Output-sensitive decoding for redundant residue systems

We study algorithm based fault tolerance techniques for supporting malicious errors in distributed computations based on Chinese remainder theorem. The description holds for both computations with integers or with polynomials over a field. It unifies the approaches of redundant residue number systems and redundant polynomial systems through the Reed Solomon decoding algorithm proposed by Gao. We propose several variations on the application of the extended Euclid algorithm, where the error correction rate is adaptive. Several improvements are studied, including the use of various criterions for the termination of the Euclidean Algorithm, and an acceleration using the Half-GCD techniques. When there is some redundancy in the input, a gap in the quotient sequence is stated at the step matching the error correction, which enables early termination parallel computations. Experiments are shown to compare these approaches.