High-order perceptrons for decoding error-correcting codes

The authors prove that the single-error correcting (2/sup n/-1, 2/sup n/-1-n) Hamming code and its extended single-error correcting/double-error detecting (2/sup n/, 2/sup n/-1-n) code can be decoded by low-complexity single-layer perceptrons which use high-order polynomials as their discriminant functions. It is illustrated that multiple-error correcting codes can be decoded by two-layer networks with high-order perceptrons in the first layer and linear perceptrons in the second layer.<>