[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81580-en":3,"doc-seo-81580-105":30,"detail-sidebar-cat-0-en-105":92},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81580,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","On the Suboptimality of Linear Codes for Binary Distributed Hypothesis Testing","Binary distributed hypothesis testing studies how two agents, observing correlated binary vectors, compress information at the same rate and send it to a central decision maker. The work analyzes linear compression schemes and proves truncation is optimal for opposite-sign correlations with equal magnitudes and for testing independence. It further conjectures truncation remains optimal for any opposite-sign correlations, and computes classical random-coding exponents showing truncation—and thus any linear code—is strictly suboptimal when testing against independence.","arXiv :2601 . 10526v2 [ cs .IT] 9 Jul 2026  \nOn the Suboptimality of Linear Codes for Binary Distributed  \nHypothesis Testing  \nAdway Girish, Robinson D. H. Cung, Emre Telatar  \nSchool of Computer and Communication Sciences, EPFL  \n{adway.girish,robinson.cung,[emre.telatar}@epfl.ch](emre.telatar}@epfl.ch)  \nJuly 13, 2026  \nAbstract  \nWe study a binary distributed hypothesis testing problem where two agents observe correlated binary vectors and communicate compressed information at the same rate to a central decision maker. In particular, we study linear compression schemes and show that simple truncation is the best linear scheme in two cases: (1) testing opposite signs of the same magnitude of correlation, and (2) testing for or against independence. We conjecture, supported by numerical evidence, that truncation is the best linear code for testing any correlations of opposite signs. Further, for testing against independence, we also compute classical random coding exponentsand show that truncation, and consequently any linear code, is strictly suboptimal.  \n1 Introduction  \nConsider the following distributed hypothesis testing (DHT) setup with two sensors and a central decision maker. Under hypothesis H = i ∈ {0, 1}, the pair of random variables (X, Y ) has joint distribution PiXY . The two sensors observe n independent copies of X and Y respectively and send a compressed version of these observations to the central decision maker, who then declares ˆH = 0 or 1 according to some decision rule, as shown in Fig. 1. More precisely, under hypothesis H = i, with (Xℓ, Yℓ) , ℓ = 1 , . . . , n drawn i.i.d. from distribution PiXY, agent A observes Xn and agent Bobserves Yn. These agents compress Xn and Yn using encoding functions g and h respectively, and send g(Xn ) and h (Yn ) to the central decision maker C, who then declares ˆH .  \nThis is an instance of the more general problem of statistical inference under communication constraints, first studied by Berger [Ber79], see the classical survey by Han and Amari [HA98] for an extensive overview of the early results and techniques. The DHT problem has received renewed interest in recent years owing to such distributed setups arising, for example, in modern remote sensor networks, where raw data cannot be centrally aggregated due to communication, latency, or privacy limitations [OX09 ; TD25] . Several variants of the above problem have been studied, such as allowing multiple rounds of interaction [XK12], making decisions at multiple centers [EWZ20], adding an explicit privacy metric [LSCT17], over noisy channels [SG20], and so on. For the setup in Fig. 1 , most choices of g and h proposed in the literature are based on typicality-based quantization and binning arguments, as in Ahlswede–Csiszár [AC86], Han [Han87], Shimokawa–Han–Amari [SHA94], Kochman–Wang [KW25], and Watanabe [Wat22], but the optimal choice remains unknown.  \nIn this paper, we take X and Y to be binary random variables uniformly distributed on {0, 1} , with the hypothesis determining the correlation between X and Y. Explicitly, we have Y = X ⊕ Z , where Z ∼ Bernoulli(pi) is independent of X (and also Y ) under hypothesis H = i. This is exactly  \nXn  \nYn  \nˆH  \nFigure 1: Distributed hypothesis testing setup considered. The communication from A and B to Cis constrained. We take (Xn , Yn ) ∼ DSBS(pi)⊗n under hypothesis H = i ∈ {0, 1} and study the performance of linear g, h.  \nthe setup considered by Haim and Kochman [HK16; HK18], except that they restrict themselves to the case with p0 ≤ p 1 ≤ ~~1~~2 (i.e. , X and Y are positively correlated under both hypotheses) . They show, inspired by the Körner–Marton scheme [KM79] for distributed computation, that linear codes can be used to obtain performance comparable to the unconstrained/co-located problem (where there is no compression), even obtaining a better Stein exponent than with classical typicalitybased random quantization schemes [AC86 ; Han87] . Linear codes are al","cbCaimw8nzHPPr3i","https://ap.wps.com/l/cbCaimw8nzHPPr3i","pdf",1047203,5,1,11,"English","en",105,"# Introduction\n## Distributed hypothesis testing setup\n## Linear compression and main claims\n# Preliminaries and Problem Setup\n## General one-shot setup","[{\"question\":\"What problem does the paper study in distributed hypothesis testing?\",\"answer\":\"It studies a binary distributed hypothesis testing setting where two agents observe correlated binary vectors and communicate compressed information to a central decision maker under communication-rate constraints.\"},{\"question\":\"In which cases is truncation the best linear compression scheme?\",\"answer\":\"Truncation is shown to be optimal for testing opposite signs of the same magnitude of correlation and for testing for or against independence.\"},{\"question\":\"Why are linear codes strictly suboptimal for testing against independence?\",\"answer\":\"Classical random-coding exponents are computed, and truncation is found to be strictly suboptimal; since truncation is a special linear choice, any linear code inherits this suboptimality.\"}]",1784174467,28,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"on-the-suboptimality-of-linear-codes-for-binary-distributed-hypothesis-testing","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"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/on-the-suboptimality-of-linear-codes-for-binary-distributed-hypothesis-testing/81580/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the paper study in distributed hypothesis testing?","Question",{"text":76,"@type":77},"It studies a binary distributed hypothesis testing setting where two agents observe correlated binary vectors and communicate compressed information to a central decision maker under communication-rate constraints.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"In which cases is truncation the best linear compression scheme?",{"text":81,"@type":77},"Truncation is shown to be optimal for testing opposite signs of the same magnitude of correlation and for testing for or against independence.",{"name":83,"@type":74,"acceptedAnswer":84},"Why are linear codes strictly suboptimal for testing against independence?",{"text":85,"@type":77},"Classical random-coding exponents are computed, and truncation is found to be strictly suboptimal; since truncation is a special linear choice, any linear code inherits this suboptimality.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":20,"slug":138},19,"General","general"]