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GitHub - crozone/ReedSolomonCCSDS: Reed Solomon (255, 223) CCSDS in C#.
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octicon-link-external HeaderMenu-external-icon color-fg-subtle"> <path d="M3.75 2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary Link--external" target="_blank" data-analytics-event="{"location":"navbar","action":"blog","context":"product","tag":"link","label":"blog_link_product_navbar"}" href="https://github.blog"> Blog <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-link-external HeaderMenu-external-icon color-fg-subtle"> <path d="M3.75 2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> </ul> </div> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Solutions <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 d-lg-flex flex-wrap dropdown-menu-wide"> <div class="HeaderMenu-column px-lg-4 border-lg-right mb-4 mb-lg-0 pr-lg-7"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0 pb-lg-3 mb-3 mb-lg-0"> <span class="d-block h4 color-fg-default my-1" id="solutions-by-company-size-heading">By company size</span> <ul class="list-style-none f5" aria-labelledby="solutions-by-company-size-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"enterprises","context":"solutions","tag":"link","label":"enterprises_link_solutions_navbar"}" href="https://github.com/enterprise"> Enterprises </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"small_and_medium_teams","context":"solutions","tag":"link","label":"small_and_medium_teams_link_solutions_navbar"}" href="https://github.com/team"> Small and medium teams </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"startups","context":"solutions","tag":"link","label":"startups_link_solutions_navbar"}" href="https://github.com/enterprise/startups"> Startups </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"nonprofits","context":"solutions","tag":"link","label":"nonprofits_link_solutions_navbar"}" href="/solutions/industry/nonprofits"> Nonprofits </a></li> </ul> </div> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="solutions-by-use-case-heading">By use case</span> <ul class="list-style-none f5" aria-labelledby="solutions-by-use-case-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"devsecops","context":"solutions","tag":"link","label":"devsecops_link_solutions_navbar"}" href="/solutions/use-case/devsecops"> DevSecOps </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"devops","context":"solutions","tag":"link","label":"devops_link_solutions_navbar"}" href="/solutions/use-case/devops"> DevOps </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"ci_cd","context":"solutions","tag":"link","label":"ci_cd_link_solutions_navbar"}" href="/solutions/use-case/ci-cd"> CI/CD </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"view_all_use_cases","context":"solutions","tag":"link","label":"view_all_use_cases_link_solutions_navbar"}" href="/solutions/use-case"> View all use cases </a></li> </ul> </div> </div> <div class="HeaderMenu-column px-lg-4"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="solutions-by-industry-heading">By industry</span> <ul class="list-style-none f5" aria-labelledby="solutions-by-industry-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"healthcare","context":"solutions","tag":"link","label":"healthcare_link_solutions_navbar"}" href="/solutions/industry/healthcare"> Healthcare </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"financial_services","context":"solutions","tag":"link","label":"financial_services_link_solutions_navbar"}" href="/solutions/industry/financial-services"> Financial services </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"manufacturing","context":"solutions","tag":"link","label":"manufacturing_link_solutions_navbar"}" href="/solutions/industry/manufacturing"> Manufacturing </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"government","context":"solutions","tag":"link","label":"government_link_solutions_navbar"}" href="/solutions/industry/government"> Government </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"view_all_industries","context":"solutions","tag":"link","label":"view_all_industries_link_solutions_navbar"}" href="/solutions/industry"> View all industries </a></li> </ul> </div> </div> <div class="HeaderMenu-trailing-link rounded-bottom-2 flex-shrink-0 mt-lg-4 px-lg-4 py-4 py-lg-3 f5 text-semibold"> <a href="/solutions"> View all solutions <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-right HeaderMenu-trailing-link-icon"> <path d="M6.22 3.22a.75.75 0 0 1 1.06 0l4.25 4.25a.75.75 0 0 1 0 1.06l-4.25 4.25a.751.751 0 0 1-1.042-.018.751.751 0 0 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d-lg-flex flex-wrap dropdown-menu-wide"> <div class="HeaderMenu-column px-lg-4 