A new Reed-Solomon code decoding algorithm based on Newton's interpolation

• Published in: IEEE transactions on information theory Vol. 39; no. 2; pp. 358 - 365
• Main Author: Sorger, U.K.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.1993; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Coding, codes; Decoding; Delay; Encoding; Equations; Exact sciences and technology; Fourier transforms; Information, signal and communications theory; Interpolation; Polynomials; Redundancy; Reed-Solomon codes; Signal and communications theory; Telecommunications and information theory; Time domain analysis; Reed Solomon code; Interpolation; Parallel algorithm; Minimal distance; Decoding
• ISSN: 0018-9448
• DOI: 10.1109/18.212267

A Reed-Solomon code decoding algorithm based on Newton's interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-minimum-distance decoding complexity becomes O(dn), with n the length and d the distance of the code (including the calculation of all error locations and values). This asymptotic complexity is optimal. Other applications are the possibility of fast decoding of Reed-Solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay.< >