Accounting the Ways of Weighing the Bits of the Data Vector when Constructing a Code with Summation in the Ring of Deductions Modulo M = 4 in the Synthesis of Self-Checking Discrete Devices Based on Boolean Signals Correction
Authors:   Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251, Russian Federation, Efanov D. V. ,   Russian University of Transport, Moscow, 127994, Russian Federation,   Tashkent State Transport University, Tashkent, 100167, Uzbekistan,   Scientific Research and Design Institute "Transport and Construction Safety" LLC, St. Petersburg, 192102, Russian Federation, Yelina Y. I. ,   Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251, Russian Federation
Published: January 2025

The article shows that in the synthesis of concurrent error-detection circuit based on Boolean signals correction, weighted codes with summation in the ring of deductions modulo M = 4 (weight-based Bose — Lin codes) with various arrays of weighting coefficients can be effectively used. The codes with four data and two test symbols used in organizing the control of calculations in a group of six outputs of the diagnostic object are considered in more detail. Four arrays of weight coefficients are highlighted: [1, 1, 1, 2], [1, 1, 2, 3], [1, 2, 2, 3], [2, 2, 2, 3] — the use of which in the construction of a weight-based Bose — Lin code leads to the formation of for each the test vector has exactly one data vector of the following types: <00ab>, <01 ab>, <10ab>, <11 ab>, where a, b ' {0, 1}. This property allows the use of codes with the specified arrays of weighting coefficients in the synthesis of concurrent error-detection circuit with the conversion of only part of the signals from the diagnostic object — two signals involved in the formation of the lower bits of the data vector. The article presents the results of experimental studies of weight-based Bose — Lin codes in the synthesis of concurrent error-detection circuit based on the Boolean signals correction using two algorithms. The first algorithm is based on the use of converting only those signals from the diagnostic object that are involved in the formation of test symbols. The second algorithm is based on the conversion of only those signals from the diagnostic object that participate in the formation of the two lowest digits of the data vector. It has been experimentally established that self-checking devices synthesized using a code with an array of weighting coefficients have the highest efficiency in terms of structural redundancy [2, 2, 2, 3] (on average, the value of the structural redundancy index has been reached at 73 % of the duplication structure). Next, according to this indicator, there are devices synthesized using a code with an array of weighting coefficients [1, 2, 2, 3] (on average, 76—77 % of the duplication structure). The use of arrays of weighting coefficients [1, 1, 2, 3] and [1, 1, 1, 2] in the construction of the code gives a slightly lower effect (on average 79—81 % from the duplication structure). It is shown that in order to ensure complete self-checking of device structures, it will be necessary to use permutations of outputs within controlled groups of outputs of the initial diagnostic object and between groups. The results of the study can be taken into account when developing self-checking digital devices, as well as software tools for their computer-aided design.