border-lg-right mb-4 mb-lg-0 pr-lg-7"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="resources-topics-heading">Topics</span> <ul class="list-style-none f5" aria-labelledby="resources-topics-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"ai","context":"resources","tag":"link","label":"ai_link_resources_navbar"}" href="/resources/articles/ai"> AI </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"devops","context":"resources","tag":"link","label":"devops_link_resources_navbar"}" href="/resources/articles/devops"> DevOps </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"security","context":"resources","tag":"link","label":"security_link_resources_navbar"}" href="/resources/articles/security"> Security </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"software_development","context":"resources","tag":"link","label":"software_development_link_resources_navbar"}" href="/resources/articles/software-development"> Software Development </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"view_all","context":"resources","tag":"link","label":"view_all_link_resources_navbar"}" href="/resources/articles"> View all </a></li> </ul> </div> </div> <div class="HeaderMenu-column px-lg-4"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0 border-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="resources-explore-heading">Explore</span> <ul class="list-style-none f5" aria-labelledby="resources-explore-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary Link--external" target="_blank" data-analytics-event="{"location":"navbar","action":"learning_pathways","context":"resources","tag":"link","label":"learning_pathways_link_resources_navbar"}" href="https://resources.github.com/learn/pathways"> Learning Pathways <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-link-external HeaderMenu-external-icon color-fg-subtle"> <path d="M3.75 2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary Link--external" target="_blank" data-analytics-event="{"location":"navbar","action":"events_amp_webinars","context":"resources","tag":"link","label":"events_amp_webinars_link_resources_navbar"}" href="https://resources.github.com"> Events & Webinars <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-link-external HeaderMenu-external-icon color-fg-subtle"> <path d="M3.75 2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"ebooks_amp_whitepapers","context":"resources","tag":"link","label":"ebooks_amp_whitepapers_link_resources_navbar"}" href="https://github.com/resources/whitepapers"> Ebooks & Whitepapers </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"customer_stories","context":"resources","tag":"link","label":"customer_stories_link_resources_navbar"}" href="https://github.com/customer-stories"> Customer Stories </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary Link--external" target="_blank" data-analytics-event="{"location":"navbar","action":"partners","context":"resources","tag":"link","label":"partners_link_resources_navbar"}" href="https://partner.github.com"> Partners <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-link-external HeaderMenu-external-icon color-fg-subtle"> <path d="M3.75 2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"executive_insights","context":"resources","tag":"link","label":"executive_insights_link_resources_navbar"}" href="https://github.com/solutions/executive-insights"> Executive Insights </a></li> </ul> </div> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Open Source <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 px-lg-4"> <div class="HeaderMenu-column"> <div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"github_sponsors","context":"open_source","tag":"link","label":"github_sponsors_link_open_source_navbar"}" href="/sponsors"> <div> <div class="color-fg-default h4">GitHub Sponsors</div> Fund open source developers </div> </a></li> </ul> </div> <div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"the_readme_project","context":"open_source","tag":"link","label":"the_readme_project_link_open_source_navbar"}" href="https://github.com/readme"> <div> <div class="color-fg-default h4">The ReadME Project</div> GitHub community articles </div> </a></li> </ul> </div> <div class="border-bottom pb-3 pb-lg-0 border-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="open-source-repositories-heading">Repositories</span> <ul class="list-style-none f5" aria-labelledby="open-source-repositories-heading"> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" data-analytics-event="{"location":"navbar","action":"topics","context":"open_source","tag":"link","label":"topics_link_open_source_navbar"}" href="https://github.com/topics"> Topics </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary" 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dir=\"auto\"\u003eReed-Solomon\u003c/h1\u003e\u003ca id=\"user-content-reed-solomon\" class=\"anchor\" aria-label=\"Permalink: Reed-Solomon\" href=\"#reed-solomon\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eReed Solomon (255, 223) CCSDS in C#.