On Constructions Of Unitary Space-Time Codes And Their Bounds

Recent advances in wireless communication systems have increased the throughput over wireless channels and networks. At the same time, the reliability of wireless communication has been increased. As a result, customers use wireless systems more often. Recent study of information theory shows that it can obviously increase the communicative capacity using the multiple-input multiple-output system. Over multiple-input and multiple-output channels, space-time coding is one of practical coding that can make the informational capacity approaching the theoretical capacity. Tarokh, Se-shadri and Calderbank introduced the fundamental principle of space-time coding in 1998. After that, space-time coding and the signal processing technology of multiple-input multiple-output system have been significantly developed and broadly applied over wireless communication system.This dissertation is organized as follows.In Chapter 1, the motivation and background on space-time codes are introduced. Moreover, the main results of this dissertation are also given.The preliminary results and theory on algebraic function fields such as the Riemann-Roch theorem, approximation theorem, algebraic extension theory, Hermitian function fields, Hurwitz genus formula etc, are introduced in Chapter 2.In Chapter 3, we mainly concentrate on algebraic geometric codes. Some basic notations and results in coding theory such as communication channels, binary error-correcting codes, maximum likelihood decoding rule. Reed-Solomon codes and some bounds are introduced. Furthermore, we study some codes over rings and some simple properties of algebraic geometric codes, Hermitian codes.Chapter 4 is devoted to constructions of space-time codes. After analyzing multi-input and multi-output systems and their capacities, we derive requirements of encoding and decoding a space-time code and give a few design criterions for space-time codes. Finally in this chapter, we design a class of space-time codes through various methods. It turns out that codes constructed in this chapter are better than previously best-known codes.A constructive lower bound on kissing number is derived from algebraic geometric codes in Chapter 5. Afterwards, this bound is applied to bounds on unitary space-time codes.In the last chapter, we suggest some future research work on space-time codes.