Correcting DCT Codes With Laurent Euclidean Algorithm and Syndrome Extension

Real number block codes derived from the discrete cosine transform (DCT) are corrupted by a few large errors along with low-level noise. Checking syndromes are encapsulated in Laurent polynomials and a special Euclidean algorithm determines the locations of large errors. These locations are adjusted properly to give an error-modeling polynomial that is used to extend syndromes which are in turn transformed to codeword error values. A probabilistic analysis describes the effects of the low-level noise on corrected values after they pass through the syndrome extension process. Simulations yield probability of codeword errors, mean-squared decoding errors and sample means and variances of low-level noise effects.