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eOverview\u003c/h1\u003e\u003ca id=\"user-content-overview\" class=\"anchor\" aria-label=\"Permalink: Overview\" href=\"#overview\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis is an implementation of an RS (255, 223) encoder and decoder.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe encoder is capable of encoding 223 bytes of data to produce 32 bytes of parity.\nWhen the parity is concatenated with the data, it forms a 255 bytes long encoded block.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe decoder is capable of decoding a block to correct up to 16 errors of unknown position, at any position within the 255 byte block.\nIf the error locations are known, the indexes of the bad bytes can be specified as erasures,\nallowing up to 32 bytes to be corrected within the 255 byte block.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe encoder and decoder use the RS (255,223) code with 8-bit symbols as specified by the CCSDS.\nSpecifically, they use a field generator polynomial of 1 + X + X^2 + X^7 + X^8,\nand a code generator with first consecutive root = 112 and a primitive element of 11.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe conventional polynomial form is used by default. If required, the the strict CCSDS dual-basis polynomial form can be\nenabled with the \u003ccode\u003edualBasis\u003c/code\u003e parameter.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eA summary of the CCSDS standard \u003ca href=\"https://public.ccsds.org/pubs/130x1g2.pdf\" rel=\"nofollow\"\u003ecan be found at their website.\u003c/a\u003e (Page 5-1)\nIn depth reference \u003ca href=\"https://public.ccsds.org/Pubs/131x0b3e1.pdf\" rel=\"nofollow\"\u003eis also available\u003c/a\u003e (Page 4-1)\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAttribution\u003c/h1\u003e\u003ca id=\"user-content-attribution\" class=\"anchor\" aria-label=\"Permalink: Attribution\" href=\"#attribution\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe Reed-Solomon encoder and decoder, found in \u003ccode\u003e/ReedSolomon/Rs8.cs\u003c/code\u003e, is derived from code from \"General purpose Reed-Solomon decoder for 8-bit symbols or less\", Copyright 2003 Phil Karn, KA9Q.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIt is used under the terms of the GNU Lesser General Public License (LGPL). See the file \"LICENSE\" in this package for license details.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe version used for this derivation can be found \u003ca href=\"http://www.ka9q.net/code/fec/fec-3.0.1.tar.bz2\" rel=\"nofollow\"\u003ehere\u003c/a\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe latest version of the original source code can be found \u003ca href=\"http://www.ka9q.net/code/fec/\" rel=\"nofollow\"\u003ehere\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eMethods\u003c/h1\u003e\u003ca id=\"user-content-methods\" class=\"anchor\" aria-label=\"Permalink: Methods\" href=\"#methods\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRs8.Encode(Span block, bool dualBasis = false)\u003c/h3\u003e\u003ca id=\"user-content-rs8encodespan-block-bool-dualbasis--false\" class=\"anchor\" aria-label=\"Permalink: Rs8.Encode(Span block, bool dualBasis = false)\" href=\"#rs8encodespan-block-bool-dualbasis--false\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003epublic static void Encode(Span\u0026lt;byte\u0026gt; block, bool dualBasis = false)\u003c/code\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTakes a \u003ccode\u003eSpan\u0026lt;byte\u0026gt;\u003c/code\u003e \u003ccode\u003eblock\u003c/code\u003e of length \u003ccode\u003eRs8.BlockLength\u003c/code\u003e (255), of which the first 223 bytes are data, and the last 32 bytes are space for parity. Parity is calculated for data, and then written to the last 32 bytes of the block.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThis overload is the equivalent of calling:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eEncode(block.Slice(0, Rs8.DataLength), block.Slice(Rs8.DataLength, Rs8.ParityLength), dualBasis);\u003c/code\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRs8.Encode(Span data, Span parity, bool dualBasis = false)\u003c/h3\u003e\u003ca id=\"user-content-rs8encodespan-data-span-parity-bool-dualbasis--false\" class=\"anchor\" aria-label=\"Permalink: Rs8.Encode(Span data, Span parity, bool dualBasis = false)\" href=\"#rs8encodespan-data-span-parity-bool-dualbasis--false\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003epublic static void Encode(Span\u0026lt;byte\u0026gt; data, Span\u0026lt;byte\u0026gt; parity, bool dualBasis = false)\u003c/code\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTakes a \u003ccode\u003eSpan\u0026lt;byte\u0026gt;\u003c/code\u003e \u003ccode\u003edata\u003c/code\u003e of length \u003ccode\u003eRs8.DataLength\u003c/code\u003e (223), and writes the parity of it into a \u003ccode\u003eSpan\u0026lt;byte\u0026gt;\u003c/code\u003e \u003ccode\u003eparity\u003c/code\u003e of length \u003ccode\u003eRs8.ParityLength\u003c/code\u003e (32).