An Early-Termination Method for the Welch-Berlekamp Algorithm

This paper presents an early-termination method for the Welch-Berlekamp algorithm. Specifically, if e ≤ t (where e is the number of errors and t is the error correction capability), the Welch–Berlekamp algorithm can be terminated at latest at the completion of the (t + e)-th iteration. Based on the early-termination mechanism, a new variant of the Welch–Berlekamp algorithm called eFDMA is presented, and a systolic architecture is designed for the eFDMA algorithm. This provides an efficient implementation for the key equation solver for a new class of Reed–Solomon codes recently proposed by Lin et al. [9].