Efficient implementation of error correction codes in modular code

Abstract

The article develops an efficient implementation of an algorithm for detecting and correcting multivalued residual errors with a fixed number of calculations of the syndrome, regardless of the set of moduli size. Criteria for uniqueness are given that can be met by selecting moduli from a set of primes to satisfy the desired error correction capability. An extended version of the algorithm with an increase in the number of syndromes depending on the number of information moduli is proposed. It is proposed to remove the restriction imposed on the size of redundant moduli. Identifying the location of the error and finding the error vector requires only look-up tables and does not require arithmetic operations. In order to minimize the excess space, an extended algorithm is also proposed in which the number of syndromes and look-up tables increases with the number of information moduli, but the locations of errors can still be identified without requiring iterative computations. By using the approximate method, we have reduced the computational complexity of the algorithm for calculating the syndrome from quadratic to linear-logarithmic, depending on the number of bits in the dynamic range.