{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T22:53:50Z","timestamp":1772837630562,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,26]],"date-time":"2025-05-26T00:00:00Z","timestamp":1748217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62373197"],"award-info":[{"award-number":["62373197"]}]},{"name":"National Natural Science Foundation of China","award":["61971240"],"award-info":[{"award-number":["61971240"]}]},{"name":"National Natural Science Foundation of China","award":["2023JJ50116"],"award-info":[{"award-number":["2023JJ50116"]}]},{"name":"National Natural Science Foundation of China","award":["2025JJ70144"],"award-info":[{"award-number":["2025JJ70144"]}]},{"name":"National Natural Science Foundation of China","award":["24A0655"],"award-info":[{"award-number":["24A0655"]}]},{"name":"Natural Science Foundation of Hunan Province of China","award":["62373197"],"award-info":[{"award-number":["62373197"]}]},{"name":"Natural Science Foundation of Hunan Province of China","award":["61971240"],"award-info":[{"award-number":["61971240"]}]},{"name":"Natural Science Foundation of Hunan Province of China","award":["2023JJ50116"],"award-info":[{"award-number":["2023JJ50116"]}]},{"name":"Natural Science Foundation of Hunan Province of China","award":["2025JJ70144"],"award-info":[{"award-number":["2025JJ70144"]}]},{"name":"Natural Science Foundation of Hunan Province of China","award":["24A0655"],"award-info":[{"award-number":["24A0655"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["62373197"],"award-info":[{"award-number":["62373197"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["61971240"],"award-info":[{"award-number":["61971240"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["2023JJ50116"],"award-info":[{"award-number":["2023JJ50116"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["2025JJ70144"],"award-info":[{"award-number":["2025JJ70144"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["24A0655"],"award-info":[{"award-number":["24A0655"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a new short reference differential chaos shift keying (SR-DCSK) cooperative communication system based on modified code index modulation, referred to as the MCIM-SR-DCSK-CC system, is proposed. In the proposed MCIM-SR-DCSK-CC system, the information bits are transmitted to both the relay and the destination in the first time slot. On the other hand, in the second time slot, the relay not only forwards the information bits but also sends new information bits to the destination. Specifically, the relay adopts the modified code index modulation to transmit more information bits to the destination. The theoretical bit error rate (BER) expressions of the proposed MCIM-SR-DCSK-CC system are obtained over additive white Gaussian noise (AWGN) and the multipath Rayleigh fading channels. It is demonstrated that the simulation results of BER performance match the theoretical results. The energy efficiency (EE), the data rate, and transmission throughput are carefully analyzed. The performance of the proposed system is better than its competitors\u2019.<\/jats:p>","DOI":"10.3390\/e27060562","type":"journal-article","created":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T08:12:47Z","timestamp":1748419967000},"page":"562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Short Reference Differential Chaos Shift Keying Cooperative Communication System Based on Modified Code Index Modulation"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-7632-5892","authenticated-orcid":false,"given":"Bin","family":"Yu","sequence":"first","affiliation":[{"name":"School of Electrical Information Engineering, Hunan Institute of Technology, Hengyang 421002, China"},{"name":"School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China"},{"name":"Micro and Nano Optoelectronic Devices and Integrated Technology Key Laboratory of Universities in Hunan Province, Hengyang 421002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8882-3081","authenticated-orcid":false,"given":"Hua","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-8867-6165","authenticated-orcid":false,"given":"Yaqiong","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Electrical Information Engineering, Hunan Institute of Technology, Hengyang 421002, China"},{"name":"Micro and Nano Optoelectronic Devices and Integrated Technology Key Laboratory of Universities in Hunan Province, Hengyang 421002, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6602-338X","authenticated-orcid":false,"given":"Hao","family":"Liao","sequence":"additional","affiliation":[{"name":"School of Electrical Information Engineering, Hunan Institute of Technology, Hengyang 421002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0195-1441","authenticated-orcid":false,"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical Information Engineering, Hunan Institute of Technology, Hengyang 421002, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115609","DOI":"10.1016\/j.chaos.2024.115609","article-title":"Design and analysis of a novel differential chaos shift keying system with joint three-dimensional index modulation","volume":"189","author":"He","year":"2024","journal-title":"Chaos Solitons Fract."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1804","DOI":"10.1109\/COMST.2016.2547458","article-title":"A survey on DCSK-based communication systems and their application to UWB scenarios","volume":"18","author":"Fang","year":"2016","journal-title":"IEEE Commun. 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