FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313203163> ?p ?o ?g. }

• W4313203163 abstract "Guruswami and Smith (J. ACM 2016) considered codes for channels that are poly-size circuits which modify at most a p-fraction of the bits of the codeword. This class of channels is significantly stronger than Shannon’s binary symmetric channel (BSC), but weaker than Hamming’s channels which are computationally unbounded. Guruswami and Smith gave an explicit Monte-Carlo construction of codes with optimal rate of R(p) = 1 − H(p) that achieve list-decoding in this scenario. Here, “explicit Monte-Carlo” means that both encoding and decoding algorithms run in polynomial time. However, the encoding and decoding algorithms also receive a uniformly chosen string of polynomial length (which is chosen and published, once and for all, in a pre-processing stage) and their correctness is guaranteed w.h.p. over this random choice. Guruswami and Smith asked whether it is possible to obtain uniquely decodable codes for poly-size channels with rate that beats the Gilbert-Varshamov bound $R^{GV}(p)=1-H(2p)$. We give an affirmative answer, Specifically:•For every $0leq pltfrac{1}{4}$, we give an explicit Monte-Carlo construction of uniquely-decodable codes with optimal rate R(p) = 1 − H(p). This matches the rate achieved by Guruswami and Smith for the easier task of list-decoding, and also matches the capacity of binary symmetric channels. Moreover, this rate is strictly larger than that of codes for the standard coding scenario (namely, uniquely-decodable codes for Hamming channels).•Even ignoring explicitness, our result implies a characterization of the capacity of poly-size channels, which was not previously understood.Our technique builds on the earlier list-decodable codes of Guruswami and Smith, achieving unique-decoding by extending and modifying the construction so that we can identify the correct message in the list. For this purpose we use ideas from coding theory and pseudorandomness, specifically:•We construct codes for binary symmetric channels that beat the Gilbert-Varshamov bound, and are “evasive” in the sense that a poly-size circuit that receives a random (or actually pseudorandom) string, cannot find a codeword within relative distance 2p. This notion of evasiveness is inspired by the recent work of Shaltiel and Silbak (STOC 2021) on codes for space bounded channels.•We develop a methodology (that is inspired by proofs of t-wise independent tail inequalities, and may be of independent interest) to analyze random codes, in scenarios where the success of the channel is measured in an additional random experiment (as in the evasiveness experiment above).•We introduce a new notion of “small-set non-malleable codes” that is tailored for our application, and may be of independent interest." @default.
• W4313203163 created "2023-01-06" @default.
• W4313203163 creator A5062263696 @default.
• W4313203163 creator A5086894856 @default.
• W4313203163 date "2022-10-01" @default.
• W4313203163 modified "2023-09-26" @default.
• W4313203163 title "Error Correcting Codes that Achieve BSC Capacity Against Channels that are Poly-Size Circuits" @default.
• W4313203163 cites W2021736779 @default.
• W4313203163 cites W2109084006 @default.
• W4313203163 cites W2143299189 @default.
• W4313203163 cites W2164908759 @default.
• W4313203163 cites W2569930253 @default.
• W4313203163 cites W2625364733 @default.
• W4313203163 cites W2903482297 @default.
• W4313203163 cites W2963279554 @default.
• W4313203163 cites W2963628132 @default.
• W4313203163 cites W3105388109 @default.
• W4313203163 cites W3122736160 @default.
• W4313203163 cites W3166668984 @default.
• W4313203163 cites W3171131516 @default.
• W4313203163 cites W3193074191 @default.
• W4313203163 cites W4312790435 @default.
• W4313203163 cites W4313203163 @default.
• W4313203163 doi "https://doi.org/10.1109/focs54457.2022.00009" @default.
• W4313203163 hasPublicationYear "2022" @default.
• W4313203163 type Work @default.
• W4313203163 citedByCount "2" @default.
• W4313203163 countsByYear W43132031632022 @default.
• W4313203163 countsByYear W43132031632023 @default.
• W4313203163 crossrefType "proceedings-article" @default.
• W4313203163 hasAuthorship W4313203163A5062263696 @default.
• W4313203163 hasAuthorship W4313203163A5086894856 @default.
• W4313203163 hasConcept C105795698 @default.
• W4313203163 hasConcept C11413529 @default.
• W4313203163 hasConcept C114614502 @default.
• W4313203163 hasConcept C118615104 @default.
• W4313203163 hasConcept C157125643 @default.
• W4313203163 hasConcept C166530166 @default.
• W4313203163 hasConcept C173988684 @default.
• W4313203163 hasConcept C193319292 @default.
• W4313203163 hasConcept C193969084 @default.
• W4313203163 hasConcept C19499675 @default.
• W4313203163 hasConcept C204397858 @default.
• W4313203163 hasConcept C33923547 @default.
• W4313203163 hasConcept C48372109 @default.
• W4313203163 hasConcept C55439883 @default.
• W4313203163 hasConcept C57273362 @default.
• W4313203163 hasConcept C67692717 @default.
• W4313203163 hasConcept C73150493 @default.
• W4313203163 hasConcept C78944582 @default.
• W4313203163 hasConcept C94375191 @default.
• W4313203163 hasConceptScore W4313203163C105795698 @default.
• W4313203163 hasConceptScore W4313203163C11413529 @default.
• W4313203163 hasConceptScore W4313203163C114614502 @default.
• W4313203163 hasConceptScore W4313203163C118615104 @default.
• W4313203163 hasConceptScore W4313203163C157125643 @default.
• W4313203163 hasConceptScore W4313203163C166530166 @default.
• W4313203163 hasConceptScore W4313203163C173988684 @default.
• W4313203163 hasConceptScore W4313203163C193319292 @default.
• W4313203163 hasConceptScore W4313203163C193969084 @default.
• W4313203163 hasConceptScore W4313203163C19499675 @default.
• W4313203163 hasConceptScore W4313203163C204397858 @default.
• W4313203163 hasConceptScore W4313203163C33923547 @default.
• W4313203163 hasConceptScore W4313203163C48372109 @default.
• W4313203163 hasConceptScore W4313203163C55439883 @default.
• W4313203163 hasConceptScore W4313203163C57273362 @default.
• W4313203163 hasConceptScore W4313203163C67692717 @default.
• W4313203163 hasConceptScore W4313203163C73150493 @default.
• W4313203163 hasConceptScore W4313203163C78944582 @default.
• W4313203163 hasConceptScore W4313203163C94375191 @default.
• W4313203163 hasLocation W43132031631 @default.
• W4313203163 hasOpenAccess W4313203163 @default.
• W4313203163 hasPrimaryLocation W43132031631 @default.
• W4313203163 hasRelatedWork W1985422039 @default.
• W4313203163 hasRelatedWork W2031570691 @default.
• W4313203163 hasRelatedWork W2085730761 @default.
• W4313203163 hasRelatedWork W2125294893 @default.
• W4313203163 hasRelatedWork W2140899540 @default.
• W4313203163 hasRelatedWork W2149553727 @default.
• W4313203163 hasRelatedWork W2999647262 @default.
• W4313203163 hasRelatedWork W3001144200 @default.
• W4313203163 hasRelatedWork W4298392639 @default.
• W4313203163 hasRelatedWork W1905328716 @default.
• W4313203163 isParatext "false" @default.
• W4313203163 isRetracted "false" @default.
• W4313203163 workType "article" @default.