[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-228137-en":3,"doc-seo-228137-105":30,"detail-sidebar-cat-0-en-105":97},{"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":27,"seo_description":14,"update_tm":28,"read_time":29},228137,1236954509970,"Mack Lee","https://us-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",8,"Research & Report","Semi-Quantitative Group Testing - Research - capacity and code construction","Semi-quantitative group testing (SQGT) introduces a non-binary pooling framework motivated by limits of precision in tasks such as genome sequence processing. SQGT is modeled as an adder followed by quantization, enabling information-theoretic evaluation via the defined capacity. The work develops SQ-disjunct codes tailored to SQGT and provides both explicit and probabilistic code constructions. Simple decoding algorithms are provided for these codes, supporting practical testing under constrained experimental conditions.","Semi-Quantitative Group Testing  \nAmin Emad and Olgica Milenkovic  \nUniversity of Illinois, Urbana-Champaign, ILE-mail: {emad2,[milenkov}@illinois.edu](milenkov}@illinois.edu)  \narXiv : 1202 .2887v2 [ cs .IT] 20 May 2012  \nAbstract—We consider a novel group testing procedure, termed semi-quantitative group testing, motivated by a class of problems arising in genome sequence processing. Semi-quantitative group testing (SQGT) is a non-binary pooling scheme that may be viewed as a combination of an adder model followed by aquantizer. For the new testing scheme we define the capacity and evaluate the capacity for some special choices of parameters using information theoretic methods. We also define a new class of disjunct codes suitable for SQGT, termed SQ-disjunct codes. We also provide both explicit and probabilistic code construction methods for SQGT with simple decoding algorithms.  \nI. INTRODUCTION  \nGroup testing (GT) is a pooling scheme for identifying a number of subjects with some particular characteristic – called“positives” – among a large pool of subjects. The idea behind GT is that if the number of positives is much smaller than the number of subjects, one can reduce the number of experiments by testing adequately chosen groups of subjects rather than testing each subject individually. In its full generality, GT maybe viewed as the problem of inferring the state of a system from a superposition of the state vectors of a subset of the system's elements. As such, it has found many applications in communication theory, signal processing, computer science, mathematics, biology, etc. (for example see [1]-[3]) .  \nAlthough many models have been considered for combinatorial GT, two main models include the original model considered by Dorfman [4] (henceforth, conventional GT) and the adder model (also known as the adder channel or quantitative GT) [1] . In the former case, the result of a test isan indicator determining if there exist at least one positive in the test (equal to 0 if no positive in the test, and 1 otherwise), while in the latter case, the result of a test specifies the exact number of positives in that test. Motivated by applications in genome sequence processing, we propose a novel non-adaptive test model termed semi-quantitative group testing (SQGT) . This model accounts for the fact that in most applications a test is not precise enough to exactly determine the number of positives, but it is more informative than a simple indicator of the presence of at least one positive. In other words, schemesin which results are obtained using a test device with limited precision may be modeled as instances of SQGT 1.  \nWe also allow for the possibility of having different amounts of sample material for different test subjects, which results in non-binary test matrices. Although binary testing is required for some applications – such as coin weighing – in other  \n1 One may view the SQGT scheme as a generalization of thresholded group testing to multiple thresholds and zero gaps [5] .  \napplications, such as conflict resolution in multiple access channel (MAC) and genotyping, non-binary tests may be used to further reduce the number of tests. In the former example, different non-binary values in a test correspond to different power levels of the users, while in the latter example, they correspond to different amounts of genetic material of different subjects. The reason that non-binary tests are extremely important is that in applications like genotyping, tests are very expensive so that one may be inclined to reduce the number of tests at the expense of extracting more genetic material. While there exists information theoretic analysis that is applicable to the non-binary test matrices [10, Ch. 6], to the best of the authors' knowledge, the only attempts of nonbinary code construction relevant to group testing is limited toa handful of papers, including [6] and [7], where constructions are considered for an adder MAC channe","cbCainWdrdzgMLY9","https://ap.wps.com/l/cbCainWdrdzgMLY9","pdf",391612,1,5,"English","en",105,"# Introduction\n# Semi-Quantitative Group Testing\n## Notation and problem setup\n# Capacity of SQGT\n# SQ-Disjunct codes\n## Properties\n# Constructions for SQGT codes\n## Explicit and probabilistic methods","[{\"question\":\"What is semi-quantitative group testing (SQGT)?