Abstract
Random binning is a widely used technique in information theory with diverse applications. In this paper, we focus on the output statistics of random binning (OSRB) using the Tsallis divergence T_(α) . We analyze all values of α ∈ (0, ∞)∪ {∞ } and consider three scenarios: (i) the binned sequence is generated i.i.d., (ii) the sequence is randomly chosen from an ∊ -typical set, and (iii) the sequence originates from an ∊ -typical set and is passed through a non-memoryless virtual channel. Our proofs cover both achievability and converse results. To address the unbounded nature of T_(∞) , we extend the OSRB framework via Rényi's divergence with order infinity, denoted D_(∞) . As part of our exploration, we analyze a specific form of Rényi's conditional entropy and its properties. Additionally, we demonstrate the application of this framework in deriving achievability results for the wiretap channel, where Tsallis divergence serves as a security measure. The secure rate we obtain through the OSRB analysis matches the secure capacity for α ∈ (0, 2]∪ {∞ } and serves as a potential candidate for the secure capacity when α ∈ (2, ∞).