{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:08:11Z","timestamp":1760234891724,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,6]],"date-time":"2021-07-06T00:00:00Z","timestamp":1625529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Joint Fund for Smart Computing of Natural Science Foundation of Shandong Province","award":["ZR2019LZH001"],"award-info":[{"award-number":["ZR2019LZH001"]}]},{"name":"Shandong University Youth Innovation Supporting Program","award":["2019KJN020, 2019KJN024"],"award-info":[{"award-number":["2019KJN020, 2019KJN024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Polar code has been adopted as the control channel coding scheme for the fifth generation (5G), and the performance of short polar codes is receiving intensive attention. The successive cancellation flipping (SC flipping) algorithm suffers a significant performance loss in short block lengths. To address this issue, we propose a double long short-term memory (DLSTM) neural network to locate the first error bit. To enhance the prediction accuracy of the DLSTM network, all frozen bits are clipped in the output layer. Then, Gaussian approximation is applied to measure the channel reliability and rank the flipping set to choose the least reliable position for multi-bit flipping. To be robust under different codewords, padding and masking strategies aid the network architecture to be compatible with multiple block lengths. Numerical results indicate that the error-correction performance of the proposed algorithm is competitive with that of the CA-SCL algorithm. It has better performance than the machine learning-based multi-bit flipping SC (ML-MSCF) decoder and the dynamic SC flipping (DSCF) decoder for short polar codes.<\/jats:p>","DOI":"10.3390\/e23070863","type":"journal-article","created":{"date-parts":[[2021,7,6]],"date-time":"2021-07-06T11:36:44Z","timestamp":1625571404000},"page":"863","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["DLSTM-Based Successive Cancellation Flipping Decoder for Short Polar Codes"],"prefix":"10.3390","volume":"23","author":[{"given":"Jianming","family":"Cui","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1196-1918","authenticated-orcid":false,"given":"Wenxiu","family":"Kong","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0032-4905","authenticated-orcid":false,"given":"Xiaojun","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China"},{"name":"State Key Laboratory of High-End Server and Storage Technology, Jinan 250101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Da","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingtian","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ar\u0131kan, E. 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