V.V. Berezhnoy - Ph.D. (Eng.), Associate Professor, Department of the Applied Mathematics and Mathematical Modeling, Institute of Mathematics and Natural Sciences, North Caucasus Federal University (Stavropol) E-mail: beregnoj@yandex.ru N.N. Nagornov - Post-graduate Student, Institute of Mathematics and Natural Sciences, North Caucasus Federal University (Stavropol) E-mail: sparta1392@mail.ru

Programmable logic devices (PLD) in comparison with specialized digital integrated circuits (ASIC) have a significant advantage in that the development cycle of devices on PLD takes much less time and far cheaper. With the help of the architecture of the PLD hardware may be implemented in various computational structures and algorithms. This article proposes hardware imple-mentation methods of detecting and correcting errors in the system of residual classes: projection, syndrome decoding and error intervals on programmable logic integrated circuits by using block design LabVIEW. Each of implemented methods use different approaches to detect and correct errors on the basis of the system, but clearly leads to the same result: guaranteed error cor-rection on one ground with the introduction of one or several bases. The area of block design LabVIEW for the simulation of algorithms and structures uses a variety of units that perform cer-tain mathematical and program operations. All blocks have the minimum required for storage and transmission of incoming in-formation capacity, which allows to optimize the number of used hardware resources. Because of their cumbersome programming model was designed structurally for multiple components for each set of bases. The article gives model only for the first set of grounds. Each method has been implemented in the following main com-ponents: method of projections: 1) transfer the number in the generalized positional system and error detection; 2) the calculation of projections; 3) localization and error correction; method of syndrome decoding: 1) definition of the syndrome of the error; 2) correction of errors; method of incorrect intervals: 1) translation of a number in a positional number system; 2) error correction. The software model was implemented on hardware FPGA Board Spartan-3E, which allowed us to obtain information about the time and hardware resources for each of the methods of error correction in the system of residual classes. Analysis of the obtained results allowed to formulate the following conclusions: the least hardware resources in all ranges of number representation requires a method of syndrome decoding. Method of incorrect intervals at small operating ranges uses almost the same hardware resources as the method of syndrome decoding, but with the increase of the range of hardware cost increases significantly, exceeding even the cost projection method that es-sentially loses to the method of syndrome decoding in all ranges of number representation; the best indicators of time detecting and correcting errors belong to the method of incorrect intervals. This is due to the fact that the error correction method of projections and the method of syndrome decoding use the transfer numbers in the gene-ralized positional system, and the method incorrect intervals directly translates the number in the usual positional number system that greatly reduces the time intervals of processing.

 

1. Potekhin D.S., Tarasov I.E. Razrabotka sistem cifrovojj obrabotki signalov na baze PLIS. M.: Gorjachaja linija - Telekom. 2007. 248 s.
2. Akushskijj I.JA., JUdickijj D.I. Mashinnaja arifmetika v ostatochnykh klassakh. M.: Sov. radio. 1968. 440 s.
3. Suranov A.JA. LabVIEW 8.20: Spravochnik po funkcijam. M.: DMK Press. 2007. 536 s.
4. CHervjakov N.I., Berezhnojj V.V., Olenev A.A., Kalmykov I.A. Minimizacija izbytochnosti koda sistemy ostatochnykh klassov s odnim kontrolnym osnovaniem // EHlektronnoe modelirovanie. 1994. T. 16. № 1. S. 56-61.
5. CHervjakov N.I., Nagornov N.N. Korrekcija oshibok pri peredache i obrabotke informacii, predstavlennojj v SOK, metodom sindromnogo dekodirovanija // Nauchnyjj zhurnal Severo-Kavkazskogo federalnogo universiteta: Nauka. Innovacii. Tekhnologii. 2015. № 2. S. 15-40.
6. CHervjakov N.I., Berezhnojj V.V., Kalmykov I.A., Goncharova E.N. Lokalizacija i ispravlenie arifmeticheskikh oshibok v moduljarnykh nejjrokompjuterakh // Nejjrokompjutery: razrabotka, primenenie. 2003. № 7. S. 28-32.