Cyclic Division Algebras: A Tool for Space-Time Coding (Foundations and Trends in Communications and Information Theory)

✍ Scribed by Frederique Oggier, Jean-Claude Belfiore, Emanuele Viterbo

• Year: 2007
• Tongue: English
• Leaves: 108
• Category: Library

✦ Synopsis

Cyclic Division Algebras: A Tool for Space-Time Coding provides a tutorial introduction to the algebraic tools involved in the design of codes based on division algebras. The different design criteria involved are illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property and the diversity multiplexing tradeoff. Finally complete mathematical background underlying the construction of the Golden code and the other Perfect Space-Time block codes is given.

✦ Table of Contents

Contents......Page 10
1. Introduction......Page 12
1.1 Division Algebra Based Codes......Page 13
1.2 Organization......Page 14
2.1 Introduction......Page 16
2.2 Design Criteria for Space–Time Codes......Page 18
2.3 Modulations and Full-Rate Codes......Page 21
2.4 Decoding......Page 24
2.5 Constellation Shaping......Page 25
3. An Information Theoretic Perspective......Page 32
3.1 Mutual Information of a Gaussian MIMO Channel......Page 33
3.2 The Outage Probability......Page 34
3.3 Diversity-Multiplexing Gain Trade-off of MIMO Channels......Page 38
3.4 Trade-off Achieving Codes......Page 43
3.5 Non-Vanishing Determinant Codes......Page 48
3.6 Information Preserving Codes......Page 50
4. Cyclic Division Algebras......Page 52
4.1 Fields and Algebras......Page 53
4.2 Algebras on Number Fields......Page 56
4.3 Norm and Ring of Integers......Page 66
4.4 Shaping, Lattices and Discriminant......Page 72
5.1 Definition of Perfect Space–Time Codes......Page 80
5.2 The Golden Code......Page 83
5.3 A Perfect STBC for 3 Antennas......Page 86
5.4 A Perfect STBC for 4 Antennas......Page 88
5.5 A Perfect STBC for 5 Antennas......Page 90
5.6 A Perfect STBC for 6 Antennas......Page 92
5.7 Optimality of Perfect STBCs......Page 94
6.1 Coding for Wireless Networks......Page 96
6.2 Trellis/Block Coded Modulations......Page 98
6.3 Other Issues......Page 99
6.4 Conclusion......Page 100
Acknowledgments......Page 102
References......Page 104