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Digital fingerprinting is a technique to deter unauthorized redistribution of multimedia content by embedding a unique identifying signal in each legally distributed copy. The embedded fingerprint can later be extracted and used to trace the originator of an unauthorized copy. A group of users may collude and attempt to create a version of the content that cannot be traced back to any of them. As multimedia data is commonly stored in compressed form, this paper addresses the problem of fingerprinting compressed signals. Analysis is carried out to show that due to the quantized nature of the host signal and the embedded fingerprint, directly extending traditional fingerprinting techniques for uncompressed signals to the compressed case leads to low collusion resistance. To overcome this problem and improve the collusion resistance, a new technique for fingerprinting compressed signals called Anti-Collusion Dither (ACD) is proposed, whereby a random dither signal is added to the compressed host before embedding so as to make the effective host signal appear more continuous. The proposed technique is shown to reduce the accuracy with which attackers can estimate the host signal, and from an information theoretic perspective, the proposed ACD technique increases the maximum number of users that can be supported by the fingerprinting system under a given attack. Both analytical and experimental studies confirm that the proposed technique increases the probability of identifying a guilty user and can approximately quadruple the collusion resistance compared to conventional Gaussian fingerprinting.