# Neural Net Decoders for Linear Block Codes

V.N. Dumachev, A.N. Kopylov, V.V. ButovThe 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.Full text

- Keywords
- error-correction codes; neural network decoders; neural network classification.
- References
- 1. Zeng G., Hush D., Ahmed N. An Application of Neural Net in Decoding Error-Correcting Codes. IEEE International Symposium on Circuits and Systems, 1989, vol. 2, pp. 782-785. DOI: 10.1109/ISCAS.1989.100467

2. Htay M.M. A Computational Framework for Eicient Error Correcting Codes Using an Artificial Neural Network Paradigm. PhD Dissertation. Louisiana State University and Agricultural and Mechanical College, 1992.

3. Ortu'o I., Ortu'o M., Delgado J. Error Correcting Neural Networks for Channels with Gaussian Noise. IJCNN International Joint Conference on Neural Networks, Baltimore, 1992, vol. 4, pp. 295-300.

4. Ja-Ling Wu, Yuen-Hsien Tseng, Yuh-Ming Huang. Neural Network Decoders for Linear Block Codes. International Journal of Computational Engineering Science, 2002, vol. 3, no. 3, pp. 235-255. DOI: 10.1142/S1465876302000629

5. Berezkin A.A. [Construction of Optimal Neural Decoders Block Codes]. St. Petersburg Polytechnic University Journal, 2008, no. 5, pp. 34-41. (in Russian)

6. Nachmani E., Be'ery Y., Burshtein D. Learning to Decode Linear Codes Using Deep Learning. 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, 2016, pp. 341-346. DOI: 10.1109/ALLERTON.2016.7852251

7. Nachmani E., Marciano E., Burshtein D., Be'ery Y. RNN Decoding of Linear Block Codes, 2017. Available at: arXiv.1702.07560.

8. Lugosch L., Gross W.J. Neural Offset Min-Sum Decoding. IEEE International Symposium on Information Theory (ISIT), Aachen, 2017, pp. 1361-1365. DOI: 10.1109/ISIT.2017.8006751