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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.13243 |
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| _version_ | 1866910495119769600 |
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| author | Pang, James Chin-Jen Pradhan, Sandeep Mahdavifar, Hessam |
| author_facet | Pang, James Chin-Jen Pradhan, Sandeep Mahdavifar, Hessam |
| contents | We study the problem of transmission of information over classical and classical-quantum channels in the one-shot regime where the underlying codes are constrained to be group codes. In the achievability part, we introduce a new input probability distribution that incorporates the encoding homomorphism and the underlying channel law. Using a random coding argument, we characterize the performance of group codes in terms of hypothesis testing relative-entropic quantities. In the converse part, we establish bounds by leveraging a hypothesis testing-based approach. Furthermore, we apply the one-shot result to the asymptotic stationary memoryless setting, and establish a single-letter lower bound on group capacities for both classes of channels. Moreover, we derive a matching upper bound on the asymptotic group capacity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13243 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abelian Group Codes for Classical and Classical-Quantum Channels: One-shot and Asymptotic Rate Bounds Pang, James Chin-Jen Pradhan, Sandeep Mahdavifar, Hessam Information Theory We study the problem of transmission of information over classical and classical-quantum channels in the one-shot regime where the underlying codes are constrained to be group codes. In the achievability part, we introduce a new input probability distribution that incorporates the encoding homomorphism and the underlying channel law. Using a random coding argument, we characterize the performance of group codes in terms of hypothesis testing relative-entropic quantities. In the converse part, we establish bounds by leveraging a hypothesis testing-based approach. Furthermore, we apply the one-shot result to the asymptotic stationary memoryless setting, and establish a single-letter lower bound on group capacities for both classes of channels. Moreover, we derive a matching upper bound on the asymptotic group capacity. |
| title | Abelian Group Codes for Classical and Classical-Quantum Channels: One-shot and Asymptotic Rate Bounds |
| topic | Information Theory |
| url | https://arxiv.org/abs/2406.13243 |