COHOMCODES

Robust Codes from Higher Dimesional Expanders

Coordinatore	BAR ILAN UNIVERSITY    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Israel [IL]
Totale costo	1˙302˙000 €
EC contributo	1˙302˙000 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2013-StG
Funding Scheme	ERC-SG
Anno di inizio	2014
Periodo (anno-mese-giorno)	2014-02-01   -   2019-01-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	BAR ILAN UNIVERSITY  Organization address address: BAR ILAN UNIVERSITY CAMPUS city: RAMAT GAN postcode: 52900 contact info Titolo: Dr. Nome: Tali Cognome: Kaufman Halman Email: send email Telefono: +972 77 5610813 Fax: +972 3 6353277	IL (RAMAT GAN)	hostInstitution	1˙302˙000.00
2	BAR ILAN UNIVERSITY  Organization address address: BAR ILAN UNIVERSITY CAMPUS city: RAMAT GAN postcode: 52900 contact info Titolo: Ms. Nome: Estelle Cognome: Waise Email: send email Telefono: +972 3 5317439 Fax: +972 3 6353277	IL (RAMAT GAN)	hostInstitution	1˙302˙000.00

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 Obiettivo del progetto (Objective)

'Error correcting codes play a fundamental role in computer science. Good codes are codes with rate and distance that are asymptotically optimal. Some of the most successful good codes are constructed using expander graphs. In recent years a new notion of {em robust} error correcting codes, known as locally testable codes (LTCs), has emerged. Locally testable codes are codes in which a proximity of a vector to an error correcting code can be achieved by probing the vector in {em constant} many locations (independent of its length). LTCs are at the heart of Probabilistically Checkable Proofs (PCPs) and their construction has been sought since the discovery of the PCP theorem in the early 1990s.

Despite 20 years of research, it is still widely open whether good locally testable codes exist. LTCs present completely new challenge to the field of error correcting codes. In the old paradigm a random code is a good code and the main focus was to construct explicit codes that imitate the random code. However, a random code is not an LTC. Thus, contrary to traditional codes, there are no natural candidates for LTCs. The known constructions of robust codes are ad hoc, and there is a lack of theory that explains their existence.

The goal of the current research plan is to harness the emerging field of higher dimensional expanders and their topological properties for a systematic study of robust error correcting codes. Higher dimensional expanders are natural candidates for obtaining robust codes since they offer a strong form of redundancy that is essential for robustness. Such form of redundancy is lacking by their one dimensional analogue (i.e., expander graphs). Hence, the known expander codes are not robust. We expect that our study will draw new connections between error correcting codes, high dimensional expanders, topology and probability that will shed new light on these fields, and in particular, will advance the constructing of good and robust codes.'