{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T15:41:30Z","timestamp":1773762090187,"version":"3.50.1"},"reference-count":29,"publisher":"Institution of Engineering and Technology (IET)","issue":"1","license":[{"start":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T00:00:00Z","timestamp":1773705600000},"content-version":"vor","delay-in-days":75,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62201160"],"award-info":[{"award-number":["62201160"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62201160"],"award-info":[{"award-number":["62201160"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62361003"],"award-info":[{"award-number":["62361003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Natural Science Foundation of Guangxi Province","doi-asserted-by":"publisher","award":["2024JJA170151"],"award-info":[{"award-number":["2024JJA170151"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["ietresearch.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["IET Communications"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>The sphere decoding (SD) algorithm for polar codes can achieve maximum likelihood decoding performance, but suffers from high computational complexity. Based on the polar codes with symmetrical structure, the complexity of the SD algorithm can be reduced at the expense of a slight performance loss. To further improve the performance of the SD algorithm for symmetric polar codes, an improved flip SD algorithm is proposed in this paper. When the estimated codeword fails the cyclic redundancy check (CRC), the proposed algorithm flips an unreliable combined value and re\u2010performs the decoding process. Specifically, using the structure of symmetric polar codes, a flipping set is first constructed to incorporate unreliable combined values. The combined values in the flipping set are sorted according to their reliability. Then, a new flipping operation is developed for the flipped values to further improve performance. Simulation results show that, compared to the symmetric SD algorithms, the proposed algorithm can achieve a performance gain of up to 1.6 dB for the polar code of length 64 with different rates at the frame error rate (FER) of , with a slightly higher computational complexity; when compared to the original SD algorithm, the proposed algorithm can achieve a maximum of 1.58 dB performance gain at FER\u00a0=  but with a lower computational\u00a0complexity.<\/jats:p>","DOI":"10.1049\/cmu2.70144","type":"journal-article","created":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T13:26:07Z","timestamp":1773753967000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Improved Flip SD Algorithm for Symmetric Polar Codes"],"prefix":"10.1049","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9317-7298","authenticated-orcid":false,"given":"Yanfeng","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer, Electronics and Information Guangxi University Nanning China"}]},{"given":"Xiuyu","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Computer, Electronics and Information Guangxi University Nanning China"}]},{"given":"Xiangcheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer, Electronics and Information Guangxi University Nanning China"},{"name":"Guangxi Key Laboratory of Multimedia Communications and Network Technology Nanning China"}]},{"given":"Youming","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Computer, Electronics and Information Guangxi University Nanning China"},{"name":"Guangxi Key Laboratory of Multimedia Communications and Network Technology Nanning China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0694-1595","authenticated-orcid":false,"given":"Haiqiang","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer, Electronics and Information Guangxi University Nanning China"},{"name":"Guangxi Key Laboratory of Multimedia Communications and Network Technology Nanning China"}]}],"member":"265","published-online":{"date-parts":[[2026,3,17]]},"reference":[{"key":"e_1_2_10_2_1","first-page":"1493","volume-title":"Proceedings of the 2009 IEEE International Symposium on Information Theory","author":"Arikan E.","year":"2009"},{"issue":"7","key":"e_1_2_10_3_1","doi-asserted-by":"crossref","first-page":"3051","DOI":"10.1109\/TIT.2009.2021379","article-title":"Channel Polarization: A Method for Constructing Capacity\u2010Achieving Codes for Symmetric Binary\u2010Input Memoryless Channels","volume":"55","author":"Arikan E.","year":"2009","journal-title":"IEEE Transactions on Information Theory"},{"key":"e_1_2_10_4_1","unstructured":"Recommendation ITU\u2010R M.2160\u20100: Framework and Overall Objectives of the Future Development of IMT for 2030 and Beyond(International Telecommunication Union 2023)."