Ruth Erlanson, Yaser Abu-Mostafa
Analog neural networks with feedback can be used to implement l((cid:173) Winner-Take-All (KWTA) networks. In turn, KWTA networks can be used as decoders of a class of nonlinear error-correcting codes. By in(cid:173) terconnecting such KWTA networks, we can construct decoders capable of decoding more powerful codes. We consider several families of inter(cid:173) connected KWTA networks, analyze their performance in terms of coding theory metrics, and consider the feasibility of embedding such networks in VLSI technologies.
INTRODUCTION: THE K-WINNER-TAKE-ALL NETWORK
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.
• currently at: Hughes Network Systems, 10790 Roselle St., San Diego, CA 92121