Abstract
This article considers the synthesis of a neural-like Hamming network with a view to implementing the problem of classification of an input set of binary vectors. The formation of a sequence sorted by the Hamming distance as the proximity measure is based on the conversion of cyclic Hamming codes. The correctness of the synthesis of such an implementation for an arbitrary Hamming distance and a binary input vector of arbitrary length is proved.
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References
T. K. Vintsiuk, Analysis, Recognition, and Understanding of Speech Signals [in Russian], Naukova Dumka, Kyiv (1987).
J. Bruck and M. Blaum, “Neural networks, error-correcting codes, and polynomials over the binary n-cube,” IEEE Transactions on Information Theory, Vol. 35, No. 5, 976–987 (1989).
M. E. Robinson, H. Yoneda, and E. Sanchez-Sinencio, “A modular CMOS design of a Hamming network,” IEEE Transactions on Neural Networks, Vol. 3, No 3, 444–456 (1992).
V. D. Dmitrienko and A. Yu. Zakovorotnyi, “A neural network using the Hamming distance for image recognition on the border of several classes,” Herald of the NTU “KhPI,” No. 39 (1012), 57–67 (2013).
A. V. Palagin, V. N. Opanasenko, and L. G. Chigirik, “Synthesis of a Hamming network on the basis of programmable logic integrated circuits,” Engineering Simulation, Vol. 13, 651–666 (1996).
Y. P. Kondratenko and E. Gordienko, “Implementation of neural networks for adaptive control system on FPGA,” in: Proc. 23rd DAAAM Intern. Symp. on Intelligent Manufacturing and Automation, Vol 23 (1), B. Katalinic (ed.), DAAAM International, Vienna, Austria (2012), pp. 0389–0392.
A. V. Palagin, V. N. Opanasenko, and S. L. Kryvyi, FPGA-Based Reconfigurable Structures: Synthesis of Problem-Oriented Structures, Lambert Academic Publishing (2014).
A. Palagin, V. Opanasenko, and S. Kryvyi, “The structure of FPGA-based cyclic-code converters,” Optical Memory & Neural Networks (Information Optics), Vol. 22, No. 4, 207–216 (2013).
A. V. Palagin and V. N. Opanasenko, “Reconfigurable computing technology,” Cybernetics and Systems Analysis, Vol. 43, No. 5, 675–686 (2007).
A. V. Palagin and V. N. Opanasenko, “Design and application of the PLD-based reconfigurable devices,” in: M. Adamski, A. Barkalov, and M. Wegrzyn (eds.), Design of Digital Systems and Devices, Lecture Notes in Electrical Engineering, Vol. 79, Springer, Berlin-Heidelberg (2011), pp. 59–91.
A. V. Palagin and V. N. Opanasenko, and S. L. Kryvyi, “Method for synthesis of structures for transformations of a cyclic code on the basis of FPGA,” Electronic Modeling, Vol. 36, No. 2, 27–48 (2014).
R. K. Brayton, G. D. Hachtel, and A. L. Sangiovanni-Vincentelli, “Multi-level logic synthesis,” in: Proc. IEEE, Vol. 78, No. 2, 38–83 (1990).
V. N. Opanasenko and S. L. Kryvyi, “Partitioning the full range of Boolean functions based on the threshold and threshold relation,” Cybernetics and Systems Analysis, Vol. 48, No. 3, 459–468 (2012).
V. N. Opanasenko and S. L. Kryvyi, “Synthesis of adaptive logical networks on the basis of Zhegalkin polynomials,” Cybernetics and Systems Analysis. Vol. 51, No. 6, 969–977 (2015).
V. N. Opanasenko and S. L. Kryvyi, “Synthesis of multilevel structures with multiple outputs,” in: CEUR Workshop Proceeding of 10th International Conference of Programming (UkrPROG 2016), Vol. 1631, Code 122904, Kyiv, Ukraine (2016), pp. 32–37.
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Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2017, pp. 155–164.
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Opanasenko, V.N., Kryvyi, S.L. Synthesis of Neural-Like Networks on the Basis of Conversion of Cyclic Hamming Codes. Cybern Syst Anal 53, 627–635 (2017). https://doi.org/10.1007/s10559-017-9965-z
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DOI: https://doi.org/10.1007/s10559-017-9965-z