{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:53:34Z","timestamp":1776783214280,"version":"3.51.2"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T00:00:00Z","timestamp":1773619200000},"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":"crossref","award":["62371070"],"award-info":[{"award-number":["62371070"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Beijing Natural Science Foundation","award":["L222043"],"award-info":[{"award-number":["L222043"]}]},{"name":"Beijing University of Posts and Telecommunications Excellent Ph.D. Students Foundation","award":["CX2021101"],"award-info":[{"award-number":["CX2021101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>U-shaped Split Federated Learning (U-SFL) is a promising paradigm for distributed image coding, offering parallel training capabilities and privacy preservation while mitigating computational burdens on edge devices. However, the frequent bidirectional transmission of intermediate features between dual-split points incurs substantial communication overhead. To mitigate this issue, we propose a compact-feature U-shaped split federated learning framework (CoF U-SFL), which reduces communication overhead and improves training efficiency while maintaining low image distortion. We introduce a feature entropy estimation network to model the distribution of split-layer features, enabling effective compression during transmission. Furthermore, we formulate a joint optimization objective incorporating entropy constraints to guide the end-to-end training. Experimental results demonstrate that CoF U-SFL reduces communication overhead by 104.6 times while maintaining reconstruction performance.<\/jats:p>","DOI":"10.3390\/e28030331","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T13:32:07Z","timestamp":1773667927000},"page":"331","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["U-Shaped Split Federated Learning with Compact Features for Deep Learning-Based Image Coding"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9359-6824","authenticated-orcid":false,"given":"Qizheng","family":"Sun","sequence":"first","affiliation":[{"name":"Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caili","family":"Guo","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meiyi","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Engineering, King\u2019s College London, London WC2R 2LS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Yang","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1109\/MWC.002.2400348","article-title":"Collaborative perception for connected and autonomous driving: Challenges, possible solutions and opportunities","volume":"32","author":"Hu","year":"2025","journal-title":"IEEE Wirel. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/MSP.2021.3125282","article-title":"Federated learning: A signal processing perspective","volume":"39","author":"Gafni","year":"2022","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2010","DOI":"10.1109\/TMI.2022.3202106","article-title":"Specificity-preserving federated learning for MR image reconstruction","volume":"42","author":"Feng","year":"2022","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"14104","DOI":"10.1109\/TVT.2020.3028011","article-title":"Federated learning assisted multi-UAV networks","volume":"69","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","unstructured":"Vepakomma, P., Gupta, O., Swedish, T., and Raskar, R. (2018). Split learning for health: Distributed deep learning without sharing raw patient data. arXiv."},{"key":"ref_6","first-page":"8485","article-title":"SplitFed: When federated learning meets split learning","volume":"36","author":"Thapa","year":"2022","journal-title":"Proc. AAAI Conf. Artif. Intell. (AAAI)"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1109\/TVT.2023.3304176","article-title":"Federated split learning with data and label privacy preservation in vehicular networks","volume":"73","author":"Wu","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.future.2024.03.020","article-title":"PPSFL: Privacy-preserving split federated learning for heterogeneous data in edge-based internet of things","volume":"156","author":"Zheng","year":"2024","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Lin, Z., Qu, G., Wei, W., Chen, X., and Leung, K.K. (2024). AdaptSFL: Adaptive split federated learning in resource-constrained edge networks. arXiv.","DOI":"10.1109\/TON.2025.3577790"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1109\/MNET.131.2200409","article-title":"UDSem: A unified distributed learning framework for semantic communications over wireless networks","volume":"38","author":"Nan","year":"2023","journal-title":"IEEE Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"17237","DOI":"10.1109\/JIOT.2024.3360230","article-title":"Mobility-aware split-federated with transfer learning for vehicular semantic communication networks","volume":"11","author":"Zheng","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5946","DOI":"10.1109\/JBHI.2023.3317632","article-title":"Dynamic corrected split federated learning with homomorphic encryption for u-shaped medical image networks","volume":"27","author":"Yang","year":"2023","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1539","DOI":"10.1109\/TIFS.2023.3243490","article-title":"Privacy-preserving split learning for large-scaled vision pre-training","volume":"18","author":"Wang","year":"2023","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Kathariya, B., Li, Z., Chen, J., and Van der Auwera, G. (2021). Gradient compression with a variational coding scheme for federated learning. 