Neural Networks, Error-Correcting Codes, and Polynomials over the Binary n-Cube

Several ways of relating the concept of error-correcting codes to the concept of neural networks are presented. Performing maximum likelihood decoding in a linear block error-correcting code is shown to be equivalent to finding a global maximum of the energy function of a certain neural network. Given a linear block code, a neural network can be constructed in such a way that every local maximum of the energy function corresponds to a codeword and every codeword corresponds to a local maximum. The connection between maximization of polynomials over the n-cube and error-correcting codes is also investigated; the results suggest that decoding techniques can be a useful tool for solving problems of maximization of polynomials over the n-cube. The results are generalized to both nonbinary and nonlinear codes. © 1989 IEEE