Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2407.06132 |
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Inhaltsangabe:
- In this note, we provide analytic expressions for the Rényi common information of orders in $(1,\infty)$ for the doubly symmetric binary source (DSBS). Until now, analytic expressions for the Rényi common information of all orders in $[0,\infty]$ have been completely known for this source. We also consider the Rényi common information of all orders in $[-\infty,0)$ and evaluate it for the DSBS. We provide a sufficient condition under which the Rényi common information of such orders coincides with Wyner's common information for the DSBS. Based on numerical analysis, we conjecture that there is a certain phase transition as the crossover probability increasing for the Rényi common information of negative orders for the DSBS. Our proofs are based on a lemma on splitting of the entropy and the analytic expression of relaxed Wyner's common information.