Perfect Space–Time Block Codes

In this paper, we introduce the notion of perfect space-time block codes (STBCs). These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas

[1]  Alexander Schiemann,et al.  Classification of Hermitian Forms with the Neighbour Method , 1998, J. Symb. Comput..

[2]  Hesham El Gamal,et al.  A new approach to layered space-Time coding and signal processing , 2001, IEEE Trans. Inf. Theory.

[3]  S. Lang Algebraic Number Theory , 1971 .

[4]  P. Vijay Kumar,et al.  Explicit Space–Time Codes Achieving the Diversity–Multiplexing Gain Tradeoff , 2006, IEEE Transactions on Information Theory.

[5]  Mohamed Oussama Damen,et al.  Universal space-time coding , 2003, IEEE Trans. Inf. Theory.

[6]  Emanuele Viterbo,et al.  A universal lattice code decoder for fading channels , 1999, IEEE Trans. Inf. Theory.

[7]  J. Neukirch Algebraic Number Theory , 1999 .

[8]  Harvey Cohn,et al.  Advanced Number Theory , 1980 .

[9]  Babak Hassibi,et al.  On the sphere-decoding algorithm I. Expected complexity , 2005, IEEE Transactions on Signal Processing.

[10]  Frédérique E. Oggier,et al.  Algebraic lattice constellations: bounds on performance , 2006, IEEE Transactions on Information Theory.

[11]  Huguette Napias,et al.  A generalization of the LLL-algorithm over euclidean rings or orders , 1996 .

[12]  Frédérique E. Oggier,et al.  New algebraic constructions of rotated cubic lattice constellations for the Rayleigh fading channel , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[13]  Emanuele Viterbo,et al.  The golden code: a 2 x 2 full-rate space-time code with non-vanishing determinants , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[14]  J. G. Pierce,et al.  Geometric Algorithms and Combinatorial Optimization , 2016 .

[15]  Frédérique E. Oggier,et al.  Algebraic Number Theory and Code Design for Rayleigh Fading Channels , 2004, Found. Trends Commun. Inf. Theory.

[16]  Mohamed Oussama Damen,et al.  Lattice code decoder for space-time codes , 2000, IEEE Communications Letters.

[17]  Frédérique E. Oggier,et al.  New algebraic constructions of rotated Z/sup n/-lattice constellations for the Rayleigh fading channel , 2004, IEEE Transactions on Information Theory.

[18]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[19]  Lizhong Zheng,et al.  Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels , 2003, IEEE Trans. Inf. Theory.

[20]  A. Blokhuis SPHERE PACKINGS, LATTICES AND GROUPS (Grundlehren der mathematischen Wissenschaften 290) , 1989 .

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

[22]  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,.

[23]  DRAFT. April , 2004 .

[24]  Pranav Dayal,et al.  An optimal two transmit antenna space-time code and its stacked extensions , 2005, IEEE Transactions on Information Theory.

[25]  P. Dayal,et al.  An optimal two transmit antenna space-time code and its stacked extensions , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[26]  Thomas C. Hales Sphere packings, I , 1997, Discret. Comput. Geom..

[27]  Jean-Claude Belfiore,et al.  On the complexity of ml lattice decoders for decoding linear full rate space-time codes , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[28]  M. Carral,et al.  Quadratic and λ-hermitian forms , 1989 .

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

[30]  Emanuele Viterbo,et al.  The golden code: a 2×2 full-rate space-time code with nonvanishing determinants , 2004, IEEE Trans. Inf. Theory.

[31]  P. Vijay Kumar,et al.  Explicit, Minimum-Delay Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeo , 2004 .

[32]  H. P. F. Swinnerton-Dyer A brief guide to algebraic number theory , 2001 .

[33]  G. David Forney,et al.  Efficient Modulation for Band-Limited Channels , 1984, IEEE J. Sel. Areas Commun..

[34]  Fernando Q. Gouvêa,et al.  P-Adic Numbers: An Introduction , 1993 .

[35]  A. Robert Calderbank,et al.  Space-Time Codes for High Data Rate Wireless Communications : Performance criterion and Code Construction , 1998, IEEE Trans. Inf. Theory.

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

[37]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

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