An after-shannon measure of the storage capacity of an associative noise-like coding memory

The maximum amount of information that can be stored, on the average, in each storage element, according to an associative scheme, has been measured for the memory model proposed by the author (Bottini 1980). In this model, the (binary) items being stored are coded by noise-like keys and the memory traces formed in this way are superimposed, by algebraic addition, on the same many-level storage elements. It is shown that the problem of measuring the information retrieved from the memory in a single recall and the problem — concerning the data-communication field —of measuring the information transmitted over a noisy channel are formally similar. In particular, the Shannon noisy-channel coding theorem can find an application also in our case of an associative memory. Finally, it is evidenced that the so-called matrix model of an associative memory has the same storage capacity as the model studied here.