An Earlier Termination Algorithm to Find Error Locator Polynomial in Error Correction of RS Codes

Reed-Solomon (RS) codes are widely used to correct errors, finding the error locator polynomial is one of the key steps in the error correction procedure of RS codes. Modular Approach (MA) is a classical algorithm to solve the Welch-Berlekamp (WB) key-equation problem to find the error locator polynomial that needs
$2t$
steps, where
$t$
is the error correction capability. In this paper, we present a new MA algorithm that only requires
$2e$
steps, where
$e$
is the number of errors. Moreover, we propose a new error correction algorithm based on our MA algorithm, which is called the Improved-Frequency Domain Modular Approach (I-FDMA) algorithm. We show that, compared with the existing methods based on MA algorithms, our I-FDMA algorithm can effectively reduce the decoding complexity of RS codes when
$e < t$
.