I. Introduction
Reed-Solomon (RS) codes are among the most widely used codes. Their applications range from consumer electronics such as Compact Disc (CD) and Digital Versatile Disc (DVD) players to optical communication and data storage systems. Most high-throughput RS codec architectures are based on reformulated versions [10], [18] of either the Berlekamp-Massey algorithm [2], [4] or the extended Euclidean algorithm (EEA) [3], [11], [12], [13], [15], [17]. A variable number of iterations—at most for correcting up to errors— are used in most EEA-based decoders. One exception is the errors-only hypersystolic Reed-Solomon decoder proposed by Berlekamp et al. [3] that uses exactly iterations regardless of the number of errors. Of course, decoders based on the Berlekamp-Massey algorithm also use exactly iterations.