{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T19:57:20Z","timestamp":1775937440888,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"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":"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"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a modified code index modulation scheme based on the multi-carrier M-ary DCSK system, referred to as a MC-MCIM-MDCSK system, is proposed. In the proposed MC-MCIM-MDCSK system, a modified code index modulation scheme is carried out, which selects two orthogonal Walsh codes for realizing the M-ary DCSK encoder. The theoretical BER expression of the proposed system is obtained over additive white Gaussian noise (AWGN) and the multipath Rayleigh fading channels. Abundant simulation results showed that the simulation results matched the theoretical results. The energy efficiency (EE), spectrum efficiency (SE), the data rate, and the complexity of the proposed system were carefully analyzed. The BER performance of the proposed system was compared with those of other systems. It is shown that the proposed system has better BER performance than its competitors.<\/jats:p>","DOI":"10.3390\/e27030216","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T06:10:21Z","timestamp":1740031821000},"page":"216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Modified Code Index Modulation Scheme Based on Multi-Carrier M-ary DCSK System"],"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 Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China"},{"name":"School of Electrical Information Engineering, Hunan Institute of Technology, Hengyang 421002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9448-0989","authenticated-orcid":false,"given":"Guo-Ping","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023, 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":"Ya-Qiong","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Electrical Information Engineering, Hunan Institute of Technology, 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":[[2025,2,20]]},"reference":[{"key":"ref_1","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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