{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:05:28Z","timestamp":1760148328448,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T00:00:00Z","timestamp":1681862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62271380"],"award-info":[{"award-number":["62271380"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Batched Sparse (BATS) codes are a type of network coding scheme that use a combination of random linear network coding (RLNC) and fountain coding to enhance the reliability and efficiency of data transmission. In order to achieve unequal error protection for different data, researchers have proposed unequal error protection BATS (UEP-BATS) codes. However, current UEP-BATS codes suffer from high error floors in their decoding performance, which restricts their practical applications. To address this issue, we propose a novel UEP-BATS code scheme that employs a precoding stage prior to the weighted BATS code. The proposed precoding stage utilizes a partially regular low-density parity-check (PR-LDPC) code, which helps to mitigate the high error floors in the weighted BATS code We derive the asymptotic performance of the proposed scheme based on density evolution (DE). Additionally, we propose a searching algorithm to optimize precoding degree distribution within the complexity range of the precoding stage. Simulation results show that compared to the conventional weighted BATS codes, our proposed scheme offers superior UEP performance and lower error floor, which verifies the effectiveness of our scheme.<\/jats:p>","DOI":"10.3390\/e25040686","type":"journal-article","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T03:25:11Z","timestamp":1681961111000},"page":"686","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Weighted BATS Codes with LDPC Precoding"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-8592","authenticated-orcid":false,"given":"Wenyue","family":"Zhang","sequence":"first","affiliation":[{"name":"The State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1052-5973","authenticated-orcid":false,"given":"Min","family":"Zhu","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China"},{"name":"Science and Technology on Communication Networks Laboratory, Shijiazhuang 050081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1109\/TIT.2005.864424","article-title":"Capacity of wireless erasure networks","volume":"52","author":"Dana","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4413","DOI":"10.1109\/TIT.2006.881746","article-title":"A random linear network coding approach to multicast","volume":"52","author":"Ho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5322","DOI":"10.1109\/TIT.2014.2334315","article-title":"Batched sparse codes","volume":"60","author":"Yang","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1109\/TIT.2017.2769122","article-title":"Finite-length analysis of BATS codes","volume":"64","author":"Yang","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2751","DOI":"10.1109\/TVT.2019.2891842","article-title":"Practical Inner Codes for BATS Codes in Multi-Hop Wireless Networks","volume":"68","author":"Zhou","year":"2019","journal-title":"IEEE Trans. Veh. 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Telecommun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/4\/686\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:18:54Z","timestamp":1760123934000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/4\/686"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,19]]},"references-count":17,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["e25040686"],"URL":"https:\/\/doi.org\/10.3390\/e25040686","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,4,19]]}}}