<p>Multimedia fingerprinting is a technique to protect the copyrighted contents against being illegally redistributed under various collusion attack models. Averaging attack is the most fair choice for each colluder to avoid detection, and also makes the pirate copy have better perceptional quality. This makes such an attack one of the most feasible approaches to carrying out collusion. In order to trace all the colluders, several types of multimedia fingerprinting codes were introduced to construct fingerprints resistant to averaging attacks on multimedia contents, such as AND anti-collusion codes (AND-ACCs), binary separable codes (SCs), logical anti-collusion codes (LACCs), binary frameproof codes (FPCs), binary strongly-separable codes (SSCs) and binary secure code with list decoding (SCLDs). Then codes with the rate as high as possible are desired. However, existing fingerprinting codes usually achieve low code rates due to their strong combinatorial structures. The main reason is that most corresponding tracing algorithms are directly derived from basic code properties, without sophisticated design or optimization. In this paper, we first propose novel tracing algorithms and then find appropriate fingerprinting codes with weaker combinatorial structure, i.e., the binary strongly identifiable parent property code for multimedia fingerprinting (SMIPPC) and its concatenated code. Theoretical comparisons and numerical comparisons show that SMIPPCs have higher code rates than those of the existing codes due to their weaker combinatorial structures. It is worth noting that SMIPPCs can only trace a part of colluders by using the previous tracing algorithm. In contrast, our algorithm enables SMIPPCs to trace all colluders. This implies that our tracing algorithms have strong traceability.</p>