[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81507-en":3,"doc-seo-81507-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},81507,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Improved Decoding of Tanner Codes","Improved decoding algorithms are developed for expander-based Tanner codes. A randomized linear-time decoder corrects up to αn errors for T(G, C0) when the bipartite expander satisfies δd0>2, strengthening earlier bounds that required δd0>3. The work then derandomizes to obtain a deterministic linear-time decoder with the same radius, analyzes the size-expansion trade-off to derive new minimum-distance bounds, and extends Viderman’s find-erasures-and-decode framework to general linear inner codes for δd0>1.8 at d0=3.","arXiv :2501 . 12293v4 [ cs .IT] 10 Jul 2026  \nImproved Decoding of Tanner Codes ∗  \nZhaienhe Zhou† Zeyu Guo‡  \nAbstract  \nIn this paper, we present improved decoding algorithms for expander-based Tanner codes.  \nWe begin by developing a randomized linear-time decoding algorithm that, under the condition that δd0 > 2, corrects up to αn errors for a Tanner code T(G, C0 ), where G is a (c, d,α,δ)-bipartite expander with n left vertices, and C0 ⊆ Fd2 is a linear inner code with minimum distance d0 . This result improves upon the previous work of Shen, Shangguan, Ouyang and Cheng (IEEE TIT 2025), which required δd0 > 3.  \nWe further derandomize the algorithm to obtain a deterministic linear-time decoding algorithm with the same decoding radius. Our algorithm improves upon the previous deterministic algorithm of Cheng et [al. by](al. by) achieving a decoding radius of αn, compared with the previous radius of d0~~ ~~(1~~α~~0.5cδ)n.  \nAdditionally, we investigate the size-expansion trade-off introduced by the recent work of Chen, Cheng, Li, and Ouyang (IEEE TIT 2023), and use it to provide new bounds on the minimum distance of Tanner codes. Specifically, we prove that the minimum distance of a Tanner code T (G, C0 ) is approximately f1 􀀐 d~~1~~0 􀀑 αn, where fδ (·) is the Size-Expansion Function. As another application, we improve the decoding radius of our decoding algorithms from αn to approximately f1 􀀐 d~~2~~0 􀀑 αn.  \nFinally, we extend Viderman’s find-erasures-and-decode framework (ACM TOCT 2013) to general linear inner codes, obtaining a deterministic linear-time decoder for δd0 > 1.8 when d0 = 3, thus pushing below the δd0 > 2 threshold of our general result.  \n1 Introduction  \nLow-density parity-check (LDPC) codes are an important class of error-correcting codes known for their near-optimal error-correction performance and low decoding complexity. They are characterized by sparse parity-check matrices, where most entries are zero, which makes them efficient in both encoding and decoding. LDPC codes were first introduced by Gallager [Gal62] in the 1960s but gained renewed attention due to their suitability for modern communication systems, including wireless and satellite communications, as well as for storage applications.  \nA key feature of LDPC codes is their representation as a bipartite graph, with bits on the left side and parity checks on the right. This leads to a parity-check graph with a constant degree, where the sparsity of the graph enables the development of efficient decoding algorithms. In particular, the belief-propagation algorithm, introduced by Gallager [Gal62], was later proven by Zyablov and Pinsker [ZP75] to correct a constant fraction of errors on random LDPC codes.  \n∗ This is an extended version of the conference paper [ZG25], presented at IEEE ISIT 2025, which includes detailed proofs and an additional result, Theorem 1.4 .  \n†[zhaienhezhou@gmail.com](zhaienhezhou@gmail.com), School of the Gifted Young & College of Computer Science, University of Science and Technology of China, Hefei 230026, China.  \n‡[zguotcs@gmail.com](zguotcs@gmail.com), Department of Computer Science and Engineering, The Ohio State University  \nLater, Tanner [Tan81] extended LDPC codes by developing a recursive approach to construct long error-correcting codes from shorter inner codes. Tanner codes are constructed by assigning alinear inner code C0 of length d and minimum distance d0 to the vertices of a sparse bipartite graph. Specifically, bits are placed on the left side of the bipartite graph, and each vertex on the right side is assigned an inner code that imposes constraints on the connected bits. Note that when the inner code is a parity-check code, the Tanner code simplifies to an LDPC code. This construction offers greater flexibility in code design, enabling codes with both large minimum distances and efficient decoding properties.  \nTo analyze the decoding algorithms of LDPC and Tanner codes, Sipser and Spielman [SS96] ","cbCainbxlXKtMe6p","https://ap.wps.com/l/cbCainbxlXKtMe6p","pdf",701036,1,36,"English","en",105,"# Abstract\n# Introduction\n## LDPC codes and bipartite graph representation\n## Tanner codes via inner codes on expander graphs\n## Expander codes and expansion-based decoding\n## Decoding algorithms and decoding-radius trade-offs","[{\"question\":\"What is the main contribution of the improved Tanner-code decoding algorithms?\",\"answer\":\"The paper presents improved randomized and deterministic linear-time decoding algorithms for expander-based Tanner codes, enlarging the guaranteed decoding radius under specific expander conditions.\"},{\"question\":\"Under what condition does the randomized linear-time decoder achieve its error-correction radius?\",\"answer\":\"It corrects up to αn errors when the expander satisfies δd0\\u003e2, where d0 is the minimum distance of the linear inner code and δ characterizes the graph expansion.\"},{\"question\":\"How does the paper relate minimum distance and decoding performance?\",\"answer\":\"It uses the size-expansion trade-off to establish new bounds on the minimum distance of Tanner codes and provides an application that improves the decoding radius accordingly.\"}]",1784173880,91,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"improved-decoding-of-tanner-codes","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/improved-decoding-of-tanner-codes/81507/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What is the main contribution of the improved Tanner-code decoding algorithms?","Question",{"text":74,"@type":75},"The paper presents improved randomized and deterministic linear-time decoding algorithms for expander-based Tanner codes, enlarging the guaranteed decoding radius under specific expander conditions.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Under what condition does the randomized linear-time decoder achieve its error-correction radius?",{"text":79,"@type":75},"It corrects up to αn errors when the expander satisfies δd0>2, where d0 is the minimum distance of the linear inner code and δ characterizes the graph expansion.",{"name":81,"@type":72,"acceptedAnswer":82},"How does the paper relate minimum distance and decoding performance?",{"text":83,"@type":75},"It uses the size-expansion trade-off to establish new bounds on the minimum distance of Tanner codes and provides an application that improves the decoding radius accordingly.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]