Cyclic Division Algebras: A Tool for Space-Time Coding

被引:52
作者
Oggier, Frederique [1 ]
Belfiore, Jean-Claude [2 ]
Viterbo, Emanuele [3 ]
机构
[1] CALTECH, Dept Elect Engn, Pasadena, CA 91125 USA
[2] Ecole Natl Super Telecommun Bretagne, F-75013 Paris, France
[3] Univ Calabria, Dipartimento Elettron Informat & Sistemist, Arcavacata Di Rende, Italy
来源
FOUNDATIONS AND TRENDS IN COMMUNICATIONS AND INFORMATION THEORY | 2007年 / 4卷 / 01期
关键词
Cyclic algebras; division algebras; full diversity; golden code; non-vanishing determinant; perfect space-time codes; space-time coding;
D O I
10.1561/0100000016
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space-Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space-Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space-Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space-Time block codes.
引用
收藏
页码:1 / 95
页数:12
相关论文
共 63 条
[1]   On the achievable diversity-multiplexing tradeoff in half-duplex cooperative channels [J].
Azarian, K ;
El Gamal, H ;
Schniter, P .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (12) :4152-4172
[2]   New algebraic constructions of rotated Zn-Lattice constellations for the Rayleigh fading channel [J].
Bayer-Fluckiger, E ;
Oggier, F ;
Viterbo, E .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (04) :702-714
[3]  
BAYERFLUCKIGER E, 1999, CONT MATH, V241, P69
[4]  
Belfiore J.-C., 2003, P ITW 2003 PAR APR
[5]  
Belfiore J.-C., 2006, SPACE TIME WIRELESS
[6]   The Golden code: A 2x2 full-rate space-time code with nonvanishing determinants [J].
Belfiore, JC ;
Rekaya, G ;
Viterbo, E .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (04) :1432-1436
[7]  
Biglieri E., 1998, IEEE T INFORM THEORY, V44
[8]  
Bolcskei H., 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252), DOI 10.1109/ISIT.2001.936082
[9]  
Champion D., 2006, CAN WORKSH INF THEOR
[10]  
Conway J.H., 1988, SPHERE PACKINGS LATT