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Digital fingerprinting protects multimedia content from illegal redistribution by uniquely marking every copy of the content distributed to each user. The collusion attack is a powerful attack where several different fingerprinted copies of the same content are combined together to attenuate or even remove the fingerprints. One major category of collusion-resistant fingerprinting employs an explicit step of coding. Most existing works on coded fingerprinting mainly focus on the code-level issues and treat the embedding issues through abstract assumptions without examining the overall performance. In this paper, we jointly consider the coding and embedding issues for coded fingerprinting systems and examine their performance in terms of collusion resistance, detection computational complexity, and distribution efficiency. Our studies show that coded fingerprinting has efficient detection but rather low collusion resistance. Taking advantage of joint coding and embedding, we propose a permuted subsegment embedding technique and a group-based joint coding and embedding technique to improve the collusion resistance of coded fingerprinting while maintaining its efficient detection. Experimental results show that the number of colluders that the proposed methods can resist is more than three times as many as that of the conventional coded fingerprinting approaches.