Reed-solomon Related Codes: New Approaches to Performance Analysis and Decoding Algorithms

Reed-Solomon (RS) codes are very important due to their ubiquity and utility. Sudan's algorithm is a breakthrough that will render the current state-of-the-art RS decoders obsolete. This work takes a few steps toward a deeper understanding of the performance of RS related codes as well as toward the design of efficient algorithms for decoding them. The performance of optimum decoding of binary images of RS codes and their product codes is carefully studied. RS related codes in network scenarios are also analyzed. Advanced decoding techniques for RS codes and their products, based on Sudan's breakthrough, are proposed in this work and their performance is analyzed: it is shown that algebraic soft-decision decoding algorithms approach the ultimate performance limits of RS codes. Sphere decoding of linear codes and Reed-Solomon related codes is also analyzed and studied in this work. This work sheds light on important new decoding techniques of Reed-Solomon codes and their related codes as well as new approaches to their performance analysis. This work should be especially useful for professionals in electrical engineering interested in data communications and channel coding.