Information Theoretic Analysis of the Fundamental Limits of Content Identification.

We investigate content identification problem from an information theoretic perspective and derive its fundamental limits. Here, a rights-holder company desires to keep track of illegal uses of its commercial content, by utilizing resources of a company, while securing privacy of its content. Due to privacy issues, rights-holder company only reveals certain hash values of original content to company. We view commercial content of rights-holder company as codebook of an encoder and hash values of content (made available to company) as codebook of a decoder, i.e., corresponding codebooks of encoder and decoder are not same. Hence, content identification is modelled as a communication problem using asymmetric codebooks by an encoder and a decoder. We further address the privacy issue in content identification by adding security constraints to communication setup to prevent estimation of encoder codewords given decoder codewords. By this modeling, proposed problem of reliable communication with asymmetric codebooks with constraints provides fundamental limits of content identification problem. To this end, we introduce an information capacity and prove that this capacity is equal to operation capacity of system under i.i.d. encoder codewords providing fundamental limits for content identification. As a well known and widely studied framework, we evaluate capacity for a binary symmetric channel and provide closed form expressions.