[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82276-en":3,"doc-seo-82276-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82276,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","Low-Complexity Successive-Cancellation List Decoding of 2×2 Kernel Non-Binary Polar Codes","Non-binary successive cancellation list (NB-SCL) decoding increases complexity because each surviving path is expanded into q candidate branches at every information symbol, then incurs heavy sorting and pruning. This paper presents low-complexity list decoders for 2×2-kernel non-binary polar codes by combining split reduction, Rate-1 structural switching, and adaptive pruning. SR-NBSCL skips splitting on sufficiently reliable symbols, ESR-NBSCL applies simplified NB-SC to the last group, and ABP-NBSCL prunes unreliable candidates using accumulated reliability deviation before sorting. Simulations show FER close to conventional NB-SCL with much lower complexity; ABP-NBSCL reduces path splitting by over 80% at tested SNRs with negligible loss.","Low-Complexity Successive-Cancellation List  \nDecoding of 2 􀀂 2 Kernel Non-Binary Polar Codes  \nXinyu Zhou, Pingping Chen  \narXiv :2607 .09257v 1 [ cs .IT] 10 Jul 2026  \nAbstract—Non-binary successive cancellation list (NB-SCL) decoding expands each surviving path into q candidate branches at every information symbol, which causes high path expansion, sorting, and pruning complexity. To address this issue, this paper proposes low-complexity list decoding algorithms for 2 × 2 kernel non-binary polar codes (NBPCs). First, we design a split-reduced non-binary successive cancellation list (SR-NBSCL) decoder that skips path splitting when the current symbol is sufficiently reliable. We then exploit the final Rate-1 node structure and switch the last group of information symbols to simplified nonbinary successive cancellation (NB-SC) decoding, resulting in the enhanced split-reduced non-binary successive cancellation list (ESR-NBSCL) decoder. To further reduce branch expansion at unreliable symbols, we introduce an accumulated reliabilitydeviation (ARD) metric and propose an adaptive branch-pruning non-binary successive cancellation list (ABP-NBSCL) decoder, which prunes unreliable candidate branches before sorting and then reducs the dominant sorting complexity. Simulation results show that the proposed decoders achieve frame-error-rate (FER) performance close to that of conventional NB-SCL decoding with much lower complexity. In particular, the ABP-NBSCL decoder reduces the path splitting number (PSN) by more than 80% at several tested signal-to-noise ratios (SNRs), with a negligible performance loss.  \nIndex Terms—Non-binary polar codes, successive cancellation list decoding, decoding complexity.  \nI. INTRODUCTION  \nPolar codes, first discovered by Arikan, are the first capacity-achieving codes for binary-input discrete memoryless channels with an explicit and deterministic structure [1], [2] . Polar codes have also been applied to finite-length packet recovery in unsourced random access, multi-user spatial modulation systems, and probabilistically-shaped polar-coded modulation for 6G systems [3]–[7] . Under successive cancellation (SC) decoding, polar codes asymptotically achieve capacity with complexity O (N log N) for the block length N [1] . For finite-length codes, successive cancellation list (SCL) decoding outperforms SC decoding and approaches maximumlikelihood (ML) decoding at high signal-to-noise ratios (SNRs)  \n[8], but with the increased complexity O (LN log N) and Lis the list size [2], [9] . Moreover, Cyclic-redundancy-check (CRC)-aided SCL decoding can further improve the error rate performance [10], [11] .  \nHowever, the increased decoding complexity for SCL with larger values of L makes polar codes less attractive for practical purposes [12] . This issue becomes more pronounced for non-binary polar codes (NBPCs) over GF (q), since each non-binary information symbol has q possible decisions [13],  \nX. Zhou and P. Chen are with the College of Physics and Information Engineering, Fuzhou University, Fuzhou 350108, China.  \n[14] . Under similar decoding algorithm and coding rate, nonbinary NBPCs often performs superior to their binary counterparts [15]–[17] . Recent studies on NBPCs focus on code construction, kernel design, and efficient SC-based decoding [18]–[21] .  \nLow-complexity SCL decoding has been extensively studied for binary polar codes. Zhang et al. proposed a splitreduced SCL decoder that skips splitting when the current unfrozen bit is sufficiently reliable [2] . Other works further introduced reliability tests, path-decision rules, tree pruning, partitioned list decoding, and fast SC/SCL decoding to reduce redundant path operations [22]–[27] . Quantized-softinformation GRAND decoding has also been investigated for CRC-concatenated polar codes, showing lower time and memory complexity than CA-SCL decoding under short-code settings [28] . For short CRC-polar codes, a guessing-flipping framework further combines GR","cbCailzJFIr6B019","https://ap.wps.com/l/cbCailzJFIr6B019","pdf",603633,3,1,13,"English","en",105,"# Abstract\n# Introduction\n## Background on polar codes and decoding\n## Complexity challenge of NB-SCL decoding\n## Related work on low-complexity SCL/NB decoding\n## Motivation and contributions for 2×2 kernel NBPCs","[{\"question\":\"Why is NB-SCL decoding more complex than binary SCL decoding?\",\"answer\":\"In non-binary polar codes over GF(q), each information symbol produces q candidate branches per surviving path, so the number of path-metric candidates grows with both list size L and field order q, making sorting and pruning dominant.\"},{\"question\":\"What does the split-reduced SR-NBSCL decoder do?\",\"answer\":\"SR-NBSCL skips path splitting when the current symbol is sufficiently reliable, reducing unnecessary q-ary branch expansion during list decoding.\"},{\"question\":\"How does ABP-NBSCL reduce complexity further at unreliable symbols?\",\"answer\":\"ABP-NBSCL introduces an accumulated reliability deviation (ARD) metric to prune unreliable candidate branches before sorting, which reduces the dominant sorting complexity while keeping FER close to conventional NB-SCL.\"}]",1784179332,33,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"low-complexity-successive-cancellation-list-decoding-of-22-kernel-non-binary-polar-codes","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/low-complexity-successive-cancellation-list-decoding-of-22-kernel-non-binary-polar-codes/82276/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-22","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is NB-SCL decoding more complex than binary SCL decoding?","Question",{"text":75,"@type":76},"In non-binary polar codes over GF(q), each information symbol produces q candidate branches per surviving path, so the number of path-metric candidates grows with both list size L and field order q, making sorting and pruning dominant.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What does the split-reduced SR-NBSCL decoder do?",{"text":80,"@type":76},"SR-NBSCL skips path splitting when the current symbol is sufficiently reliable, reducing unnecessary q-ary branch expansion during list decoding.",{"name":82,"@type":73,"acceptedAnswer":83},"How does ABP-NBSCL reduce complexity further at unreliable symbols?",{"text":84,"@type":76},"ABP-NBSCL introduces an accumulated reliability deviation (ARD) metric to prune unreliable candidate branches before sorting, which reduces the dominant sorting complexity while keeping FER close to conventional 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