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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2407.06132 |
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| _version_ | 1866917715168460800 |
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| author | Yu, Lei |
| author_facet | Yu, Lei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rényi Common Information for Doubly Symmetric Binary Sources Yu, Lei Information Theory 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. |
| title | Rényi Common Information for Doubly Symmetric Binary Sources |
| topic | Information Theory |
| url | https://arxiv.org/abs/2407.06132 |