New Approaches to the Analysis and Design of Reed-Solomon Related Codes

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.</p

Blind Detection Of High Data Rate Wireless CDMA In Multipath Channels

ABSTRACT We study the performance of a DS-CDMA blind multiuser detector in multipath Rayleigh fading channels for high data rates where the delay spread can be larger than one symbol duration. We propose blind recursive minimum output variance detectors for multipath channels with an additional constraint on the energy of the filter tap weights. This constraint prevents the cancellation of the desired signal in case the estimated subspace of the desired signal suffers from a mismatch. Simulations show that in cases of high Signal to Interference and Noise Ratios (SINR) as well as in cases of severe Inter-Symbol Interference (ISI), our proposed detector is superior to previously proposed detectors for multipath channels