Analog Neural Networks as Decoders

We have previously demonstrated the use of a continuous Hopfield neural network as a K-Winner-Take-All (KWTA) network [Majani et al., 1989, Erlanson and Abu(cid:173) Mostafa, 1988}. Given an input of N real numbers, such a network will converge to a vector of K positive one components and (N - K) negative one components, with the positive positions indicating the K largest input components. In addition, we have shown that the () such vectors are the only stable states of the system. One application of the KWTA network is the analog decoding of error-correcting codes [Majani et al., 1989, Platt and Hopfield, 1986]. Here, a known set of vectors (the codewords) are transmitted over a noisy channel. At the receiver's end of the channel, the initial vector must be reconstructed from the noisy vector.