordered codes and orthogonal arrays,
with Punarbasu Purkayastha.
arXiv:cs/0702033
Fingeprinting
·
Digital fingerprinting codes: Problem statements,
constructions, identification of traitors, with
G. R. Blakley and G. Kabatiansky, IEEE Trans. Inform. Theory,
April 2003.
·
A hypergraph approach to IPP codes: the case of multiple
parents, joint with G. Cohen, S. Encheva, G. Kabatisanky and
G. Zémor, SIAM J. Discrete Math., Nov. 2001.
·
A class of IPP codes with efficient identification, with G. Kabatiansky, Journal of Complexity, 2004.
·
Fingerprinting capacity under the marking assumption, with N.P. Anthapadmanabhan and I. Dumer,
IEEE Trans. Inform. Theory, Jun. 2008.
Concatenated codes
·
Concatenated codes with fixed inner codes and random outer codes,
with J. Justesen and C. Thommesen,
IEEE Trans. Inform. Theory, Jan. 2001.
·
Improved bounds for list decoding of concatenated codes, with
A. McGregor, preprint (2004)
Surveys, popular
·
Complexity issues in coding theory, in book: Handbook of Coding
Theory, vol. 1, Elsevier Science, 1998, pp. 649-754
·
At the dawn of the theory of codes
The Mathematical Intelligencer, 15, 1, 1993, 20-26.
·
What is the Fortune,
Kvant 9 (1990) (in Russian).
Working notes on error bounds are now included in Lecture Notes for ENEE739C, see in particular Lect. 5. See also the paper "Extremal problems" on this page.