Abstract
This survey paper gives an overview of algebraic unitary codes. It describes the coding problem involved, and present several algebraic approaches yielding interesting constructions, as well as the latest bounds.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abarbanel, J., Averbuch, A., Rosset, S., Zlotnick, J.: Unitary non-group STBC codes from cyclic algebras. IEEE Trans. Inform. Theory 52, 3903–3912 (2006)
Creignou, J., Diete, H.: Linear programming bounds for unitary space time codes. In: Proceedings of International Symposium on Information Theory (ISIT), Toronto (2008)
Han, G., Rosenthal, J.: Unitary Space-Time Constellation Analysis: An Upper Bound for the Diversity. IEEE Trans. Inform. Theory 52(10), 4713–4721 (2006)
Hassibi, B., Hochwald, B.: Cayley Differential Unitary Space-Time Codes. IEEE Trans. on Information Theory 48 (June 2002)
Hochwald, B., Sweldens, W.: Differential unitary space time modulation. IEEE Trans. Commun. 48 (December 2000)
Hassibi, B., Khorrami, M.: Fully-diverse multiple-antenna signal constellations and fixed-point free Lee groups. In: Proceedings of International Symposium on Information Theory (ISIT), Washington DC (2001), mars.bell-labs.com/cm/ms/what/mars/papers/lie/lie.ps
Hughes, B.: Differential space-time modulation. IEEE Trans. Inform. Theory 46 (November 2000)
Hughes, B.L.: Optimal space-time constellations from groups. IEEE Trans. Inform. Theory 49, 401–410 (2003)
Jing, Y., Hassibi, B.: Three-Transmit-Antenna Space-Time Codes Based on SU(3). IEEE Trans. Signal Processing 53(10) (October 2005)
Jing, Y., Hassibi, B.: Design of full-diverse multiple-antenna codes based on Sp(2). IEEE Trans. on Information Theory 50(11) (November 2004)
Liang, X.-B., Xia, X.-G.: Unitary Signal Constellations for Differential Space-Time Modulation With Two Transmit Antennas: Parametric Codes, Optimal Designs, and Bounds. IEEE Trans. on Inform. Theory 48(8) (August 2002)
Oggier, F., Lequeu, E.: Families of unitary matrices achieving full diversity., Proceedings of the International Symposium on Information Theory (ISIT), Adelaide (2005)
Oggier, F.: Cyclic Algebras for Noncoherent Differential Space-Time Coding. IEEE Transactions on Information Theory 53(9) (September 2007)
Oggier, F., Hassibi, B.: Algebraic Cayley differential Space-Time Codes. IEEE Transactions on Information Theory 53(5) (May 2007)
Oggier, F.: Design of Algebraic Cyclic Codes. In: Proceedings of the Information Theory Workshop (ITW), Porto (2008)
Pierce, R.S.: Associative Algebras. Springer, New York (1982)
Reiner, I.: Maximal Orders. Academic Press, London (1975)
Sethuraman, B.A., Rajan, B.S., Shashidhar, V.: Full-diversity, high-rate space-time block codes from division algebras. IEEE Trans. Inform. Theory 49, 2596–2616 (2003)
Shokrollahi, A., Hassibi, B., Hochwald, B.M., Sweldens, W.: Representation Theory for High-Rate Multiple-Antenna Code Design. IEEE Trans. Information Theory 47(6) (September 2001)
Xing, C.: Constructions of unitary space-time codes from number fields (preprint)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oggier, F. (2009). A Survey of Algebraic Unitary Codes. In: Chee, Y.M., Li, C., Ling, S., Wang, H., Xing, C. (eds) Coding and Cryptology. IWCC 2009. Lecture Notes in Computer Science, vol 5557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01877-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-01877-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01813-8
Online ISBN: 978-3-642-01877-0
eBook Packages: Computer ScienceComputer Science (R0)