A single-iteration threshold Hamming network

We analyze in detail the performance of a Hamming network classifying inputs that are distorted versions of one of its m stored memory patterns, each being a binary vector of length n. It is shown that the activation function of the memory neurons in the original Hamming network may be replaced by a simple threshold function. By judiciously determining the threshold value, the "winner-take-all" subnet of the Hamming network (known to be the essential factor determining the time complexity of the network's computation) may be altogether discarded. For m growing exponentially in n, the resulting threshold Hamming network correctly classifies the input pattern in a single iteration, with probability approaching 1.