The price of privacy and the limits of LP decoding

This work is at the intersection of two lines of research. One line, initiated by Dinur and Nissim, investigates the price, in accuracy, of protecting privacy in a statistical database. The second, growing from an extensive literature on compressed sensing (see in particular the work of Donoho and collaborators [14, 7, 13, 11]) and explicitly connected to errorcorrecting codes by Cand`es and Tao ([4]; see also [5, 3]), is in the use of linear programming for error correction. Our principal result is the discovery of a sharp threshhold 0.239, so that if < and A is a random m ? n encoding matrix of independently chosen standard Gaussians, where m = O(n), then with overwhelming probability over choice of A, for all x Rn , LP decoding corrects m arbitrary errors in the encoding Ax, while decoding can be made to fail if the error rate exceeds . Our bound resolves an open question of Cand`es, Rudelson, Tao, and Vershyin [3] and (oddly, but explicably) refutes empirical conclusions of ...

• Type: Conference
• Year: 2007
• Where: STOC
• Authors: Cynthia Dwork, Frank McSherry, Kunal Talwar
• Keywords: Algorithms, Arbitrary Errors, Error Control Codes, Error Rate Exceeds, STOC 2007