{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:17:11Z","timestamp":1760145431725,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T00:00:00Z","timestamp":1722297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Relay channels capture the essence of several important communication scenarios such as sensor network and satellite communication. In this paper, first, we propose an efficient coding scheme for an additive white Gaussian noise (AWGN) relay channel in the presence of AWGN feedback, which generalizes the conventional scheme for the AWGN relay channel with noiseless feedback by introducing a lattice-based strategy to eliminate the impact of the feedback channel noise on the performance of the original scheme. Next, we further extend the proposed scheme to the multi-input single-output (MISO) fading relay channel (FRC) with noisy feedback. The key to this extension is to use a pre-coding strategy to transform the MISO channel into a single-input single-output (SISO) channel and applying a two-dimensional lattice coding strategy to deal with the feedback fading channel noise. Finally, we analyze the security performance of our proposed scheme in several cases, and the results of this paper are further illustrated by numerical examples.<\/jats:p>","DOI":"10.3390\/e26080651","type":"journal-article","created":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T17:08:34Z","timestamp":1722359314000},"page":"651","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Feedback Approach for the Relay Channel with Noisy Feedback and Its Security Analysis"],"prefix":"10.3390","volume":"26","author":[{"given":"Rong","family":"Hu","sequence":"first","affiliation":[{"name":"School of Intelligence Technology, Geely University of China, Chengdu 610000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-9608-7217","authenticated-orcid":false,"given":"Haonan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Southwest JiaoTong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Southwest JiaoTong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1109\/JIOT.2015.2487046","article-title":"Satellite communications supporting internet of remote things","volume":"3","author":"Cianca","year":"2016","journal-title":"IEEE Internet Things J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4390","DOI":"10.1109\/TCOMM.2015.2474865","article-title":"Performance analysis of multi-Antenna hybrid satellite-terrestrial relay networks in the presence of interference","volume":"63","author":"An","year":"2015","journal-title":"IEEE Trans. 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