Tutorial On Reed Solomon Error Correction Coding

Tutorial on Reed-Solomon Error Correction Coding

Tutorial on Reed-Solomon Error Correction Coding

This tutorial attempts to provide a frank, step-by-step approach to Reed-Solomon (RS) error correction coding. RS encoding and RS decoding both with and without erasing code symbols are emphasized. There is no need to present rigorous proofs and extreme mathematical detail. Rather, the simple concepts of groups and fields, specifically Galois fields, are presented with a minimum of complexity. Before RS codes are presented, other block codes are presented as a technical introduction into coding. A primitive (15, 9) RS coding example is then completely developed from start to finish, demonstrating the encoding and decoding calculations and a derivation of the famous error-locator polynomial. The objective is to present practical information about Reed-Solomon coding in a manner such that it can be easily understood. Geisel, William A. Johnson Space Center CODING; DECODING; ERROR ANALYSIS; FIELD THEORY (ALGEBRA); MAXIMUM LIKELIHOOD ESTIMATES; POLYNOMIALS; ERRORS; PROVING; SYMBOLS...

Algebraic Codes for Data Transmission

Error-correcting codes play a fundamental role in modern communications and data-storage systems. This volume provides an accessible introduction to the basic elements of algebraic codes and discusses their use in a variety of applications. The author describes a range of important coding techniques, including Reed-Solomon codes, BCH codes, trellis codes, and turbocodes. Throughout the book, mathematical theory is illustrated by reference to many practical examples. The book is written for graduate students of electrical and computer engineering and practicing engineers whose work involves communications or signal processing.