Frameproof codes and compressive sensing

Charles J Colbourn, Daniel Horsley, Violet R Syrotiuk

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

8 Citations (Scopus)

Abstract

Fingerprinting of digital content is often employed to prevent a small coalition of legitimate users from constructing a copy whose fingerprint is registered to a user not in the coalition. Sets of fingerprints that prevent t or fewer users from framing another user in this way are frameproof codes. A frameproof code is termed secure when no fingerprint constructed by a coalition of t or fewer users can also be constructed by a disjoint coalition of t or fewer users. Secure frameproof codes are related to cover-free families arising in combinatorial group testing. Here a different connection is explored. Interpreting frameproof codes and secure frameproof codes as certain types of separating hash families, it is shown that each underlies a useful measurement matrix for compressive sensing. Indeed frameproof codes for coalitions of t users underlie measurement matrices that admit ℓ0-recoverability of t-sparse vectors, while secure frameproof codes for coalitions of t users underlie measurement matrices that admit ℓ1-recoverability of t-sparse vectors. Consequences for the construction of measurement matrices are briefly outlined, but the focus is on the combinatorial similarities of frameproof codes, separating and distributing hash families, and measurement matrices.

Original languageEnglish
Title of host publication2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
Pages985-990
Number of pages6
DOIs
Publication statusPublished - 2010
Externally publishedYes
Event2010 Annual Allerton Conference on Communication, Control and Computing - Allerton Park and Retreat Center, University of Illinois, Monticello, United States of America
Duration: 29 Sep 20101 Oct 2010
Conference number: 48th

Conference

Conference2010 Annual Allerton Conference on Communication, Control and Computing
CountryUnited States of America
CityMonticello
Period29/09/101/10/10

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