},{"issue":"12","key":"e_1_2_10_5_1","doi-asserted-by":"crossref","first-page":"6698","DOI":"10.1109\/TIT.2016.2616117","article-title":"Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors","volume":"62","author":"Mondelli M.","year":"2016","journal-title":"IEEE Transactions on Information Theory"},{"issue":"5","key":"e_1_2_10_6_1","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1109\/TIT.2015.2410251","article-title":"List Decoding of Polar Codes","volume":"61","author":"Tal I.","year":"2015","journal-title":"IEEE Transactions on Information Theory"},{"issue":"12","key":"e_1_2_10_7_1","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1049\/el.2012.1459","article-title":"Stack Decoding of Polar Codes","volume":"48","author":"Niu K.","year":"2012","journal-title":"Electronics Letters"},{"issue":"8","key":"e_1_2_10_8_1","doi-asserted-by":"crossref","first-page":"3100","DOI":"10.1109\/TCOMM.2013.070213.120789","article-title":"Improved Successive Cancellation Decoding of Polar Codes","volume":"61","author":"Chen K.","year":"2013","journal-title":"IEEE Transactions on Communications"},{"key":"e_1_2_10_9_1","doi-asserted-by":"crossref","unstructured":"O.Afisiadis A.Balatsoukas\u2010Stimming andA.Burg \u201cA Low\u2010Complexity Improved Successive Cancellation Decoder for Polar Codes \u201d inProceedings of the 48th Asilomar Conference on Signals Systems and Computers(IEEE 2014) 2116\u20132120.","DOI":"10.1109\/ACSSC.2014.7094848"},{"key":"e_1_2_10_10_1","doi-asserted-by":"crossref","unstructured":"L.Chandesris V.Savin andD.Declercq \u201cAn Improved Scflip Decoder for Polar Codes \u201d inProceedings of the IEEE Global Communications Conference (GLOBECOM)(IEEE 2016) 1\u20136.","DOI":"10.1109\/GLOCOM.2016.7841594"},{"issue":"14","key":"e_1_2_10_11_1","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1049\/cmu2.12651","article-title":"Judgement of Error Frames Using Frozen Bits and Its Applications in Decoding of Polar Codes","volume":"17","author":"Yang D.","year":"2023","journal-title":"IET Communications"},{"issue":"4","key":"e_1_2_10_12_1","doi-asserted-by":"crossref","first-page":"183","DOI":"10.3390\/e19040183","article-title":"Low Complexity List Decoding for Polar Codes With Multiple CRC Codes","volume":"19","author":"Kim J.\u2010H.","year":"2017","journal-title":"Entropy"},{"key":"e_1_2_10_13_1","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1007\/s11801-023-2164-4","article-title":"Simplified SCL Decoding Algorithm of Polar Codes Based on Critical Sets","volume":"19","author":"Yuan J.","year":"2023","journal-title":"Optoelectronics Letters"},{"key":"e_1_2_10_14_1","doi-asserted-by":"crossref","unstructured":"S.KahramanandM. E.\u00c7elebi \u201cCode Based Efficient Maximum\u2010Likelihood Decoding of Short Polar Codes \u201d inProceedings of the IEEE International Symposium on Information Theory Proceedings(IEEE 2012) 1967\u20131971.","DOI":"10.1109\/ISIT.2012.6283643"},{"key":"e_1_2_10_15_1","doi-asserted-by":"crossref","unstructured":"J.GuoandA.Guill\u00e9n i F\u00e0bregas \u201cEfficient Sphere Decoding of Polar Codes \u201d inProceedings of the IEEE International Symposium on Information Theory (ISIT)(IEEE 2015) 236\u2013240.","DOI":"10.1109\/ISIT.2015.7282452"},{"key":"e_1_2_10_16_1","doi-asserted-by":"crossref","unstructured":"S. A.Hashemi C.Condo andW. J.Gross \u201cList Sphere Decoding of Polar Codes \u201d inProceedings of the 49th Asilomar Conference on Signals Systems and Computers(IEEE 2015) 1346\u20131350.","DOI":"10.1109\/ACSSC.2015.7421362"},{"issue":"2","key":"e_1_2_10_17_1","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1109\/LCOMM.2018.2885771","article-title":"CRC\u2010Aided Sphere Decoding for Short Polar Codes","volume":"23","author":"Piao J.","year":"2019","journal-title":"IEEE Communications Letters"},{"issue":"6","key":"e_1_2_10_18_1","doi-asserted-by":"crossref","first-page":"5236","DOI":"10.1109\/TVT.2019.2912709","article-title":"An Improved Software List Sphere Polar Decoder With Synchronous Determination","volume":"68","author":"Zhou H.","year":"2019","journal-title":"IEEE Transactions on Vehicular Technology"},{"issue":"5","key":"e_1_2_10_19_1","doi-asserted-by":"crossref","first-page":"6810","DOI":"10.1109\/TVT.2022.3229557","article-title":"Low\u2010Complexity