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eConventional form is used by default, but can be switched to dual-basis form by setting \u003ccode\u003edualBasis\u003c/code\u003e to \u003ccode\u003etrue\u003c/code\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eA common scenario is to create a single contiguous 255 byte block of memory, fill the first 223 bytes with data, and pass the whole thing to the first overload of the encode method:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"// Create a 255 byte block\nSpan\u0026lt;byte\u0026gt; block = (new byte[Rs8.BlockLength]).AsSpan();\n\n// or with C# 7.2\n// Span\u0026lt;byte\u0026gt; block = stackalloc byte[Rs8.BlockLength];\n\n// Fill the first 223 bytes of block with data\n// ...\n\n// Encode the block, filling the last 32 bytes with parity data\nRs8.Encode(block);\n\n// The block is now encoded.\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e// Create a 255 byte block\nSpan\u0026lt;byte\u0026gt; block = (new byte[Rs8.BlockLength]).AsSpan();\n\n// or with C# 7.2\n// Span\u0026lt;byte\u0026gt; block = stackalloc byte[Rs8.BlockLength];\n\n// Fill the first 223 bytes of block with data\n// ...\n\n// Encode the block, filling the last 32 bytes with parity data\nRs8.Encode(block);\n\n// The block is now encoded.\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDecode(Span block, Span erasurePositions, bool dualBasis = false)\u003c/h3\u003e\u003ca id=\"user-content-decodespan-block-span-erasurepositions-bool-dualbasis--false\" class=\"anchor\" aria-label=\"Permalink: Decode(Span block, Span erasurePositions, bool dualBasis = false)\" href=\"#decodespan-block-span-erasurepositions-bool-dualbasis--false\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003epublic static int Decode(Span\u0026lt;byte\u0026gt; block, Span\u0026lt;int\u0026gt; erasurePositions, bool dualBasis = false)\u003c/code\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTakes a \u003ccode\u003eSpan\u0026lt;byte\u0026gt;\u003c/code\u003e \u003ccode\u003eblock\u003c/code\u003e of length \u003ccode\u003eRs8.BlockLength\u003c/code\u003e (255), and corrects errors within the block, in place.\nAnother \u003ccode\u003eSpan\u0026lt;byte\u0026gt;\u003c/code\u003e \u003ccode\u003eerasurePositions\u003c/code\u003e may be given, to specify erasure indexes. Erasures are the indexes of known bad bytes within the block.\nSpecifying erasures can increase the number of recoverable errors from 16 to 32. It may be \u003ccode\u003eSpan\u0026lt;byte\u0026gt;.Empty\u003c/code\u003e if no erasures are known.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eConventional form is used by default, but can be switched to dual-basis by setting \u003ccode\u003edualBasis\u003c/code\u003e to \u003ccode\u003etrue\u003c/code\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIf correction was possible, the function returns the number of bytes that were corrected.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIf correction was not possible (because there were too many errors), the function returns -1.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ePerformance\u003c/h1\u003e\u003ca id=\"user-content-performance\" class=\"anchor\" aria-label=\"Permalink: Performance\" href=\"#performance\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis implementation differs from some others in that it \u003cstrong\u003eonly\u003c/strong\u003e supports the common RS (255, 223) CCSDS encoding.\nThis allows the use of precalculated lookup tables, as well as more tightly optimised code than the general case.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThis library also takes advantage of the new \u003ccode\u003eSpan\u0026lt;T\u0026gt;\u003c/code\u003e class introduced in dotnet Core 2.1,\nincluding the now safe \u003ccode\u003estackalloc\u003c/code\u003e method (C# 7.2/7.3) for allocating temporary arrays.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThis allows the \u003ccode\u003eEncode\u003c/code\u003e and \u003ccode\u003eDecode\u003c/code\u003e methods to be zero-allocating, and work entirely on the stack. GC pressure and the associated performance impacts of collection are therefore eliminated.