2021 International Conference on Visual Communications and Image Processing (VCIP), IEEE.","DOI":"10.1109\/VCIP53242.2021.9675436"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Cui, L., Su, X., Zhou, Y., and Zhang, L. (2020). Clustergrad: Adaptive gradient compression by clustering in federated learning. GLOBECOM 2020\u20142020 IEEE Global Communications Conference, IEEE.","DOI":"10.1109\/GLOBECOM42002.2020.9322527"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6495","DOI":"10.1109\/TMC.2022.3190510","article-title":"Hcfl: A high compression approach for communication-efficient federated learning in very large scale iot networks","volume":"22","author":"Nguyen","year":"2022","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2520","DOI":"10.1109\/TVT.2023.3313593","article-title":"Metadata and image features co-aware semi-supervised vertical federated learning with attention mechanism","volume":"73","author":"Chen","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_18","unstructured":"Isik, B., Pase, F., Gunduz, D., Weissman, T., and Zorzi, M. (2022). Sparse random networks for communication-efficient federated learning. arXiv."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ayad, A., Renner, M., and Schmeink, A. (2021). Improving the communication and computation efficiency of split learning for iot applications. 2021 IEEE Global Communications Conference (GLOBECOM), IEEE.","DOI":"10.1109\/GLOBECOM46510.2021.9685493"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hsieh, C.-Y., Chuang, Y.-C., and Wu, A.-Y. (2022). C3-sl: Circular convolution-based batch-wise compression for communication-efficient split learning. 2022 IEEE 32nd International Workshop on Machine Learning for Signal Processing (MLSP), IEEE.","DOI":"10.1109\/MLSP55214.2022.9943507"},{"key":"ref_21","unstructured":"Lin, Z., Lin, Z., Yang, M., Huang, J., Zhang, Y., Fang, Z., Du, X., Chen, Z., Zhu, S., and Ni, W. (2025). Sl-acc: A communication-efficient split learning framework with adaptive channel-wise compression. arXiv."},{"key":"ref_22","unstructured":"Han, D.-J., Bhatti, H.I., Lee, J., and Moon, J. (2021). Accelerating federated learning with split learning on locally generated losses. arXiv."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1109\/TMC.2025.3591744","article-title":"Federated split learning with improved communication and storage efficiency","volume":"25","author":"Mu","year":"2025","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1308","DOI":"10.1109\/TGCN.2025.3624654","article-title":"Adaptive low-latency split federated learning with dynamic model partitioning in resource-constrained healthcare iot","volume":"10","author":"Gupta","year":"2025","journal-title":"IEEE Trans. Green Commun. Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"10844","DOI":"10.1109\/TNNLS.2025.3526227","article-title":"Communication-efficient split learning via adaptive feature-wise compression","volume":"36","author":"Oh","year":"2025","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"17851","DOI":"10.1109\/TITS.2025.3554247","article-title":"Model partition and resource allocation for split learning in vehicular edge networks","volume":"26","author":"Yu","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_27","first-page":"90","article-title":"Split computing and early exiting for deep learning applications: Survey and research challenges","volume":"55","author":"Matsubara","year":"2022","journal-title":"ACM Comput. Surv."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Pasquini, D., Ateniese, G., and Bernaschi, M. (2021). Unleashing the tiger: Inference attacks on split learning. Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, Association for Computing Machinery.","DOI":"10.1145\/3460120.3485259"},{"key":"ref_29","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_30","unstructured":"Theis, L., Shi, W., Cunningham, A., and Husz\u00e1r, F. (2017). Lossy image compression with compressive autoencoders. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Sun, Q., Guo, C., Yang, Y., Tang, R., and Liu, C. (2023). Deep joint source-channel coding based on semantics of pixels for wireless image transmission. 2023 IEEE 34th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), IEEE.","DOI":"10.1109\/PIMRC56721.2023.10293843"},{"key":"ref_32","unstructured":"Balle, J., Minnen, D., Singh, S., Hwang, S.J., and Johnston, N. (2018). Variational image compression with a scale hyperprior. arXiv."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Yang, K., Wang, S., Dai, J., Tan, K., Niu, K., and Zhang, P. (2023). WITT: A wireless image transmission transformer for semantic communications. ICASSP 2023\u20142023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE.","DOI":"10.1109\/ICASSP49357.2023.10094735"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Agustsson, E., and Timofte, R. (2017). Ntire 2017 challenge on single image super-resolution: Dataset and study. 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPRW.2017.150"},{"key":"ref_35","unstructured":"Kodak (2026, March 13). Kodak Photocd Dataset. Available online: http:\/\/r0k.us\/graphics\/kodak\/."},{"key":"ref_36","unstructured":"(2026, March 13). CLIC 2021: Challenge on Learned Image Compression. Available online: http:\/\/compression.cc."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/331\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:00:01Z","timestamp":1773813601000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/331"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,16]]},"references-count":36,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["e28030331"],"URL":"https:\/\/doi.org\/10.3390\/e28030331","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,16]]}}}