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UID:8252@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20141113T110000
DTEND;TZID=Europe/Paris:20141113T120000
DTSTAMP:20241120T210312Z
URL:https://www.i2m.univ-amu.fr/evenements/discrete-compressed-sensing-as-
 coding-theory-problem/
SUMMARY:Grigory Kabatiansky (...): Discrete compressed sensing as coding th
 eory problem
DESCRIPTION:Grigory Kabatiansky: Compressed sensing (CS) attracted a lot of
  attention in last few years\, starting from first papers published in 200
 6. Nevertheless a discrete version of CS was not even stated properly unti
 l last year\, when in a joint paper of Serge Vladuts and the speaker the c
 orresponding problem have been formulated and first results have been obta
 ined (G.Kabatiansky\, S.Vladuts\, "What to do if syndromes are corrupted a
 lso"\, in Proc. Int. Workshop Optimal Codes\, Albena\, Bulgaria\, 2013). I
 n some sense this talk can be considered as a report on what was done in t
 he direction of discrete CS during this year.\nDiscrete CS problem can be 
 stated in the following way – to find linear code C and its parity-check
  matrix H such that an error vector e of Hamming weight T or less can be r
 ecovered from the syndrome equation He=s even if the syndrome s is given w
 ith L or less errors. A particular case of this problem is for instance fa
 mous Erdosh-Ulam problem on 20 questions.\nIn the talk we give a solution 
 of discrete CS problem in the same way as RS-codes provide the solution of
  main problem of coding theory for the cases when code length is at most f
 ield cardinality. It is worth to remark that RS codes aren’t good for di
 screte CS problem as they demand the redundancy at least 4TL\, see R.Prony
 \, ``Essai experimantal et analytique sur les lois del Dilatabilite de flu
 ides'' J. de Ecole Polytechnique 1\, pp.24-76\, 1795 and M.T. Comer\, E.L.
  Kaltofen\, C.Pernet\, "Sparse Polynomial Interpolationb and Berlekamp-Mas
 sey Algorithms That Correct Outlier Errors in Input Values"\, in Proc. ISS
 AC 2011\, pp. 138-145. The optimal solution\, which will be described in t
 he talk\, uses redundancy only 2(T+L).\n-\nIn the conclusion it will be sh
 own how these results can be applied for a limited version of ordinary CS 
 problem.\n-\nThe talk is based on joint research of the speaker with Serge
  Vladuts\, Cedric Tavernier and Valery Lomakov.\n-\nGrigory Kabatiansky\, 
 Skolkovo Institute of Science and Technology\n\n
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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