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBenchmarks on an Intel(R) Core(TM) i7-8650U CPU (@ ~3GHz):\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eEncode: ~29,000 blocks per second = ~52 Mbps data throughput\u003c/li\u003e\n\u003cli\u003eDecode: ~13,000 blocks per second = ~23 Mbps data throughput\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eCLI Tool:\u003c/h1\u003e\u003ca id=\"user-content-cli-tool\" class=\"anchor\" aria-label=\"Permalink: CLI Tool:\" href=\"#cli-tool\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eA CLI tool is provided for basic command line encoding and decoding.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage\u003c/h3\u003e\u003ca id=\"user-content-usage\" class=\"anchor\" aria-label=\"Permalink: Usage\" href=\"#usage\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e-e : Encode mode. 223 bytes will be read from input, encoded, and then written to the output.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e-d : Decode mode. 255 bytes will be read from input, decoded, and then written to output. Some additional information will be written to standard error regarding errors corrected.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e-v : Enable verbose output. All log output is written to standard error.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e-t : Enable text mode for input and output. In this mode, input should be formatted as hexedecimal ASCII (each byte is two characters 0-9,a-f,A-F). All non-alphanumeric characters will be ignored on input. Output is formatted the same, with newlines after every 16 bytes.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e-b : Enable binary mode for input and output (default). In this mode, input and output will be read as raw bytes with no conversion performed.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e-x : Enable dual-basis representation for parity.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e-c : Enable conventional representation for parity (default)\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e-i : Read from a file specifid by path instead of standard input. '-' may be given as the path to read from standard input anyway.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e-o : Write to a file specified by path instead of standard output. '-' may be given as the path to write to standard output anyway.\u003c/p\u003e\n\u003c/article\u003e","loaded":true,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":[{"level":1,"text":"Reed-Solomon","anchor":"reed-solomon","htmlText":"Reed-Solomon"},{"level":1,"text":"Overview","anchor":"overview","htmlText":"Overview"},{"level":1,"text":"Attribution","anchor":"attribution","htmlText":"Attribution"},{"level":1,"text":"Methods","anchor":"methods","htmlText":"Methods"},{"level":3,"text":"Rs8.Encode(Span block, bool dualBasis = false)","anchor":"rs8encodespan-block-bool-dualbasis--false","htmlText":"Rs8.Encode(Span block, bool dualBasis = false)"},{"level":3,"text":"Rs8.Encode(Span data, Span parity, bool dualBasis = false)","anchor":"rs8encodespan-data-span-parity-bool-dualbasis--false","htmlText":"Rs8.Encode(Span data, Span parity, bool dualBasis = false)"},{"level":3,"text":"Decode(Span block, Span erasurePositions, bool dualBasis = 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1 0 1 1-2 0 1 1 0 0 1 2 0ZM2 4a1 1 0 1 1 0-2 1 1 0 0 1 0 2Z"></path></svg></button></div><div class="Box-sc-g0xbh4-0 QkQOb js-snippet-clipboard-copy-unpositioned undefined" data-hpc="true"><article class="markdown-body entry-content container-lg" itemprop="text"><div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Reed-Solomon</h1><a id="user-content-reed-solomon" class="anchor" aria-label="Permalink: Reed-Solomon" href="#reed-solomon"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Reed Solomon (255, 223) CCSDS in C#.</p> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Overview</h1><a id="user-content-overview" class="anchor" aria-label="Permalink: Overview" href="#overview"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This is an implementation of an RS (255, 223) encoder and decoder.</p> <p dir="auto">The encoder is capable of encoding 223 bytes of data to produce 32 bytes of parity. When the parity is concatenated with the data, it forms a 255 bytes long encoded block.</p> <p dir="auto">The decoder is capable of decoding a block to correct up to 16 errors of unknown position, at any position within the 255 byte block. If the error locations are known, the indexes of the bad bytes can be specified as erasures, allowing up to 32 bytes to be corrected within the 255 byte block.</p> <p dir="auto">The encoder and decoder use the RS (255,223) code with 8-bit symbols as specified by the CCSDS. Specifically, they use a field generator polynomial of 1 + X + X^2 + X^7 + X^8, and a code generator with first consecutive root = 112 and a primitive element of 11.