BERGER CODES IN CONCURRENT ERROR-DETECTION SYSTEMS, IMPLEMENTED ON THE BASIS OF BOOLEAN COMPLEMENT METHOD
The article deals with the previously unknown characteristics of the error detection by using classical Berger codes based on their multiplicities and types (unidirectional, symmetrical and asymmetrical), which can be applied in the concurrent error-detection (CED) systems synthesis, for example, through the use of Boolean complement method. The article shows that Berger codes do not detect a certain amount of both symmetrical, unidirectional and asymmetrical errors in code words. This differs from the previously identified characteristics of the error detection only in data vectors of Berger codes (in this case, any symmetrical errors are not detected, and any unidirectional and asymmetrical errors are detected, which is used in the synthesis of systems with fault detection). The share of undetectable errors from their total number for Berger codes with data vector lengths r = 4,...,7 is less than 2%, and for Berger codes with data vector lengths r = 8,...,15 it is less than 0.5%. The use of classical sum codes is effective in the CED systems synthesis, including the Boolean complement method, in which both data and check bits of code words are calculated using the diagnostic object itself.
Keywords: CED system, operating diagnosis, Boolean complement method, sum code, Berger code, error detection, undetectable error, error checking