Study of the characteristics of error detection with Hamming codes, the consideration of which is appropriate for the synthesis of automatic devices with fault detection

Abstract

The peculiarities of using Hamming codes in the synthesis of automatic devices with fault detection are investigated. Such devices imply the organization of embedded control schemes to detect occur-ring faults indirectly based on the results of calculating the values of operational functions. Various methods can be used by the implementation of embedded control schemes. In this study, the focus is shifted to the issues of synthesizing embedded control schemes using the method of logical signal correction (the method of logical complementation). This method involves transforming all or part of the signals coming from the diagnostic object in the embedded control scheme in such a way that the code word generated after the signal correction block belongs to a preselected block uniform code. The study considers the application of classical Hamming codes for these purposes. The use of the method of logical signal correction allows obtaining the values of the informational symbols of the code words of the Hamming code directly as values at the operational outputs of the diagnostic object, while the check symbols are obtained by correcting signals from some of the operational out-puts. However, it is also possible to use transformations of operational function values to obtain in-formational symbols, which expands the number of ways to organize the embedded control scheme. The article presents previously unknown absolute and relative error detection metrics in the code words of the Hamming code, taking into account their categorization based on types (according to the number of distortions in zero and one bits) and multiplicities. The experimental results with test combinational circuits confirm the effectiveness of using the method of logical signal correction with computation control using Hamming codes for synthesizing embedded control schemes. The results obtained in this study extend the theory of synthesis for self-checking digital devices and computational systems and can be practically applied in improving the methods for synthesizing au-tomatic devices with fault detection.