\",\"answer\":\"SQGT is a non-binary group testing model where test outcomes capture more than a simple yes/no indicator. It is motivated by situations where the experiment provides limited-precision quantitative information.\"},{\"question\":\"How is capacity defined and evaluated in this work?\",\"answer\":\"The paper defines the concept of capacity for SQGT and evaluates it for special parameter choices using information-theoretic methods.\"},{\"question\":\"What are SQ-disjunct codes and how are they used?\",\"answer\":\"SQ-disjunct codes are a new generalized family of disjunct codes designed for SQGT. They can be decoded using a simple, low-complexity algorithm, and the paper supplies code construction methods.\"}]","Semi-Quantitative Group Testing - Research - capacity and code construction | PDF",1789021473,13,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":92,"head_meta":94,"extra_data":96,"updated_unix":28},"semi-quantitative-group-testing-research-capacity-and-code-construction","",{"@graph":36,"@context":91},[37,54,74],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/semi-quantitative-group-testing-research-capacity-and-code-construction/228137/",4,{"url":52,"name":13,"@type":55,"image":56,"author":61,"headline":13,"publisher":63,"fileFormat":66,"inLanguage":23,"description":14,"dateModified":67,"datePublished":68,"encodingFormat":66,"isAccessibleForFree":69,"interactionStatistic":70},"DigitalDocument",{"url":57,"@type":58,"width":59,"height":60},"https://docshare.wps.com/thumbnails/semi-quantitative-group-testing-research-capacity-and-code-construction/228137.png","ImageObject",300,407,{"name":9,"@type":62},"Person",{"url":41,"name":64,"@type":65},"DocShare","Organization","application/pdf","2026-09-12","2026-09-10",true,{"@type":71,"interactionType":72,"userInteractionCount":20},"InteractionCounter",{"@type":73},"ViewAction",{"@type":75,"mainEntity":76},"FAQPage",[77,83,87],{"name":78,"@type":79,"acceptedAnswer":80},"What is semi-quantitative group testing (SQGT)?","Question",{"text":81,"@type":82},"SQGT is a non-binary group testing model where test outcomes capture more than a simple yes/no indicator. It is motivated by situations where the experiment provides limited-precision quantitative information.","Answer",{"name":84,"@type":79,"acceptedAnswer":85},"How is capacity defined and evaluated in this work?",{"text":86,"@type":82},"The paper defines the concept of capacity for SQGT and evaluates it for special parameter choices using information-theoretic methods.",{"name":88,"@type":79,"acceptedAnswer":89},"What are SQ-disjunct codes and how are they used?",{"text":90,"@type":82},"SQ-disjunct codes are a new generalized family of disjunct codes designed for SQGT. They can be decoded using a simple, low-complexity algorithm, and the paper supplies code construction methods.","https://schema.org",{"og:url":52,"og:type":93,"og:title":13,"og:site_name":64,"og:description":14},"article",{"robots":95,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":98},[99,103,107,111,115,120,125,128,133,136,140],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":100,"show_sort_weight":101,"slug":102},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},"Exam",70,"exam",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},"Comic",60,"comic",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},6,"Technology",50,"technology",{"id":121,"doc_module":4,"doc_module_name":46,"category_name":122,"show_sort_weight":123,"slug":124},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":126,"slug":127},30,"research-report",{"id":129,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":131,"slug":132},9,"Religion & Spirituality",20,"religion-spirituality",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":131,"slug":135},"World Cup","world-cup",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":137,"slug":139},10,"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":46,"category_name":142,"show_sort_weight":21,"slug":143},19,"General","general"]