{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T12:12:51Z","timestamp":1785413571949,"version":"3.56.0"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T00:00:00Z","timestamp":1779753600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62293481"],"award-info":[{"award-number":["62293481"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["62293481"],"award-info":[{"award-number":["62293481"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Beijing University of Posts and Telecommunications\u2013China Mobile Communications Group Co., Ltd. Joint Institute"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Classical information theory (CIT) characterizes the transmission limit for communication systems under syntactic accuracy, whereas semantic information theory (SIT) studies communication from the perspective of semantic fidelity induced by synonymous mapping. In this paper, we investigate the semantic channel capacity of Rayleigh fading channels under synonymous mapping of the channel gain and additive noise. We first derive the semantic capacity formula when synonymous mapping is applied to the channel fading coefficient and establish corresponding upper and lower bounds using Jensen\u2019s inequality. To determine an optimized synonymous partition, the partition design is formulated as a constrained optimization problem and solved numerically using a neural network-based approach with the Adam optimizer. Furthermore, we extend the framework by applying synonymous mapping to both the channel fading coefficient and the additive noise and derive the corresponding semantic capacity formula together with its theoretical bounds. The numerical results illustrate the theoretical semantic channel capacity under synonymous mapping and validate the compatibility of the proposed framework with both CIT and SIT. At a 20-dB SNR with K=8 channel gain intervals and J=4 noise intervals, the semantic capacity reached 9.86 sebits\/s\/Hz.<\/jats:p>","DOI":"10.3390\/e28060588","type":"journal-article","created":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T11:02:51Z","timestamp":1779793371000},"page":"588","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Semantic Channel Capacity of Rayleigh Fading Channels Based on Synonymous Mapping"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-1665-0767","authenticated-orcid":false,"given":"Yuxin","family":"Han","sequence":"first","affiliation":[{"name":"Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China"},{"name":"Department of Broadband Communication, Pengcheng Laboratory, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sen","family":"Wang","sequence":"additional","affiliation":[{"name":"China Mobile Research Institute, Beijing 100080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaping","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Broadband Communication, Pengcheng Laboratory, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8076-1867","authenticated-orcid":false,"given":"Kai","family":"Niu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2302-7148","authenticated-orcid":false,"given":"Nan","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Broadband Communication, Pengcheng Laboratory, Shenzhen 518055, China"},{"name":"Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0269-104X","authenticated-orcid":false,"given":"Ping","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1109\/26.539767","article-title":"Near optimum error correcting coding and decoding: Turbo-codes","volume":"44","author":"Berrou","year":"2002","journal-title":"IEEE Trans. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1109\/18.910578","article-title":"Design of capacity-approaching irregular low-density parity-check codes","volume":"47","author":"Richardson","year":"2002","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3051","DOI":"10.1109\/TIT.2009.2021379","article-title":"Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels","volume":"55","author":"Arikan","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","first-page":"261","article-title":"Recent contributions to the mathematical theory of communication","volume":"10","author":"Weaver","year":"1953","journal-title":"ETC A Rev. Gen. Semant."},{"key":"ref_6","unstructured":"Carnap, R., and Bar-Hillel, Y. (1953). An outline of a theory of semantic information. Br. J. Philos. Sci., 4, Available online: http:\/\/hdl.handle.net\/1721.1\/4821."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/B:MIND.0000021684.50925.c9","article-title":"Outline of a theory of strongly semantic information","volume":"14","author":"Floridi","year":"2004","journal-title":"Minds Mach."},{"key":"ref_8","unstructured":"Qin, Z., Tao, X., Lu, J., Tong, W., and Li, G.Y. (2021). Semantic communications: Principles and challenges. arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/MCOM.001.2001239","article-title":"From semantic communication to semantic-aware networking: Model, architecture, and open problems","volume":"59","author":"Shi","year":"2021","journal-title":"IEEE Commun. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1109\/COMST.2022.3223224","article-title":"Semantic communications for future internet: Fundamentals, applications, and challenges","volume":"25","author":"Yang","year":"2022","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_11","first-page":"5","article-title":"Beyond transmitting bits: Context, semantics, and task-oriented communications","volume":"41","author":"Qin","year":"2022","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1109\/MWC.101.2100269","article-title":"Semantic communications: Overview, open issues, and future research directions","volume":"29","author":"Luo","year":"2022","journal-title":"IEEE Wirel. