On decoding methods beyond the BCH bound and their applications to soft-decision decoding

For the two-dimensional BCH code, several decoding methods exceeding the BCH bound and correcting the errors that cannot be corrected by the conventional limited distance decoding method have been proposed. This article proposes an algorithm that allows reduction of the computational volume in a decoding method exceeding the BCH bound by solving the equation for unknown variables beforehand and limiting the range of the error location. Further, this decoding method exceeding the BCH bound is applied to soft-decision decoding methods that use limited-distance decoding multiple times, and especially to Chase decoding, the decoding of Tanaka et al., and that of Kaneko et al. It is shown that the amount of computation and the decoding error rate are improved.