On the Fingerprinting Capacity Under the Marking Assumption

TL;DR

This paper investigates the maximum rate of fingerprinting codes under the marking assumption, providing new bounds by modeling the problem as a communication channel and analyzing coalition sizes.

Contribution

It introduces a novel approach using typical coalitions for lower bounds and models fingerprinting as a channel capacity problem for upper bounds, improving existing bounds.

Findings

Lower bounds for coalitions of size two and three are improved.

Upper bounds are derived using channel capacity models, including mutual information bounds.

Specific capacity bounds are established for binary and general alphabet cases.

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.