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2051","DOI":"10.1109\/COMST.2024.3443193","article-title":"Intellicise wireless networks from semantic communications: A survey, research issues, and challenges","volume":"27","author":"Zhang","year":"2024","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/COMST.2024.3412852","article-title":"Less data, more knowledge: Building next-generation semantic communication networks","volume":"27","author":"Chaccour","year":"2024","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.eng.2021.11.003","article-title":"Toward wisdom-evolutionary and primitive-concise 6G: A new paradigm of semantic communication networks","volume":"8","author":"Zhang","year":"2022","journal-title":"Engineering"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Farsad, N., Rao, M., and Goldsmith, A. (2018, January 15\u201320). Deep learning for joint source-channel coding of text. Proceedings of the 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, Canada.","DOI":"10.1109\/ICASSP.2018.8461983"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2434","DOI":"10.1109\/JSAC.2021.3087240","article-title":"Semantic communication systems for speech transmission","volume":"39","author":"Weng","year":"2021","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1109\/TCCN.2019.2919300","article-title":"Deep joint source-channel coding for wireless image transmission","volume":"5","author":"Bourtsoulatze","year":"2019","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2584","DOI":"10.1109\/JSAC.2022.3191326","article-title":"Task-oriented multi-user semantic communications","volume":"40","author":"Xie","year":"2022","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2663","DOI":"10.1109\/TSP.2021.3071210","article-title":"Deep learning enabled semantic communication systems","volume":"69","author":"Xie","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2300","DOI":"10.1109\/JSAC.2022.3180802","article-title":"Nonlinear transform source-channel coding for semantic communications","volume":"40","author":"Dai","year":"2022","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1109\/TCCN.2024.3394867","article-title":"SCAN: Semantic communication with adaptive channel feedback","volume":"10","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_23","unstructured":"Zhong, Y. (2002). Principles of Information Science, Beijing University of Posts and Telecommunications Press. [3rd ed.]."},{"key":"ref_24","unstructured":"Zhong, Y. (2007). Introduction to Information Science and Technology, Beijing University of Posts and Telecommunications Press."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5946","DOI":"10.1109\/TCOMM.2022.3194978","article-title":"An indirect rate-distortion characterization for semantic sources: General model and the case of gaussian observation","volume":"70","author":"Liu","year":"2022","journal-title":"IEEE Trans. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3918","DOI":"10.1109\/TCOMM.2023.3274122","article-title":"The role of fidelity in goal-oriented semantic communication: A rate distortion approach","volume":"71","author":"Stavrou","year":"2023","journal-title":"IEEE Trans. Commun."},{"key":"ref_27","unstructured":"Shao, S., Bo, Y., and Tao, M. (2022, January 4\u20138). Task-Oriented Semantic Communication: From Rate\u2013Distortion to Semantic Efficiency. Proceedings of the IEEE Global Communications Conference (GLOBECOM), Rio de Janeiro, Brazil."},{"key":"ref_28","first-page":"7","article-title":"A mathematical theory of semantic communication","volume":"45","author":"Niu","year":"2024","journal-title":"J. Commun."},{"key":"ref_29","unstructured":"Liang, Z., Niu, K., Wang, C., Xu, J., and Zhang, P. (2025, January 13\u201319). Synonymous Variational Inference for Perceptual Image Compression. Proceedings of the 42nd International Conference on Machine Learning, Vancouver, BC, Canada."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Han, Y., Liu, Y., Sun, Y., Niu, K., Ma, N., Cui, S., and Zhang, P. (2025). Extended Blahut\u2013Arimoto Algorithm for Semantic Rate-Distortion Function. Entropy, 27.","DOI":"10.3390\/e27060651"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Xu, J., Du, T., Liang, Z., Niu, K., and Zhang, P. (2025). Semantic Markov Chain using Synonymous Mapping. Tsinghua Sci. Technol.","DOI":"10.26599\/TST.2025.9010064"},{"key":"ref_32","unstructured":"Guo, T., Wang, Y., Han, J., Wu, H., Bai, B., and Han, W. (2022). Semantic compression with side information: A rate-distortion perspective. arXiv."},{"key":"ref_33","unstructured":"Diederik, P.K., and Jimmy, B. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1145\/219717.219748","article-title":"WordNet: A lexical database for English","volume":"38","author":"Miller","year":"1995","journal-title":"Commun. ACM"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"21","DOI":"10.48161\/qaj.v1n2a40","article-title":"State of art for semantic analysis of natural language processing","volume":"1","author":"Maulud","year":"2021","journal-title":"Qubahan Acad. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s13218-021-00726-6","article-title":"It\u2019s the meaning that counts: The state of the art in NLP and semantics","volume":"35","author":"Hershcovich","year":"2021","journal-title":"KI-K\u00fcnstl. Intell."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1798","DOI":"10.1109\/TPAMI.2013.50","article-title":"Representation learning: A review and new perspectives","volume":"35","author":"Bengio","year":"2013","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_38","unstructured":"Luo, J., Delfani, E., Salimnejad, M., and Pappas, N. (2025). From Information Freshness to Semantics of Information and Goal-oriented Communications. arXiv."},{"key":"ref_39","unstructured":"Cover, T.M. (1999). Elements of Information Theory, John Wiley & Sons."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/6\/588\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T11:08:34Z","timestamp":1779793714000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/6\/588"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,26]]},"references-count":39,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["e28060588"],"URL":"https:\/\/doi.org\/10.3390\/e28060588","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,26]]}}}