[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81564-en":3,"doc-seo-81564-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"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},81564,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Compression with Privacy-Preserving Random Access","Lossless compression for an i.i.d. binary source is achieved at any rate above entropy while guaranteeing strong privacy for random access decoding: decoding any symbol Xi reveals no information about the remaining symbols Xj (j≠i). The study frames the task as a marginal consistency problem induced by simultaneous privacy and reliability constraints. A geometric technique based on representing codeword distribution constraints proves the existence of suitable schemes, extending beyond earlier conference results.","arXiv :2511 . 14524v2 [ cs .IT] 10 Jul 2026  \nCompression with Privacy-Preserving Random Access  \nVenkat Chandar, Aslan Tchamkerten, Shashank Vatedka  \nAbstract  \nWe show that an i.i.d. binary source sequence X1 , . . . , Xn can be losslessly compressed at any rate above entropy while ensuring that the decoding of any Xi reveals no information about the remaining symbols tXj : j ‰ iu.  \nThis problem reduces to a marginal consistency problem induced by the simultaneous privacy and reliability constraints. To address it, we develop a technique based on a geometric representation of codeword distributions, which may be of independent interest.  \nI. INTRODUCTION  \nSeveral recent works have studied compression with locality properties [1]–[11], focusing on encoding and decoding primitives, and on algorithms and information-theoretic limits that characterize the minimum number of bits that must be accessed or updated to locally decode or modify a source symbol.  \nIn [12], we introduced the problem of compression with private local decoding (also referred to as privacypreserving random access): can a binary source sequence  \nX “ pX1 ,..., Xn q (1)  \nbe losslessly compressed into a binary codeword C1 , C2 ,..., CnR such that the local decoding of any Xi depends only on a subset of codeword symbols CIi d tCj : j P Ii u, for some Ii Ď rnRs, and reveals no information about the remaining source symbols tXj : j ‰ iu?  \nTo ensure reliability, the codeword bits CIi accessed by local decoder i must enable a reliable distinction between the hypotheses Xi “ 0 and Xi “ 1. To ensure privacy, these accessed bits must be independent of all other source symbols tXj : j ‰ iu. The challenge stems from compression; some subsets CIi must overlap which potentially compromises local privacy.  \nSomewhat counterintuitively, we showed that for an i.i.d. Bernoullippq source, such a scheme exists and achievesa nontrivial compression rate  \nR “ cp log2´ ~~1~~p¯ , (2)  \nV. Chandar is with DE Shaw, New York, USA. A. Tchamkerten is with the Institut Polytechnique de Paris, Palaiseau, France. S. Vatedka is with the Indian Institute of Technology Hyderabad, Sangareddy, Telangana, India.  \nThis work was presented in part at the 2024 IEEE International Symposium on Information Theory, Athens, Greece.  \nThe work of Shashank Vatedka was supported by a Core Research Grant CRG/2022/004464 from SERB, India.  \nJuly 13, 2026 DRAFT  \nfor a universal constant c ą 0 and sufficiently small p (all logarithms are base two) . However, it remained unclear whether the gap to the entropy  \nHppq d ´plogp ´ p1 ´ pq logp1 ´ pq (3)  \nis intrinsic to the privacy constraint. In particular, the scheme exhibits a multiplicative gap of order logp1{pq in the small-p regime.  \nIn this paper, we show that for any i.i.d. Bernoulli source, private local decoding does not limit compression; there exist schemes that achieve private local decoding at any rate above entropy. The present paper provides the full version of the conference paper [13] which only sketched parts of the proofs of some of the results.  \nMost recently, [14] proposed a conceptually simple, low-complexity scheme that achieves entropy with private local decoding for any i.i.d. source, not necessarily binary. We briefly review this scheme and then highlight the differences with the one proposed in this paper.  \nGiven a source sequence X , we first draw a uniformly random permutation σ over rns and form the permuted sequence ˜X defined by ˜Xσpiq “ Xi for every i P rns. The encoder then outputs  \n`compp˜Xq,σp1q,σp2q,...,σpnq ˘,  \nwhere compp¨q denotes any lossless, entropy-achieving compression map.  \nTo recover Xi , the ith local decoder is given  \nCIi d `compp˜Xq,σpiq ˘ .  \nIt first reconstructs ˜X from compp˜Xq, then declares ˜Xσpiq.  \nAs stated, the scheme does not fully guarantee privacy since ˜X reveals the empirical type of X . This can be remedied by appending to X a fixed-length suffix of negligible size so as to obtain an e","cbCaiaTGyNOFEjf5","https://ap.wps.com/l/cbCaiaTGyNOFEjf5","pdf",572565,1,35,"English","en",105,"# Abstract\n# Introduction\n# Related Works","[{\"question\":\"What does the paper guarantee when locally decoding a symbol Xi?\",\"answer\":\"For any i, the local decoder recovers Xi reliably, and the revealed accessed information contains no information about the other source symbols Xj for j≠i.\"},{\"question\":\"How is the problem reformulated to handle both privacy and reliability constraints?\",\"answer\":\"It is reduced to a marginal consistency problem induced by the simultaneous privacy and reliability requirements for the codeword subsets accessed by each local decoder.\"},{\"question\":\"What is the main technical method used in the paper?\",\"answer\":\"The paper develops a geometric representation approach for codeword distributions (via a marginal polytope) to prove existence 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