Output Statistics of Random Binning: Tsallis Divergence and Its Applications
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913582884585472 |
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| author | Kavian, Masoud Mojahedian, Mohammad Mahdi Yassaee, Mohammad Hossein Mirmohseni, Mahtab Aref, Mohammad Reza |
| author_facet | Kavian, Masoud Mojahedian, Mohammad Mahdi Yassaee, Mohammad Hossein Mirmohseni, Mahtab Aref, Mohammad Reza |
| contents | 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 $α\in (0, \infty)\cup\{\infty\}$ and consider three scenarios: (i) the binned sequence is generated i.i.d., (ii) the sequence is randomly chosen from an $ε$-typical set, and (iii) the sequence originates from an $ε$-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 $T_\infty$, we extend the OSRB framework using Rényi's divergence with order infinity, denoted $D_\infty$. 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 $α\in (0, 2]\cup\{{\infty}\}$ and serves as a potential candidate for the secure capacity when $α\in (2, \infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_12606 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Output Statistics of Random Binning: Tsallis Divergence and Its Applications Kavian, Masoud Mojahedian, Mohammad Mahdi Yassaee, Mohammad Hossein Mirmohseni, Mahtab Aref, Mohammad Reza Information Theory 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 $α\in (0, \infty)\cup\{\infty\}$ and consider three scenarios: (i) the binned sequence is generated i.i.d., (ii) the sequence is randomly chosen from an $ε$-typical set, and (iii) the sequence originates from an $ε$-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 $T_\infty$, we extend the OSRB framework using Rényi's divergence with order infinity, denoted $D_\infty$. 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 $α\in (0, 2]\cup\{{\infty}\}$ and serves as a potential candidate for the secure capacity when $α\in (2, \infty)$. |
| title | Output Statistics of Random Binning: Tsallis Divergence and Its Applications |
| topic | Information Theory |
| url | https://arxiv.org/abs/2304.12606 |