On the Fingerprinting Capacity Under the Marking Assumption
Abstract
We address the maximum attainable rate of fingerprinting codes under the marking assumption, studying lower and upper bounds on the value of the rate for various sizes of the attacker coalition. Lower bounds are obtained by considering typical coalitions, which represents a new idea in the area of fingerprinting and enables us to improve the previously known lower bounds for coalitions of size two and three. For upper bounds, the fingerprinting problem is modelled as a communications problem. It is shown that the maximum code rate is bounded above by the capacity of a certain class of channels, which are similar to the multipleaccess channel. Converse coding theorems proved in the paper provide new upper bounds on fingerprinting capacity. It is proved that capacity for fingerprinting against coalitions of size two and three over the binary alphabet satisfies $0.25 \leq C_{2,2} \leq 0.322$ and $0.083 \leq C_{3,2} \leq 0.199$ respectively. For coalitions of an arbitrary fixed size $t,$ we derive an upper bound $(t\ln2)^{1}$ on fingerprinting capacity in the binary case. Finally, for general alphabets, we establish upper bounds on the fingerprinting capacity involving only singleletter mutual information quantities.
 Publication:

arXiv eprints
 Pub Date:
 December 2006
 arXiv:
 arXiv:cs/0612073
 Bibcode:
 2006cs.......12073P
 Keywords:

 Computer Science  Information Theory;
 Computer Science  Cryptography and Security
 EPrint:
 final version, 12 pages, 2 figures, to appear in IEEE Trans. on Inform. Theory  Special Issue on Informationtheoretic Security, Jun 2008, simplified proofs in Sections II and III, changes in Theorem 4.1