Caltech Library System

About | Browse | Search | Caltech Student Instructions

Type of Document	Dissertation
Author	El-Khamy, Mostafa
Author's Email Address	mostafa AT systems.caltech.edu
URN	etd-10102006-120159
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-10102006-120159
Title	New approaches to the analysis and design of Reed-Solomon related codes
Degree	PhD
Option	Electrical Engineering
Advisory Committee	Advisor Name Title Robert J. McEliece Committee Chair Babak Hassibi Committee Member Dariush Divsalar Committee Member Marc Fossorier Committee Member P.P. Vaidyanathan Committee Member
Keywords	iterative decoding multiuser product codes algebraic soft decoding list decoding error-correcting codes Reed-Solomon
Date of Defense	2006-09-06
Availability	unrestricted
Abstract The research that led to this thesis was inspired by Sudan's breakthrough that demonstrated that Reed-Solomon codes can correct more errors than previously thought. This breakthrough can render the current state-of-the-art Reed-Solomon decoders obsolete. Much of the importance of Reed-Solomon codes stems from their ubiquity and utility. This thesis takes a few steps toward a deeper understanding of Reed-Solomon codes as well as toward the design of efficient algorithms for decoding them. After studying the binary images of Reed-Solomon codes, we proceeded to analyze their performance under optimum decoding. Moreover, we investigated the performance of Reed-Solomon codes in network scenarios when the code is shared by many users or applications. We proved that Reed-Solomon codes have many more desirable properties. Algebraic soft decoding of Reed-Solomon codes is a class of algorithms that was stirred by Sudan's breakthrough. We developed a mathematical model for algebraic soft decoding. By designing Reed-Solomon decoding algorithms, we showed that algebraic soft decoding can indeed approach the ultimate performance limits of Reed-Solomon codes. We then shifted our attention to products of Reed-Solomon codes. We analyzed the performance of linear product codes in general and Reed-Solomon product codes in particular. Motivated by these results we designed a number of algorithms, based on Sudan's breakthrough, for decoding Reed-Solomon product codes. Lastly, we tackled the problem of analyzing the performance of sphere decoding of lattice codes and linear codes, e.g., Reed-Solomon codes, with an eye on the tradeoff between performance and complexity.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    mythesisElk.pdf 4.40 Mb 00:20:21 00:10:28 00:09:09 00:04:34 00:00:23