Optimisation of information processes using non-extensive entropies without parameters (Q2098083)

Summary: As a non-extensive statistical mechanics application, a possible path to generalised information theory is discussed by introducing a family of non-extensive entropies dependent solely on probability: \(H_D^\pm (P)\). In this scheme, two regimes of probabilities are possible; while the low-probability region exactly coincides with standard information theory, the high-probability regime offers further optimisation in certain information approaches. In this work, we explore two fundamental processes. Firstly, we propose generalisations to Shannon's coding theorems by modifying the ordinary Kraft inequality. This modification will ensure the codes to be uniquely decipherable in the framework of entropies \(H_D^\pm (P)\). Secondly, we calculate the channel capacity of a binary symmetric channel (BSC) and a binary erasure channel (BEC). Our results suggest an improvement in data compression and transmission with respect to the standard formulation.