Error correction in the transmission and processing of information, provided in RNS, by method of syndrome decoding

Abstract

In article conducted the development of the method of syndrome decoding error correction codes in the RNS, based on the method of expanding the bases RNS. Presents the basics of excess RNS. Considered the most widely used algorithms for detecting, locating and correcting errors in the RNS, as well as concrete examples of their use. For the examined methods conducted an analysis and comparison, shows the main advantages and disadvantages. Shown the complete algorithm for error correction in information and control bases by the syndrome decoding method and examples of its practical application. It is shown that using error syndromes can reduce the time of error correction. This is due to the fact that the task of identifying, locating and correcting errors performed a common procedure . The computational complexity of the method of decoding the syndrome is much less than the widely used method of projection since projection method requires n + 1 the procedure of transfer number of RNS in generalized positional number system, whereas the syndrome decoding method requires the translation in generalized positional number system only once.