  This work adopts an information theoretic framework for the design of
collusion-resistant coding/decoding schemes for digital fingerprinting. More
specifically, the minimum distance decision rule is used to identify 1 out of t
pirates. Achievable rates, under this detection rule, are characterized in two
distinct scenarios. First, we consider the averaging attack where a random
coding argument is used to show that the rate 1/2 is achievable with t=2
pirates. Our study is then extended to the general case of arbitrary $t$
highlighting the underlying complexity-performance tradeoff. Overall, these
results establish the significant performance gains offered by minimum distance
decoding as compared to other approaches based on orthogonal codes and
correlation detectors. In the second scenario, we characterize the achievable
rates, with minimum distance decoding, under any collusion attack that
satisfies the marking assumption. For t=2 pirates, we show that the rate
$1-H(0.25)\approx 0.188$ is achievable using an ensemble of random linear
codes. For $t\geq 3$, the existence of a non-resolvable collusion attack, with
minimum distance decoding, for any non-zero rate is established. Inspired by
our theoretical analysis, we then construct coding/decoding schemes for
fingerprinting based on the celebrated Belief-Propagation framework. Using an
explicit repeat-accumulate code, we obtain a vanishingly small probability of
misidentification at rate 1/3 under averaging attack with t=2. For collusion
attacks which satisfy the marking assumption, we use a more sophisticated
accumulate repeat accumulate code to obtain a vanishingly small
misidentification probability at rate 1/9 with t=2. These results represent a
marked improvement over the best available designs in the literature.
