Abstract:
This paper considers space-time coding over several independently Rayleigh faded blocks. In particular, we will concentrate on giving upper bounds for the coding gain of ...Show MoreMetadata
Abstract:
This paper considers space-time coding over several independently Rayleigh faded blocks. In particular, we will concentrate on giving upper bounds for the coding gain of lattice space-time codes as the number of blocks grow. This problem was previously considered in the single antenna case by Bayer-Fluckiger et al. in 2006. Crucial to their work was Odlyzko's bound on the discriminant of an algebraic number field, as this provides an upper bound for the normalized coding gain of number field codes. In the MIMO context natural codes are constructed from division algebras defined over number fields and the coding gain is measured by the discriminant of the corresponding (noncommutative) algebra. In this paper, we will develop analogues of the Odlyzko bounds in this context and show how these bounds limit the normalized coding gain of a very general family of division algebra based space-time codes. These bounds can also be used as benchmarks in practical code design and as tools to analyze asymptotic bounds of performance as the number of independently faded blocks increases.
Published in: IEEE Transactions on Information Theory ( Volume: 61, Issue: 4, April 2015)
Funding Agency:
Department of Mathematics, University of Michigan, Ann Arbor, MI, USA
Benjamin Linowitz received his M.Sc. and Ph.D. degrees from Dartmouth College, New Hampshire, USA, in 2009 and 2012, respectively, both in pure mathematics.
Since September 2012, he has been with the Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA. His research interests include the theory of orders in central simple algebras and their applications to other fields.
Benjamin Linowitz received his M.Sc. and Ph.D. degrees from Dartmouth College, New Hampshire, USA, in 2009 and 2012, respectively, both in pure mathematics.
Since September 2012, he has been with the Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA. His research interests include the theory of orders in central simple algebras and their applications to other fields.View more
Division of Biostatistics and Bioinformatics, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
Matthew Satriano received his Ph.D. degree from the University of California, Berkeley, USA, in 2010 in pure mathematics.
Since July 2014, he has been with the Department of Oncology and Biostatistics at Johns Hopkins University, Baltimore, Maryland, USA. From 2010-14, he was with the Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA. His research interests include algebraic geometry and mathemati...Show More
Matthew Satriano received his Ph.D. degree from the University of California, Berkeley, USA, in 2010 in pure mathematics.
Since July 2014, he has been with the Department of Oncology and Biostatistics at Johns Hopkins University, Baltimore, Maryland, USA. From 2010-14, he was with the Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA. His research interests include algebraic geometry and mathemati...View more
Department of Mathematics and Statistics, University of Turku, Turku, Finland
Roope Vehkalahti received the M.Sc. and Ph.D. degrees from the University of Turku, Finland, in 2003 and 2008, respectively, both in pure mathematics.
Since September 2003, he has been with the Department of Mathematics, University of Turku, Finland. In 2011-2012 he was visiting Swiss Federal Institute of Technology, Lausanne (EPFL). His research interest include applications of algebra and number theory to information the...Show More
Roope Vehkalahti received the M.Sc. and Ph.D. degrees from the University of Turku, Finland, in 2003 and 2008, respectively, both in pure mathematics.
Since September 2003, he has been with the Department of Mathematics, University of Turku, Finland. In 2011-2012 he was visiting Swiss Federal Institute of Technology, Lausanne (EPFL). His research interest include applications of algebra and number theory to information the...View more
Department of Mathematics, University of Michigan, Ann Arbor, MI, USA
Benjamin Linowitz received his M.Sc. and Ph.D. degrees from Dartmouth College, New Hampshire, USA, in 2009 and 2012, respectively, both in pure mathematics.
Since September 2012, he has been with the Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA. His research interests include the theory of orders in central simple algebras and their applications to other fields.
Benjamin Linowitz received his M.Sc. and Ph.D. degrees from Dartmouth College, New Hampshire, USA, in 2009 and 2012, respectively, both in pure mathematics.
Since September 2012, he has been with the Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA. His research interests include the theory of orders in central simple algebras and their applications to other fields.View more
Division of Biostatistics and Bioinformatics, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA
Matthew Satriano received his Ph.D. degree from the University of California, Berkeley, USA, in 2010 in pure mathematics.
Since July 2014, he has been with the Department of Oncology and Biostatistics at Johns Hopkins University, Baltimore, Maryland, USA. From 2010-14, he was with the Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA. His research interests include algebraic geometry and mathematical cancer modeling.
Matthew Satriano received his Ph.D. degree from the University of California, Berkeley, USA, in 2010 in pure mathematics.
Since July 2014, he has been with the Department of Oncology and Biostatistics at Johns Hopkins University, Baltimore, Maryland, USA. From 2010-14, he was with the Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA. His research interests include algebraic geometry and mathematical cancer modeling.View more
Department of Mathematics and Statistics, University of Turku, Turku, Finland
Roope Vehkalahti received the M.Sc. and Ph.D. degrees from the University of Turku, Finland, in 2003 and 2008, respectively, both in pure mathematics.
Since September 2003, he has been with the Department of Mathematics, University of Turku, Finland. In 2011-2012 he was visiting Swiss Federal Institute of Technology, Lausanne (EPFL). His research interest include applications of algebra and number theory to information theory.
Roope Vehkalahti received the M.Sc. and Ph.D. degrees from the University of Turku, Finland, in 2003 and 2008, respectively, both in pure mathematics.
Since September 2003, he has been with the Department of Mathematics, University of Turku, Finland. In 2011-2012 he was visiting Swiss Federal Institute of Technology, Lausanne (EPFL). His research interest include applications of algebra and number theory to information theory.View more