NONPOSITIVE HOPFIELD NETWORKS FOR UNIDIRECTIONAL ERROR-CORRECTING CODING

We consider a class of symmetric Hopfield networks, with nonpositive s ynapses and zero thresholds. We call such networks Nonpositive Hopfiel d networks and address a variety of design and analysis issues connect ed with their application to a specific form of Error Correcting Codin g. In particular we show that this class is naturally suited to work i n a unidirectional error environment and hence can find application in unidirectional error correcting coding. We give a necessary and suffi cient condition for a set of codewords to be storable in a Nonpositive network, We propose a simple word storage algorithm, which is amenabl e to on line implementation, and guarantees storage of all storage com patible words. We show that the storage algorithm creates a network th at is fundamentally maximally tolerant to physical faults and is free from spurious stationary points, whenever that freedom is available. W e also give a word forgetting algorithm; a tight, deterministic bound on the storage capacity, and conditions under which the network create d by our storage scheme tolerates a given number of arbitrary physical faults.