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In digital fingerprinting schemes based on the spread spectrum technique, (quasi-)orthogonal sequences are assigned to users as their fingerprints, and they are embedded into digital contents prior to distribution. Owing to the (quasi-) orthogonality, we can uniquely identify the users from a pirated copy, even if dozens of users are involved in the collusion process. Because the number of users accommodated in a fingerprinting system is generally very large, the interference among the sequences involved in a pirated copy becomes non-negligible as the number of colluders increases. In this paper, we investigate the interference from the viewpoint of a communication channel, and we propose an effective removal operation to reduce the interference as far as possible. By iteratively operating the proposed detector, we can sequentially and successively detect colluders from a pirated copy. Furthermore, two kinds of thresholds are introduced in order to perform the removal operation adaptively for detected signals. Experimental results reveal a drastic improvement in the traceability and a reduction in the amount of interference by the removal operation.