Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion Function
Semantic communication has recently gained significant attention in theoretical analysis due to its potential to improve communication efficiency by focusing on meaning rather than exact signal reconstruction. In this paper, we extend the Blahut–Arimoto (BA) algorithm, a fundamental method in classi...
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| Format: | Article |
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2025-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/6/651 |
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| author | Yuxin Han Yang Liu Yaping Sun Kai Niu Nan Ma Shuguang Cui Ping Zhang |
| author_facet | Yuxin Han Yang Liu Yaping Sun Kai Niu Nan Ma Shuguang Cui Ping Zhang |
| author_sort | Yuxin Han |
| collection | DOAJ |
| description | Semantic communication has recently gained significant attention in theoretical analysis due to its potential to improve communication efficiency by focusing on meaning rather than exact signal reconstruction. In this paper, we extend the Blahut–Arimoto (BA) algorithm, a fundamental method in classical information theory (CIT) for computing the rate-distortion (RD) function, to semantic communication by proposing the extended Blahut–Arimoto (EBA) algorithm, which iteratively updates transition and reconstruction distributions to calculate the semantic RD function based on synonymous mapping in semantic information theory (SIT). To address scenarios where synonymous mappings are unknown, we develop an optimization framework that combines the EBA algorithm with simulated annealing. Initialized with a syntactic mapping, the framework progressively merges syntactic symbols and identifies the mapping with a maximum synonymous number that satisfies objective constraints. Furthermore, by considering the semantic knowledge base (SKB) as a specific instance of synonymous mapping, the EBA algorithm provides a theoretical approach for analyzing and predicting the SKB size. Numerical results validate the effectiveness of the EBA algorithm. For Gaussian sources, the semantic RD function decreases with an increasing synonymous number and becomes significantly lower than its classical counterpart. Additionally, analysis on the CUB dataset demonstrates that larger SKB sizes lead to higher semantic communication compression efficiency. |
| format | Article |
| id | doaj-art-2426b95d4a3845aba0864cc68b545129 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-2426b95d4a3845aba0864cc68b5451292025-08-20T03:27:32ZengMDPI AGEntropy1099-43002025-06-0127665110.3390/e27060651Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion FunctionYuxin Han0Yang Liu1Yaping Sun2Kai Niu3Nan Ma4Shuguang Cui5Ping Zhang6Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaKey Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaDepartment of Broadband Communication, Pengcheng Laboratory, Shenzhen 518055, ChinaKey Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaKey Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaSchool of Science and Engineering (SSE) and the Future Network of Intelligent Institute (FNii), The Chinese University of Hong Kong (Shenzhen), Shenzhen 518172, ChinaKey Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaSemantic communication has recently gained significant attention in theoretical analysis due to its potential to improve communication efficiency by focusing on meaning rather than exact signal reconstruction. In this paper, we extend the Blahut–Arimoto (BA) algorithm, a fundamental method in classical information theory (CIT) for computing the rate-distortion (RD) function, to semantic communication by proposing the extended Blahut–Arimoto (EBA) algorithm, which iteratively updates transition and reconstruction distributions to calculate the semantic RD function based on synonymous mapping in semantic information theory (SIT). To address scenarios where synonymous mappings are unknown, we develop an optimization framework that combines the EBA algorithm with simulated annealing. Initialized with a syntactic mapping, the framework progressively merges syntactic symbols and identifies the mapping with a maximum synonymous number that satisfies objective constraints. Furthermore, by considering the semantic knowledge base (SKB) as a specific instance of synonymous mapping, the EBA algorithm provides a theoretical approach for analyzing and predicting the SKB size. Numerical results validate the effectiveness of the EBA algorithm. For Gaussian sources, the semantic RD function decreases with an increasing synonymous number and becomes significantly lower than its classical counterpart. Additionally, analysis on the CUB dataset demonstrates that larger SKB sizes lead to higher semantic communication compression efficiency.https://www.mdpi.com/1099-4300/27/6/651Blahut–Arimoto algorithmsemantic rate-distortion functionsemantic information theorysemantic knowledge base |
| spellingShingle | Yuxin Han Yang Liu Yaping Sun Kai Niu Nan Ma Shuguang Cui Ping Zhang Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion Function Entropy Blahut–Arimoto algorithm semantic rate-distortion function semantic information theory semantic knowledge base |
| title | Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion Function |
| title_full | Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion Function |
| title_fullStr | Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion Function |
| title_full_unstemmed | Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion Function |
| title_short | Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion Function |
| title_sort | extended blahut arimoto algorithm for semantic rate distortion function |
| topic | Blahut–Arimoto algorithm semantic rate-distortion function semantic information theory semantic knowledge base |
| url | https://www.mdpi.com/1099-4300/27/6/651 |
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