The Capacity of a Possibilistic Channel

Abstract

We put forward a model for transmission channels and channel coding which is possibilistic rather than probabilistic. We define a notion of possibilistic capacity, which is connected to a combinatorial notion called graph capacity. In the probabilistic case graph capacity is a relevant quantity only when the allowed decoding error probability is strictly equal to zero, while in the possibilistic case it is a relevant quantity for whatever value of the allowed decoding error possibility; as the allowed error possibility becomes larger the possibilistic capacity stepwise increases (one can reliably transmit data at a higher rate). We discuss an application, in which possibilities are used to cope with uncertainty as caused by a “vague” linguistic description of channel noise.