STBCs using capacity achieving designs from crossed-product division algebras

We construct full-rank, rate-n space-time block codes (STBC), over any a priori specified signal set for n-transmit antennas using crossed-product division algebras and give a sufficient condition for these STBCs to be information lossless. A class of division algebras for which this sufficient condition is satisfied is identified. Simulation results are presented to show that STBCs constructed in this paper perform better than the best known codes, including those constructed from cyclic division algebras and also to show that they are very close to the capacity of the channel with QAM input.

[1]  N. Jacobson,et al.  Basic Algebra I , 1976 .

[2]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[3]  Jean-Claude Belfiore,et al.  Quaternionic lattices for space-time coding , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[4]  Peter Hilton,et al.  The Algebra ℝ I , 1970 .

[5]  A. Goldie.  NON COMMUTATIVE RINGS (CARUS MATHEMATICAL MONOGRAPHS NO. 15) , 1970 .

[6]  B. Sethuraman,et al.  STBC from field extensions of the rational field , 2002, Proceedings IEEE International Symposium on Information Theory,.

[7]  A. Robert Calderbank,et al.  Space-Time block codes from orthogonal designs , 1999, IEEE Trans. Inf. Theory.

[8]  B. Sundar Rajan,et al.  Full-diversity, high-rate space-time block codes from division algebras , 2003, IEEE Trans. Inf. Theory.

[9]  B. Sundar Rajan,et al.  Optimal STBC over PSK signal sets from cyclotomic field extensions , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[10]  Mohamed Oussama Damen,et al.  A construction of a space-time code based on number theory , 2002, IEEE Trans. Inf. Theory.

[11]  Babak Hassibi,et al.  High-rate codes that are linear in space and time , 2002, IEEE Trans. Inf. Theory.

[12]  Siavash M. Alamouti,et al.  A simple transmit diversity technique for wireless communications , 1998, IEEE J. Sel. Areas Commun..

[13]  B. Sundar Rajan,et al.  Information-lossless STBCs from crossed-product algebras , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[14]  B. Sundar Rajan,et al.  STBCs using capacity achieving designs from cyclic division algebras , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[15]  B. Sundar Rajan,et al.  High-rate, full-diversity STBCs from field extensions , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[16]  Sandra Galliou,et al.  A new family of full rate, fully diverse space-time codes based on Galois theory , 2002, Proceedings IEEE International Symposium on Information Theory,.

[17]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[18]  B. Sundar Rajan,et al.  An algebraic description of orthogonal designs and the uniqueness of the Alamouti code , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.