</p> <p dir="auto">The conventional polynomial form is used by default. If required, the the strict CCSDS dual-basis polynomial form can be enabled with the <code>dualBasis</code> parameter.</p> <p dir="auto">A summary of the CCSDS standard <a href="https://public.ccsds.org/pubs/130x1g2.pdf" rel="nofollow">can be found at their website.</a> (Page 5-1) In depth reference <a href="https://public.ccsds.org/Pubs/131x0b3e1.pdf" rel="nofollow">is also available</a> (Page 4-1)</p> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Attribution</h1><a id="user-content-attribution" class="anchor" aria-label="Permalink: Attribution" href="#attribution"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The Reed-Solomon encoder and decoder, found in <code>/ReedSolomon/Rs8.cs</code>, is derived from code from "General purpose Reed-Solomon decoder for 8-bit symbols or less", Copyright 2003 Phil Karn, KA9Q.</p> <p dir="auto">It is used under the terms of the GNU Lesser General Public License (LGPL). See the file "LICENSE" in this package for license details.</p> <p dir="auto">The version used for this derivation can be found <a href="http://www.ka9q.net/code/fec/fec-3.0.1.tar.bz2" rel="nofollow">here</a>.</p> <p dir="auto">The latest version of the original source code can be found <a href="http://www.ka9q.net/code/fec/" rel="nofollow">here</a>.</p> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Methods</h1><a id="user-content-methods" class="anchor" aria-label="Permalink: Methods" href="#methods"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Rs8.Encode(Span block, bool dualBasis = false)</h3><a id="user-content-rs8encodespan-block-bool-dualbasis--false" class="anchor" aria-label="Permalink: Rs8.Encode(Span block, bool dualBasis = false)" href="#rs8encodespan-block-bool-dualbasis--false"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><code>public static void Encode(Span<byte> block, bool dualBasis = false)</code></p> <p dir="auto">Takes a <code>Span<byte></code> <code>block</code> of length <code>Rs8.BlockLength</code> (255), of which the first 223 bytes are data, and the last 32 bytes are space for parity. Parity is calculated for data, and then written to the last 32 bytes of the block.</p> <p dir="auto">This overload is the equivalent of calling:</p> <p dir="auto"><code>Encode(block.Slice(0, Rs8.DataLength), block.Slice(Rs8.DataLength, Rs8.ParityLength), dualBasis);</code></p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Rs8.Encode(Span data, Span parity, bool dualBasis = false)</h3><a id="user-content-rs8encodespan-data-span-parity-bool-dualbasis--false" class="anchor" aria-label="Permalink: Rs8.Encode(Span data, Span parity, bool dualBasis = false)" href="#rs8encodespan-data-span-parity-bool-dualbasis--false"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><code>public static void Encode(Span<byte> data, Span<byte> parity, bool dualBasis = false)</code></p> <p dir="auto">Takes a <code>Span<byte></code> <code>data</code> of length <code>Rs8.DataLength</code> (223), and writes the parity of it into a <code>Span<byte></code> <code>parity</code> of length <code>Rs8.ParityLength</code> (32).</p> <p dir="auto">Conventional form is used by default, but can be switched to dual-basis form by setting <code>dualBasis</code> to <code>true</code>.</p> <p dir="auto">A common scenario is to create a single contiguous 255 byte block of memory, fill the first 223 bytes with data, and pass the whole thing to the first overload of the encode method:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="// Create a 255 byte block Span<byte> block = (new byte[Rs8.BlockLength]).AsSpan(); // or with C# 7.2 // Span<byte> block = stackalloc byte[Rs8.BlockLength]; // Fill the first 223 bytes of block with data // ... // Encode the block, filling the last 32 bytes with parity data Rs8.Encode(block); // The block is now encoded."><pre class="notranslate"><code>// Create a 255 byte block Span<byte> block = (new byte[Rs8.BlockLength]).AsSpan(); // or with C# 7.2 // Span<byte> block = stackalloc byte[Rs8.BlockLength]; // Fill the first 223 bytes of block with data // ... // Encode the block, filling the last 32 bytes with parity data Rs8.Encode(block); // The block is now encoded. </code></pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Decode(Span block, Span erasurePositions, bool dualBasis = false)</h3><a id="user-content-decodespan-block-span-erasurepositions-bool-dualbasis--false" class="anchor" aria-label="Permalink: Decode(Span block, Span erasurePositions, bool dualBasis = false)" href="#decodespan-block-span-erasurepositions-bool-dualbasis--false"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><code>public static int Decode(Span<byte> block, Span<int> erasurePositions, bool dualBasis = false)</code></p> <p dir="auto">Takes a <code>Span<byte></code> <code>block</code> of length <code>Rs8.BlockLength</code> (255), and corrects errors within the block, in place. Another <code>Span<byte></code> <code>erasurePositions</code> may be given, to specify erasure indexes. Erasures are the indexes of known bad bytes within the block. Specifying erasures can increase the number of recoverable errors from 16 to 32. It may be <code>Span<byte>.Empty</code> if no erasures are known.