Random binning is a widely utilized tool in information theory, finding applications in various domains. In this paper, we focus on the output statistics of random binning (OSRB) using the Tsallis divergence $T_\alpha$. Our investigation encompasses all values of $\alpha$ within the range of $(0,\infty)$. The proofs provided in this paper cover both the achievability and converse aspects. To accommodate the unbounded nature of $T_\infty$, we analyze the OSRB framework using the R\'enyi's divergence criterion with the order of infinity, denoted as $D_\infty$. During our exploration of OSRB, we encounter a specific form of R\'enyi's conditional entropy and delve into its properties. Additionally, we demonstrate the effectiveness of this framework in establishing achievability results for wiretap channel, where Tsallis divergence serves as a security measure.

翻译：随机分箱是信息论中广泛使用的工具，在多个领域均有应用。本文聚焦于基于Tsallis散度$T_\alpha$的随机分箱输出统计（OSRB）。我们的研究涵盖$\alpha$在$(0,\infty)$范围内的所有取值。本文给出的证明同时覆盖可达性和逆定理两方面。为处理$T_\infty$无界性的问题，我们采用无穷阶Rényi散度准则$D_\infty$分析OSRB框架。在探索OSRB过程中，我们遇到了Rényi条件熵的特定形式，并深入研究了其性质。此外，我们展示了该框架在建立窃听信道可达性结果方面的有效性，其中Tsallis散度作为安全度量。