%0 Generic %1 Anthapadmanabhan2006 %A Anthapadmanabhan, N. Prasanth %A Barg, Alexander %A Dumer, Ilya %D 2006 %K capacity fingerprinting %T On the Fingerprinting Capacity Under the Marking Assumption %U http://arxiv.org/abs/cs/0612073 %X 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 multiple-access 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 $0.25 C_2,2 0.322$ and $0.083 C_3,2 0.199$ respectively. For coalitions of an arbitrary fixed size $t,$ we derive an upper bound $(tłn2)^-1$ on fingerprinting capacity in the binary case. Finally, for general alphabets, we establish upper bounds on the fingerprinting capacity involving only single-letter mutual information quantities.

@misc{Anthapadmanabhan2006, 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 multiple-access 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 single-letter mutual information quantities. }, added-at = {2009-02-27T23:05:23.000+0100}, author = {Anthapadmanabhan, N. Prasanth and Barg, Alexander and Dumer, Ilya}, biburl = {https://www.bibsonomy.org/bibtex/2dcc9b724e24ac825661459f8bcfca952/ywhuang}, description = {[cs/0612073] On the Fingerprinting Capacity Under the Marking Assumption}, interhash = {01d329a01a9b70f95a393db940a804bb}, intrahash = {dcc9b724e24ac825661459f8bcfca952}, keywords = {capacity fingerprinting}, note = {cite arxiv:cs/0612073 Comment: final version, 12 pages, 2 figures, to appear in IEEE Trans. on Inform. Theory - Special Issue on Information-theoretic Security, Jun 2008, simplified proofs in Sections II and III, changes in Theorem 4.1}, timestamp = {2009-02-27T23:13:25.000+0100}, title = {On the Fingerprinting Capacity Under the Marking Assumption}, url = {http://arxiv.org/abs/cs/0612073}, year = 2006 }