[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83769-en":3,"doc-seo-83769-105":29,"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":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},83769,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","SOGRAND decoding of LDPC codes","Long forward error correction schemes often rely on concatenating short component codes and decoding them iteratively using soft-input soft-output (SISO) belief propagation for each component. SOGRAND, a Soft Output Guessing Random Additive Noise Decoding method, enables accurate SISO component decoding across many code families. This work specializes SOGRAND’s SISO computation to single parity check (SPC) codes, yielding alternative check-node (CN) updates for LDPC decoding. Simulations show decoding performance comparable to or better than SPA and norm-min-sum, with two low-complexity, hardware-friendly CN rules.","SOGRAND decoding of LDPC codes  \nKen R. Duffy and Jiewei Feng  \nDept. of Mathematics & Dept. of ECE Northeastern University Boston, USA {k.duffy,[feng.ji](feng.ji}@northeastern.edu)[}](feng.ji}@northeastern.edu)[@northeastern.edu](feng.ji}@northeastern.edu)  \nLukas Rapp and Muriel Mdard  \nResearch Laboratory for Electronics Massachusetts Institute of Technology Cambridge, USA {rappl,[medard](medard}@mit.edu)[}](medard}@mit.edu)[@mit.edu](medard}@mit.edu)  \narXiv :2607 .04045v 1 [ cs .IT] 4 Jul 2026  \nAbstract—Long forward error correction codes are typically constructed by concatenating shorter component codes that are then decoded through iterative Soft-Input Soft-Output (SISO) of their components. The recently introduced Soft Output Guessing Random Additive Noise Decoding (SOGRAND) has been shown to enable accurate SISO component decoding for a broad range of component codes. Here we establish that by specializing its SISO computation to Single Parity Check codes, SOGRAND offers an alternative existing Check Node (CN) update for decoding Low Density Parity Check codes. Simulation results demonstrate similar or better decoding performance than Gallager’s sumproduct algorithm and norm-min-sum, while offering two distinct low complexity, hardware friendly CN update algorithms.  \nIndex Terms—LDPC Codes, Soft Input, Iterative Decoding, GRAND, SOGRAND  \nI. INTRODUCTION  \nThe standard mechanism for constructing long, powerful error correction codes is to concatenate short component codes. In the presence of soft input, such constructions can be efficiently decoded by iterative means using a SISO decoder for each component code in conjunction with belief propagation, e.g. [1]–[3] . Designs of this sort include turbo codes [4] as used in 4G, low-density parity-check (LDPC) codes [5]–[11] as used in 5G, turbo product codes [3], [12],[13] as used in WiMAX, staircase codes [14] and the OFEC code, etc.  \nA central element to performance is the accuracy of the SISO component code decoder and its ease of implementation in hardware. Low density parity check (LDPC) codes are constructed with single parity check (SPC) component codes. Perfect soft output (SO) can be computed from an SPC code using Gallager’s ingenious sum-product algorithm (SPA) [5] . In practical implementations, approximations to the SPA, such as normalized min-sum (NMS), are employed as they CN enable lower complexity implementation in hardware with similar decoding performance, e.g. [10], [15]–[19] .  \nRevisiting SOGRAND [20] and specializing its application to SPC codes, here we introduce two novel CN update rules. In doing so, we establish new means to get the same or better performance as the SPA-based approaches through a CN update algorithm that is based on a distinctive premise that lends itself to implementation in hardware. The key philosophical difference is that while SPA, and the approximations that  \nThis material is based upon work supported by the Defense Advanced Research Projects Agency (DARPA) under Contract No. HR00112120008 .  \nfollow from it, focus directly on evaluating a marginal perbit extrinsic log-likelihood ratio (LLR) updates, SOGRAND instead identifies block-wise beliefs that can be marginalized to form per-bit extrinsic LLR updates.  \nThe rest of this paper is organized as follows. Section II briefly reviews SPA and its NMS approximation. Section III introduces SOGRAND and its specialization to SPC codes. Section IV introduces two new SOGRAND CN update algorithms. Section V provides a performance evaluation for 5GLDPC codes. Section VI ends with a discussion.  \nII. SPA AND ITS APPROXIMATIONS  \nGiven a vector of log-likelihood ratios, λn ∈ Rn , Gallager’swell-known SPA for an SPC establishes that the a posteriori LLR of bit i exactly equals λAiPP = λi + λeixt , where λeixt is the extrinsic information, which can be calculated as  \nλeixt = 2tanh −1 i tanh 􀀒 λj2~~ ~~ 􀀓  . For each i, to evaluate this precisely requires the computation of relative","cbCaio0uYbnQpS2f","https://ap.wps.com/l/cbCaio0uYbnQpS2f","pdf",1331067,1,5,"English","en",105,"# Introduction\n# SPA and its Approximations\n# SOGRAND\n# SOGRAND CN Update Algorithms\n# Performance Evaluation for 5G LDPC\n# Discussion","[{\"question\":\"What decoding approach does SOGRAND support for component codes?\",\"answer\":\"SOGRAND performs Soft-Input Soft-Output (SISO) component decoding by guessing and inverting additive noise effects in an order guided by channel properties and soft information.\"},{\"question\":\"How is SOGRAND adapted in this paper for LDPC decoding?\",\"answer\":\"The paper specializes SOGRAND’s SISO computation to single parity check (SPC) component codes, producing alternative check-node (CN) update rules for low-density parity-check (LDPC) codes.\"},{\"question\":\"How does the proposed SOGRAND-based CN updating compare to SPA and norm-min-sum?\",\"answer\":\"Simulation results indicate similar or improved decoding performance relative to Gallager’s sum-product algorithm (SPA) and norm-min-sum, while providing two distinct low-complexity, hardware-friendly CN update algorithms.\"}]",1784190307,13,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":27},"sogrand-decoding-of-ldpc-codes","",{"@graph":35,"@context":85},[36,53,68],{"@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/sogrand-decoding-of-ldpc-codes/83769/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","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},"What decoding approach does SOGRAND support for component codes?","Question",{"text":75,"@type":76},"SOGRAND performs Soft-Input Soft-Output (SISO) component decoding by guessing and inverting additive noise effects in an order guided by channel properties and soft information.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is SOGRAND adapted in this paper for LDPC decoding?",{"text":80,"@type":76},"The paper specializes SOGRAND’s SISO computation to single parity check (SPC) component codes, producing alternative check-node (CN) update rules for low-density parity-check (LDPC) codes.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed SOGRAND-based CN updating compare to SPA and norm-min-sum?",{"text":84,"@type":76},"Simulation results indicate similar or improved decoding performance relative to Gallager’s sum-product algorithm (SPA) and norm-min-sum, while providing two distinct low-complexity, hardware-friendly CN update 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