Signature Codes for Weighted Binary Adder Channel and Multimedia Fingerprinting

AbstractIn this paper, we study binary signature codes for the weighted binary adder channel (WbAC) and collusion-resistant multimedia fingerprinting. Let $A(n, t)$ denote the maximum size of a $t$ -signature code of length $n$ , and $A(n, w, t)$ denote the maximum size of a $t$ -signature code of length $n$ and constant-weight $w$ . First, we derive asymptotic and general upper bounds on $A(n,t)$ by relating signature codes to $B_{t}$ codes and bipartite graphs with large girth respectively, and also show the upper bounds are tight for certain cases. Second, we determine the exact values of $A(n,2,2)$ and $A(n,3,2)$ for infinitely many $n$ by connecting signature codes with $C_{4}$ -free graphs and union-free families, respectively. Third, we provide two explicit constructions for $t$ -signature codes which have efficient decoding algorithms and applications to two-level signature codes. Furthermore, we show from a geometric viewpoint that there does not exist any binary code with complete traceability for noisy WbAC and multimedia fingerprinting. A new type of signature codes with a weaker requirement than complete traceability is introduced for the noisy scenario.