Abstract:
Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, ...Show MoreMetadata
Abstract:
Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of n elements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size of codes. These bounds enable us to establish the exact scaling of the size of optimal codes for large values of n. We also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors.
Published in: IEEE Transactions on Information Theory ( Volume: 56, Issue: 7, July 2010)
Department of Electrical and Computer Engineering, Institute of Systems Research, University of Maryland, College Park, MD, USA
Institute for Problems of Information Transmission, Moscow, Russia
Alexander Barg (M'00–SM'01–F'08) received the M.Sc. degree in applied mathematics and the Ph.D. degree in electrical engineering (information theory), the latter from the Institute for Information Transmission Problems (IPPI), Moscow, Russia, in 1987.
He has been a Senior Researcher at the IPPI since 1988. He spent 1995 and 1996 at the Technical University of Eindhoven, Eindhoven, The Netherlands. During 1997–2002, he was ...Show More
Alexander Barg (M'00–SM'01–F'08) received the M.Sc. degree in applied mathematics and the Ph.D. degree in electrical engineering (information theory), the latter from the Institute for Information Transmission Problems (IPPI), Moscow, Russia, in 1987.
He has been a Senior Researcher at the IPPI since 1988. He spent 1995 and 1996 at the Technical University of Eindhoven, Eindhoven, The Netherlands. During 1997–2002, he was ...View more
Department of Electrical and Computer Engineering, Institute of Systems Research, University of Maryland, College Park, MD, USA
Arya Mazumdar (S'05) received the B.E. degree in electronics and telecommunication engineering and the M.Tech. degree in electrical engineering, respectively, from Jadavpur University, India, in 2003, and the Indian Institute of Technology (Kanpur), India, in 2005. He is currently pursuing the Ph.D. degree in the Department of Electrical and Computer Engineering, University of Maryland, College Park.
During the summer of 2...Show More
Arya Mazumdar (S'05) received the B.E. degree in electronics and telecommunication engineering and the M.Tech. degree in electrical engineering, respectively, from Jadavpur University, India, in 2003, and the Indian Institute of Technology (Kanpur), India, in 2005. He is currently pursuing the Ph.D. degree in the Department of Electrical and Computer Engineering, University of Maryland, College Park.
During the summer of 2...View more
Contents Department of Electrical and Computer Engineering, Institute of Systems Research, University of Maryland, College Park, MD, USA
Institute for Problems of Information Transmission, Moscow, Russia
Alexander Barg (M'00–SM'01–F'08) received the M.Sc. degree in applied mathematics and the Ph.D. degree in electrical engineering (information theory), the latter from the Institute for Information Transmission Problems (IPPI), Moscow, Russia, in 1987.
He has been a Senior Researcher at the IPPI since 1988. He spent 1995 and 1996 at the Technical University of Eindhoven, Eindhoven, The Netherlands. During 1997–2002, he was a Member of Technical Staff, Bell Labs, Lucent Technologies. Since 2003, he has been a Professor in the Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park. His research interests include coding and information theory and its links with computer science and mathematics.
Dr. Barg served as Associate Editor for Coding Theory of the IEEE Transactions on Information Theory from 1997–2000. He was the Technical Program Co-Chair of the 2006 IEEE International Symposium on Information Theory. He is presently a member of the Board of Governors of the Information Theory Society and serves on the Editorial Board of several journals including Problems of Information Transmission, SIAM Journal on Discrete Mathematics, and Advances in Mathematics of Communications.
Alexander Barg (M'00–SM'01–F'08) received the M.Sc. degree in applied mathematics and the Ph.D. degree in electrical engineering (information theory), the latter from the Institute for Information Transmission Problems (IPPI), Moscow, Russia, in 1987.
He has been a Senior Researcher at the IPPI since 1988. He spent 1995 and 1996 at the Technical University of Eindhoven, Eindhoven, The Netherlands. During 1997–2002, he was a Member of Technical Staff, Bell Labs, Lucent Technologies. Since 2003, he has been a Professor in the Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park. His research interests include coding and information theory and its links with computer science and mathematics.
Dr. Barg served as Associate Editor for Coding Theory of the IEEE Transactions on Information Theory from 1997–2000. He was the Technical Program Co-Chair of the 2006 IEEE International Symposium on Information Theory. He is presently a member of the Board of Governors of the Information Theory Society and serves on the Editorial Board of several journals including Problems of Information Transmission, SIAM Journal on Discrete Mathematics, and Advances in Mathematics of Communications.View more
Department of Electrical and Computer Engineering, Institute of Systems Research, University of Maryland, College Park, MD, USA
Arya Mazumdar (S'05) received the B.E. degree in electronics and telecommunication engineering and the M.Tech. degree in electrical engineering, respectively, from Jadavpur University, India, in 2003, and the Indian Institute of Technology (Kanpur), India, in 2005. He is currently pursuing the Ph.D. degree in the Department of Electrical and Computer Engineering, University of Maryland, College Park.
During the summer of 2008, he visited the Hewlett-Packard Laboratories, Palo Alto, CA, as a research intern. His research interests include coding theory, information theory, and combinatorics.
Mr. Mazumdar is a recipient of the ECE Fellowship award at the University of Maryland. He was awarded scholarships from the Ministry of Human Resource and Development and National Council for Educational Research and Training in India during his graduate and undergraduate studies, respectively.
Arya Mazumdar (S'05) received the B.E. degree in electronics and telecommunication engineering and the M.Tech. degree in electrical engineering, respectively, from Jadavpur University, India, in 2003, and the Indian Institute of Technology (Kanpur), India, in 2005. He is currently pursuing the Ph.D. degree in the Department of Electrical and Computer Engineering, University of Maryland, College Park.
During the summer of 2008, he visited the Hewlett-Packard Laboratories, Palo Alto, CA, as a research intern. His research interests include coding theory, information theory, and combinatorics.
Mr. Mazumdar is a recipient of the ECE Fellowship award at the University of Maryland. He was awarded scholarships from the Ministry of Human Resource and Development and National Council for Educational Research and Training in India during his graduate and undergraduate studies, respectively.View more
