The antiphon. II. The exact evaluation of memory capacity

Abstract

An improved analysis is given of the antiphon: the device proposed in Whittle (1989) to achieve reliable memory from unreliable components. It is shown that for large systems of N such components one can reliably store KN + o(N) nats of information, and the supremum value of K (the capacity, C) is determined. It is moreover shown that a positive capacity (which is evaluated) can be achieved with the number M of processing units of no more than order N.