Sphere Decoding for Polar\u2010Coded MIMO Systems","volume":"72","author":"Zhou H.","year":"2023","journal-title":"IEEE Transactions on Vehicular Technology"},{"key":"e_1_2_10_20_1","doi-asserted-by":"crossref","unstructured":"H.Zhou Y.Liu X.Tan C.Ji W. J.Gross andC.Zhang \u201cFast Sphere Decoding of Short Systematic Polar\u2010Like Codes \u201dIEEE Transactions on Vehicular Technology(2026):1\u20136 https:\/\/doi.org\/10.1109\/TVT.2025.3627411.","DOI":"10.1109\/TVT.2025.3627411"},{"issue":"6","key":"e_1_2_10_21_1","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1038\/s41598-023-28256-1","article-title":"Low Complexity Symmetric\u2010Coded Based Sphere Decoding for Low\u2010Rate Polar Codes","volume":"13","author":"Liu Y.","year":"2023","journal-title":"Scientific Reports"},{"issue":"4","key":"e_1_2_10_22_1","doi-asserted-by":"crossref","first-page":"370","DOI":"10.23919\/ICN.2024.0025","article-title":"Received Value Flipping Based Sphere Decoding Algorithm for Polar Codes","volume":"5","author":"Wang R.","year":"2024","journal-title":"Intelligent and Converged Networks"},{"key":"e_1_2_10_23_1","doi-asserted-by":"crossref","unstructured":"F.Ercan C.Condo S. A.Hashemi andW. J.Gross \u201cPartitioned Successive\u2010Cancellation Flip Decoding of Polar Codes \u201d inProceedings of the IEEE International Conference on Communications (ICC)(IEEE 2018) 1\u20136.","DOI":"10.1109\/ICC.2018.8422464"},{"key":"e_1_2_10_24_1","doi-asserted-by":"crossref","unstructured":"P.GiardandA.Burg \u201cFast\u2010SSC\u2010Flip Decoding of Polar Codes \u201d inProceedings of the IEEE Wireless Communications and Networking Conference Workshops (WCNCW)(IEEE 2018) 73\u201377.","DOI":"10.1109\/WCNCW.2018.8369026"},{"issue":"19","key":"e_1_2_10_25_1","doi-asserted-by":"crossref","first-page":"2360","DOI":"10.1049\/cmu2.12490","article-title":"A Latency\u2010Reduced SC Flip Decoding Algorithm for Polar Codes","volume":"16","author":"Yang D.","year":"2022","journal-title":"IET Communications"},{"key":"e_1_2_10_26_1","doi-asserted-by":"crossref","first-page":"57\u00a0738","DOI":"10.1109\/ACCESS.2018.2873821","article-title":"Progressive Bit\u2010Flipping Decoding of Polar Codes: A Critical\u2010Set Based Tree Search Approach","volume":"6","author":"Zhang Z.","year":"2018","journal-title":"IEEE Access"},{"issue":"7","key":"e_1_2_10_27_1","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1109\/LCOMM.2009.090428","article-title":"Performance of Polar Codes With the Construction Using Density Evolution","volume":"13","author":"Mori R.","year":"2009","journal-title":"IEEE Communications Letters"},{"key":"e_1_2_10_28_1","doi-asserted-by":"crossref","unstructured":"G.He J.\u2010C.Belfiore I.Land et\u00a0al. \u201cBeta\u2010Expansion: A Theoretical Framework for Fast and Recursive Construction of Polar Codes \u201d inGLOBECOM 2017\u20102017 IEEE Global Communications Conference(IEEE 2017) 1\u20136.","DOI":"10.1109\/GLOCOM.2017.8254146"},{"issue":"10","key":"e_1_2_10_29_1","doi-asserted-by":"crossref","first-page":"6562","DOI":"10.1109\/TIT.2013.2272694","article-title":"How to Construct Polar Codes","volume":"59","author":"Tal I.","year":"2013","journal-title":"IEEE Transactions on Information Theory"},{"issue":"11","key":"e_1_2_10_30_1","doi-asserted-by":"crossref","first-page":"3221","DOI":"10.1109\/TCOMM.2012.081512.110872","article-title":"Efficient Design and Decoding of Polar Codes","volume":"60","author":"Trifonov P.","year":"2012","journal-title":"IEEE Transactions on Communications"}],"container-title":["IET Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/pdf\/10.1049\/cmu2.70144","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/full-xml\/10.1049\/cmu2.70144","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/pdf\/10.1049\/cmu2.70144","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T13:26:11Z","timestamp":1773753971000},"score":1,"resource":{"primary":{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/10.1049\/cmu2.70144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["10.1049\/cmu2.70144"],"URL":"https:\/\/doi.org\/10.1049\/cmu2.70144","archive":["Portico"],"relation":{},"ISSN":["1751-8628","1751-8636"],"issn-type":[{"value":"1751-8628","type":"print"},{"value":"1751-8636","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"2025-07-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-03-01","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-03-17","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70144"}}