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Hamming codes with regard to theory of self-testing digital system synthesis are characterized by the following properties: their coders and decoders are described by self-dual and self-antidual Boolean functions. It is important during synthesis of scheme of internal control according to specified diagnostic criteria to provide self-duality and self-antiduality of a device. In this work, the task of constructing self-testing digital devices using time redundancy and pulse mode of operation based on the data inversion method is considered. It is proposed to use as diagnostic features in CED the membership of the generated functions in the self-dual and self-antidual Boolean functions classes, as well as the membership of the generated code word in a pre-selected Hamming code. It has been established that the functions describing the Hamming codes checking bits can be either only self-dual, or only self-antidual, or partially self-dual and partially self-antidual. The values of the symbols number in the Hamming codes codewords are established, for which the check symbols are described only by self-dual, or only self-antidual, or partially self-dual and partially self-antidual Boolean functions. Similar conditions are established for extended Hamming codes. The CED organization structure according to several diagnostic criteria is given. It is noted that the structure can be based on any linear block code. However, for each specific code, conditions must be determined under which the check symbols will be described only by self-dual, or only by self-antidual, or by partially self-dual and partially self-antidual Boolean functions. It has been found that the Hamming codes properties use makes it possible to synthesize in practice the self-testing digital devices based on the data inversion method when checking calculations using several diagnostic criteria.

Key words: self-testing digital devices, self-dual Boolean function, self-antidual Boolean function, self-dual digital device, self-antidual digital device, calculation control at the digital device outputs, data inversion method, classical and extended Hamming codes
Published in: INFORMATION-COMMUNICATION TECHNOLOGIES
Bibliography link: Efanov D. V Special aspects of Hamming codes use in the self-checking digital devices synthesis based on the data inversion method. Proc. Univ. Electronics, 2024, vol. 29, no. 3, pp. 379–392. https://doi.org/10.24151/1561-5405-2024-29-3-379- 392

Dmitry V. Efanov
St. Petersburg Polytechnic University (Russia, 195251, St. Petersburg, Politekhnicheskaya st., 29B); Russian University of Transport (Russia, 127994, Moscow, Obraztsov st., 9, bld. 9); Tashkent State Transport University (Uzbekistan, 100167, Tashkent, 1st

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Publication type: Scientific article
DOI: 10.24151/1561-5405-2024-29-3-379-392
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