Abstract: A fast and efficient method and system for computation of cubic-spline interpolation for data compression is described. In one aspect, the present invention is a method and system for defining a cubic-spline filter; correlating the filter with the signal to obtain a correlated signal; autocorrelating the filter to obtain autocorrelated filter coefficients; computing a transform of the correlated signal and the autocorrelated filter coefficients; dividing the transform of the correlated signal by the transform of the autocorrelated filter coefficients to obtain a transform of a compressed signal; and computing an inverse transform of the transform of the compressed signal to obtain the compressed signal. The signal, the filter, and the transforms may be one dimensional or two dimensional. Further, the transforms may be a fast Fourier transform (FFT) or a Winograd discrete Fourier transform (WDFT) with an overlap-save scheme.

Abstract: A highly efficient decoding method is derived to correct both erasures and errors for Reed-Solomon (RS) codes, which takes the advantages of the Euclidean algorithm and the BM algorithm. The new decoding method computes the errata locator polynomial and the errata evaluator polynomial simultaneously without performing the polynomial divisions, and there is no need to compute the discrepancies and the field element inversions. Also, separate computations of the erasure locator polynomial and the Forney syndromes are avoided. Moreover, a simple and fast process for a finite field multiplication and finite field inversion is provided.