</p> <p dir="auto">Conventional form is used by default, but can be switched to dual-basis by setting <code>dualBasis</code> to <code>true</code>.</p> <p dir="auto">If correction was possible, the function returns the number of bytes that were corrected.</p> <p dir="auto">If correction was not possible (because there were too many errors), the function returns -1.</p> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Performance</h1><a id="user-content-performance" class="anchor" aria-label="Permalink: Performance" href="#performance"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This implementation differs from some others in that it <strong>only</strong> supports the common RS (255, 223) CCSDS encoding. This allows the use of precalculated lookup tables, as well as more tightly optimised code than the general case.</p> <p dir="auto">This library also takes advantage of the new <code>Span<T></code> class introduced in dotnet Core 2.1, including the now safe <code>stackalloc</code> method (C# 7.2/7.3) for allocating temporary arrays.</p> <p dir="auto">This allows the <code>Encode</code> and <code>Decode</code> methods to be zero-allocating, and work entirely on the stack. GC pressure and the associated performance impacts of collection are therefore eliminated.</p> <p dir="auto">Benchmarks on an Intel(R) Core(TM) i7-8650U CPU (@ ~3GHz):</p> <ul dir="auto"> <li>Encode: ~29,000 blocks per second = ~52 Mbps data throughput</li> <li>Decode: ~13,000 blocks per second = ~23 Mbps data throughput</li> </ul> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">CLI Tool:</h1><a id="user-content-cli-tool" class="anchor" aria-label="Permalink: CLI Tool:" href="#cli-tool"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">A CLI tool is provided for basic command line encoding and decoding.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Usage</h3><a id="user-content-usage" class="anchor" aria-label="Permalink: Usage" href="#usage"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">-e : Encode mode. 223 bytes will be read from input, encoded, and then written to the output.</p> <p dir="auto">-d : Decode mode. 255 bytes will be read from input, decoded, and then written to output. Some additional information will be written to standard error regarding errors corrected.</p> <p dir="auto">-v : Enable verbose output. All log output is written to standard error.</p> <p dir="auto">-t : Enable text mode for input and output. In this mode, input should be formatted as hexedecimal ASCII (each byte is two characters 0-9,a-f,A-F). All non-alphanumeric characters will be ignored on input. Output is formatted the same, with newlines after every 16 bytes.</p> <p dir="auto">-b : Enable binary mode for input and output (default). In this mode, input and output will be read as raw bytes with no conversion performed.</p> <p dir="auto">-x : Enable dual-basis representation for parity.</p> <p dir="auto">-c : Enable conventional representation for parity (default)</p> <p dir="auto">-i : Read from a file specifid by path instead of standard input. '-' may be given as the path to read from standard input anyway.</p> <p dir="auto">-o : Write to a file specified by path instead of standard output. '-' may be given as the path to write to standard output anyway.</p> </article></div></div></div></div></div> <!-- --> <!-- --> <script type="application/json" id="__PRIMER_DATA_:R0:__">{"resolvedServerColorMode":"day"}</script></div> </react-partial> <input type="hidden" data-csrf="true" value="xZAna3ESsdZOrBfHUXCa/wT+0Xt7jiYFdUhUGQhq6bVdFCzQ/qBqzhvLr7MQ3G4Bm665aniQwVPSCsYxfDBong==" /> </div> <div data-view-component="true" class="Layout-sidebar"> <div class="BorderGrid about-margin" data-pjax> <div class="BorderGrid-row"> <div class="BorderGrid-cell"> <div class="hide-sm hide-md"> <h2 class="mb-3 h4">About</h2> <p class="f4 my-3"> Reed Solomon (255, 223) CCSDS in C#. </p> <h3 class="sr-only">Resources</h3> <div class="mt-2"> <a class="Link--muted" data-analytics-event="{"category":"Repository Overview","action":"click","label":"location:sidebar;file:readme"}" href="#readme-ov-file"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" 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