Discovering the Unequal Importance of Coded Bits in the Decoding of Polar Codes

Discovering the Unequal Importance of Coded Bits in the Decoding of Polar Codes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Discovering the Unequal Importance of Coded Bits in the Decoding of Polar Codes Hossam Hassan, Ali Gaber, Mohammed Karmoose, Noha Korany This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8927676/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Polar codes are a key component of modern wireless communication systems due to their capacity-achieving properties and low-complexity decoding algorithms. In conventional polar-coded systems, all coded bits are treated equally at the transmission stage, even though their contribution to successful decoding is not necessarily the same. In this paper, we investigate the unequal importance of coded bits in the decoding process of polar codes and study how this property can be exploited to improve system performance. We first address the problem of identifying the most important coded bits for a given polar decoder. Using a Binary Symmetric Channel (BSC) abstraction, we analyze how protecting a subset of coded bits affects the decoding Bit Error Rate (BER). For small block lengths, we determine the optimal set of important bits using brute-force search, and for larger block lengths, we employ surrogate and genetic optimization techniques to obtain near-optimal solutions. Our results clearly show that only a small subset of coded bits has a dominant impact on decoding performance. We then demonstrate how this insight can be translated into practical performance gains in wireless systems. By mapping the most important coded bits to the most reliable physical resources, such as well-estimated or high-gain Orthogonal Frequency Division Multiplexing (OFDM) subcarriers, significant BER improvements are achieved with virtually no additional complexity or signaling overhead. Furthermore, we extend the study to the full permutation problem, where all coded bits are reordered based on channel reliability when full Channel State Information (CSI) is available at the transmitter. This optimal permutation further enhances decoding performance and yields several-fold BER gains. Simulation results over BSC and multipath fading OFDM channels confirm the effectiveness of the proposed strategies, showing performance improvements of up to seven times compared to conventional mapping schemes. These findings highlight the practical value of exploiting coded-bit importance in polar-coded systems and open new directions for cross-layer code–channel-aware transmission design. Physical sciences/Engineering Physical sciences/Mathematics and computing Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8927676","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":611373099,"identity":"4d583464-ec28-4b02-9453-127ca96155d8","order_by":0,"name":"Hossam Hassan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYBACAyBmhjCZDzA8QAgSpYUtgSGBRC08BsRpMWfgTmAuqKmz55/d8/FDQsXhxAb25m0SDBW1OLVYNvBuYJ5x7HDijDtnN0sknElLbOA5VibBcOY4bocdAGrhYTuQwHAjd4NEYptNYoNEjpkEY9sxAlr+1dnL38h5/CPxn0Rig/wboJZ/BLTwtjEzbriRwwZUD7KFB6iloQa3lsO8Gw7z9h1O3Hgjzcwi4ViacRtPWjGQcQC3luO9Gx/zfKuzl7uR/PjGh5rDsv3shzcCGXU4tYAiBdVANhCRwHAYtxZcAI8to2AUjIJRMNIAAHruVRHbwTToAAAAAElFTkSuQmCC","orcid":"","institution":"Alexandria University","correspondingAuthor":true,"prefix":"","firstName":"Hossam","middleName":"","lastName":"Hassan","suffix":""},{"id":611373102,"identity":"130e402f-38ee-4ae8-865c-34565f8a85ac","order_by":1,"name":"Ali Gaber","email":"","orcid":"","institution":"Alexandria University","correspondingAuthor":false,"prefix":"","firstName":"Ali","middleName":"","lastName":"Gaber","suffix":""},{"id":611373104,"identity":"8e563b66-1f12-4230-99f8-18a0ec142dc8","order_by":2,"name":"Mohammed Karmoose","email":"","orcid":"","institution":"Alexandria University","correspondingAuthor":false,"prefix":"","firstName":"Mohammed","middleName":"","lastName":"Karmoose","suffix":""},{"id":611373105,"identity":"de59ec17-0adb-4ac7-898f-8787909e8378","order_by":3,"name":"Noha Korany","email":"","orcid":"","institution":"Alexandria University","correspondingAuthor":false,"prefix":"","firstName":"Noha","middleName":"","lastName":"Korany","suffix":""}],"badges":[],"createdAt":"2026-02-20 16:23:41","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8927676/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8927676/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108951595,"identity":"66a5f93f-f994-4f29-ae9b-b82de7084887","added_by":"auto","created_at":"2026-05-11 07:15:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":606678,"visible":true,"origin":"","legend":"","description":"","filename":"DiscoveringtheUnequalImportanceofCodedBitsintheDecodingofPolarCodesedited2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8927676/v1_covered_5fb65938-ca90-4720-8fc2-1543efb6f55b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Discovering the Unequal Importance of Coded Bits in the Decoding of Polar Codes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8927676/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8927676/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Polar codes are a key component of modern wireless communication systems due to their capacity-achieving properties and low-complexity decoding algorithms. In conventional polar-coded systems, all coded bits are treated equally at the transmission stage, even though their contribution to successful decoding is not necessarily the same. In this paper, we investigate the unequal importance of coded bits in the decoding process of polar codes and study how this property can be exploited to improve system performance. We first address the problem of identifying the most important coded bits for a given polar decoder. Using a Binary Symmetric Channel (BSC) abstraction, we analyze how protecting a subset of coded bits affects the decoding Bit Error Rate (BER). For small block lengths, we determine the optimal set of important bits using brute-force search, and for larger block lengths, we employ surrogate and genetic optimization techniques to obtain near-optimal solutions. Our results clearly show that only a small subset of coded bits has a dominant impact on decoding performance. We then demonstrate how this insight can be translated into practical performance gains in wireless systems. By mapping the most important coded bits to the most reliable physical resources, such as well-estimated or high-gain Orthogonal Frequency Division Multiplexing (OFDM) subcarriers, significant BER improvements are achieved with virtually no additional complexity or signaling overhead. Furthermore, we extend the study to the full permutation problem, where all coded bits are reordered based on channel reliability when full Channel State Information (CSI) is available at the transmitter. This optimal permutation further enhances decoding performance and yields several-fold BER gains. Simulation results over BSC and multipath fading OFDM channels confirm the effectiveness of the proposed strategies, showing performance improvements of up to seven times compared to conventional mapping schemes. These findings highlight the practical value of exploiting coded-bit importance in polar-coded systems and open new directions for cross-layer code–channel-aware transmission design.","manuscriptTitle":"Discovering the Unequal Importance of Coded Bits in the Decoding of Polar Codes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-26 06:29:19","doi":"10.21203/rs.3.rs-8927676/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5e45576e-d129-444e-98aa-53b46d7ec1c6","owner":[],"postedDate":"March 26th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Rejected","date":"2026-05-11T07:05:08+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-07T09:19:52+00:00","index":68,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-30T12:30:15+00:00","index":67,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":65050394,"name":"Physical sciences/Engineering"},{"id":65050395,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-05-11T07:14:49+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-26 06:29:19","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8927676","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8927676","identity":"rs-8927676","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}