Optimistic Shannon coding theorems for arbitrary single-user systems

The conventional definitions of the source coding rate and or channel capac ity require the existence of reliable codes for all sufficiently large bloc k lengths. Alternatively, if it is required that good codes exist for infin itely many block lengths, then optimistic definitions of source coding rate and channel capacity are obtained. In this work, formulas for the optimistic minimum achievable fixed-length s ource coding rate and the minimum epsilon-achievable source coding rate for arbitrary finite-alphabet sources are established, The expressions for the optimistic capacity and the optimistic epsilon-capacity of arbitrary singl e-user channels are also provided. The expressions of the optimistic source coding rate and capacity are examined for the class of information stable sources and channels, respectively, Finally, examples for the computation o f optimistic capacity are presented.