Cyclic division algebras
Subtitle: a tool for space-time coding
By: Frédérique Oggier, Jean-Claude Belfiore, Emanuele Viterbo
Contributors: Belfiore, Jean-Claude; Viterbo, Emanuele
Series: Foundations and trends in communications and information theory -- v. 4, no. 1; Foundations and trends in communications and information theory -- v. 4, no. 1.
Publisher: Now Publishers
Published: 2007
Place of publication: Hanover, MA
Language: eng
Format: [electronic resource] :
Number of pages: 97
ISBN-13: 9781601980519
Subjects: TECHNOLOGY & ENGINEERING; Space time codes; Division algebras; Mathematics; MIMO systems; Telecommunications
Description: 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.
Notes: "This book is originally published as Foundations and trends in communications and information theory, volume 4, issue 1 (2007)"--P. [4] of cover.

Includes bibliographical references (p. 93-97).

Description based on print version record.
Table of contents: title: Abstract; title: 1. Introduction; title: 2. MIMO system model; title: 3. Information theorectic perspective; title: 4. Cyclic division algebras; title: 5. Perfect space-time block codes; title: 6. New applications and conclusion; title: Acknowledgements; title: References.