Geodesic
Neural net decoders for linear block codes
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 1, pp. 129-136

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The work is devoted to neural network decoders of linear block codes. Analytical methods for calculating synaptic weights based on a generator and parity-check matrices are considered. It is shown that to build a neural net decoder based on a parity-check matrix was sufficiently four layers feedforward neural net. The activation functions and weight matrices for each layer are determined, as well as the number of weights for the neural net decoder. An example of error correction with uses of the BCH neural net decoder is considered. As a special case of a neural network decoder built on the basis of a parity-check matrix, a model for decoding Hamming codes has been proposed. This is the two-layer feedforward neural net for with a neuron number equal to the length of the codeword and a number of weight coefficients equal to the square of the codeword length. The graphs of the number of a synaptic weight of neural net decoders based on the generator and parity-check matrices, on the number of bits and the number of corrected errors, are shown.
Keywords: neural network decoders, neural network classification.
Mots-clés : error-correction codes 
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     author = {V. N. Dumachev and A. N. Kopylov and V. V. Butov},
     title = {Neural net decoders for linear block codes},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     publisher = {mathdoc},
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     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2019_12_1_a10/}
}
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V. N. Dumachev; A. N. Kopylov; V. V. Butov. Neural net decoders for linear block codes. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 1, pp. 129-136. http://geodesic.mathdoc.fr/item/VYURU_2019_12_1_a10/