A.A. Pavlov1, A.N. Tsarkov2, Yu.A. Romanenko3, A.A. Korobkov4, A.Yu. Romanenko5, F.A. Pavlov6

1,3,6 Military Academy of the Strategic Missile Forces n.a. Peter the Great (branch in Serpukhov) (Serpukhov, Russia)

2,4,5 Autonomous Non-Profit Organization “Institute of Engineering Physics” (ANO “IIF”) (Serpukhov, Russia)

1,6 Pavlov_iif@mail.ru; 2 info@iifrf.ru; 3 info@iifrf.ru; 4 aakorobkov@iifmail.ru; 5 info@iifrf.ru; 6 iif@mail.ru

This paper examines the effectiveness of using Hamming codes to build self-healing, fault-tolerant, specialized computers with increased operational reliability. It was established that single and double errors are the most likely processor errors.

An assessment was made of the hardware costs of an algebraic linear code with syndrome decoding required to correct single and double errors. It is concluded that correcting single and double errors in the arithmetic logic unit of a processor using an algebraic code with syndrome decoding leads to a sharp increase in hardware costs and does not ensure the required processor reliability.

The necessity of an algebraic linear code that corrects single errors and detects double errors during arithmetic operations is substantiated and the feasibility of using it is assessed. The following is established:

an algebraic code cannot correct errors that occur during arithmetic operations, since the occurrence of a single error in the bits of the adder's carry function (the absence of a carry or the occurrence of an "extra" carry) leads to the occurrence of uncorrectable errors of arbitrary multiplicity in the bits of the sum;

an algebraic code with a minimum code distance of d = 3 detects 97% of errors of arbitrary multiplicity;

the use of an algebraic code to detect errors during arithmetic operations ensures its fault tolerance (repeated reading of information when errors are detected) and the reliable operation of the processor.

Rules for constructing an algebraic linear code for correcting single errors and detecting double errors during the execution of logical operations: right shift, left shift, AND, OR, NOT, and mod 2 summation were formulated. As a result, a methodological framework was developed for improving the self-healing capability and reliability of processor operation during arithmetic and logical operations.

Pavlov A.A., Tsarkov A.N., Romanenko Yu.А., Korobkov A.A., Romanenko A.Yu., Pavlov F.A. Improving the reliability and accuracy of information storage and processing devices in radiotechnical systems. Radiotekhnika. 2026. V. 90. № 5. P. 165−180. DOI: https://doi.org/10.18127/j00338486-202605-19 (In Russian)

1. Grigor'ev, V.A., Lagutenko O.I., Raspaev Yu.A. Seti i sistemy radiodostupa, M.: Eko-Trendz. 2005. 384 s. (in Russian).
2. Kulikov L.N., Moskalec M.N. Teoriya elektricheskoj svyazi. Osnovy svertochnogo kodirovaniya: Uchebnoe posobie SPb. 2006. 39 s. (in Russian).
3. Serdyukov P.N., Bel'chikov A.V., Dronov A.E. i dr. Zashchishchennye radiosistemy cifrovoj peredachi informacii. M.: AST. 2006. 403 s. (in Russian).
4. Bertsekas D., Gallager R. Seti peredachi dannyh. M.: Mir. 1989. 544 s. (in Russian).
5. Tanenbaum E.S. Komp'yuternye seti. SPb: Piter. 2003. 848 s. (in Russian).
6. Grebeshkov A.Yu. Mikroprocessornye sistemy i programmnoe obespechenie v sredstvah svyazi. Samara: PGUTI. 2009. 298 s. (in Russian).
7. GOST 27.003-2016. Nadezhnost' v tekhnike. Sostav i obshchie pravila zadaniya trebovanij po nadezhnost (in Russian).
8. GOST 27.102-2021 Nadezhnost' v tekhnike. Nadezhnost' ob"ekta. Terminy i opredeleniya (in Russian).
9. Shcherbakov N.S. Dostovernost' raboty cifrovyh ustrojstv. M.: Mashinostroenie. 1989. 224 s. (in Russian).
10. Naseer R., Draper J. Parallel double error correcting code design to mitigate multi-bit upsets in SRAMs. ESSCIRC 2008. 34th European Solid-State Circuits Conference. P. 222-225.
11. Pavlov A.A., Car'kov A.N., Romanenko Yu.A., Korneev I.I., Romanenko A.Yu., Makeev M.I., Pavlov F.A. Obnaruzhenie i korrekciya oshibok v ustrojstvah obrabotki informacii v sistemah svyazi i telekommunikacii. Radiotekhnika. 2023. T. 87. № 3. S. 6-14. DOI: https://doi.org/10.18127/j00338486-202303-14 (in Russian).
12. Pavlov A.A., Car'kov A.N., Romanenko Yu.A., Pashincev V.P., Romanenko A.Yu., Makeev M.I., Pavlov F.A. Ispol'zovanie informacionnogo rezervirovaniya dlya povysheniya nadezhnosti ustrojstv hraneniya, obrabotki i peredachi informacii. Radiotekhnika. 2024. T. 88. № 2. S. 168−176. DOI: https://doi.org/10.18127/j00338486-202402-16 (in Russian).
13. Pavlov A.A., Car'kov A.N., Romanenko Yu.A., Pashaev O.F., Romanenko A.Yu., Pavlov F.A. Ispol'zovanie svojstv algebraicheskogo koda dlya povysheniya effektivnosti obnaruzheniya i ispravleniya oshibok v ustrojstvah hraneniya i obrabotki informacii. Radiotekhnika. 2025. T. 88. № 4. S. 101−108. DOI: https://doi.org/10.18127/j00338486-202504-09 (in Russian).
14. Prager K., Vahey A M., Farwell W., et al. Fault tolerant signal processing computer. International Conference on Dependable Systems and Networks. 2000. P. 169-174.
15. Micheloni R., Marelli A., Ravasio R. Error correction codes for non-volatile memories. Springer. 2010. 337 p.
16. Todd K.M. Error correction coding. Mathematical methods and algorithms. New Jersey: Wiley. 2005. P. 7-15.