ON THE REED-SOLOMON CODES

Abstract

The Reed-Solomon (RS) codes are among the most powerful methods to preserve data integrity from errors and erasures for storage or transmission purposes. This coding technique has been proven to be a high performance while maintaining a reasonable cost and productivity. Unlike some coding techniques that enforce data transmission as a sequence of binary numbers, Reed-Solomon encodes the message as non-binary symbols. This gives Reed-Solomon the advantage of handling bursts of errors or even erasure error. It plays a significant role in modern communication systems and many daily life applications. Some known applications of this coding technique are the fault-tolerant systems in CD disks, and the communication protocol in satellites and spaceships. In the paper, we give the basic properties and structures of the Reed-Solomon codes by discussing its mathematics models. The encoding process with the original approach and the modern BCH approaches. For the decoding process, we investigate a wide range of algorithms and techniques, such as Syndrome decoding, RiBM algorithm, Chien search and Forney algorithm. Finally, we present the result is a functional Reed-Solomon encoder and decoder implemented using the MATLAB platform and give examples of encoding and decoding with different messages.