Large Deviation Analysis for the Reverse Shannon Theorem
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908393835331584 |
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| author | Li, Shi-Bing Li, Ke Yu, Lei |
| author_facet | Li, Shi-Bing Li, Ke Yu, Lei |
| contents | Channel simulation is to simulate a noisy channel using noiseless channels with unlimited shared randomness. This can be interpreted as the reverse problem to Shannon's noisy coding theorem. In contrast to previous works, our approach employs Rényi divergence (with the parameter $α\in(0,\infty)$) to measure the level of approximation. Specifically, we obtain the reverse Shannon theorem under the Rényi divergence, which characterizes the Rényi simulation rate, the minimum communication cost rate required for the Rényi divergence vanishing asymptotically. We also investigate the behaviors of the Rényi divergence when the communication cost rate is above or below the Rényi simulation rate. When the communication cost rate is above the Rényi simulation rate, we provide a complete characterization of the convergence exponent, called the reliability function. When the communication cost rate is below the Rényi simulation rate, we determine the linear increasing rate for the Rényi divergence with parameter $α\in(0,\infty]$, which implies the strong converse exponent for the $α$-order fidelity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large Deviation Analysis for the Reverse Shannon Theorem Li, Shi-Bing Li, Ke Yu, Lei Information Theory Channel simulation is to simulate a noisy channel using noiseless channels with unlimited shared randomness. This can be interpreted as the reverse problem to Shannon's noisy coding theorem. In contrast to previous works, our approach employs Rényi divergence (with the parameter $α\in(0,\infty)$) to measure the level of approximation. Specifically, we obtain the reverse Shannon theorem under the Rényi divergence, which characterizes the Rényi simulation rate, the minimum communication cost rate required for the Rényi divergence vanishing asymptotically. We also investigate the behaviors of the Rényi divergence when the communication cost rate is above or below the Rényi simulation rate. When the communication cost rate is above the Rényi simulation rate, we provide a complete characterization of the convergence exponent, called the reliability function. When the communication cost rate is below the Rényi simulation rate, we determine the linear increasing rate for the Rényi divergence with parameter $α\in(0,\infty]$, which implies the strong converse exponent for the $α$-order fidelity. |
| title | Large Deviation Analysis for the Reverse Shannon Theorem |
| topic | Information Theory |
| url | https://arxiv.org/abs/2410.07984 |