In biometric privacy-preserving authentication systems that are based on key-binding, two terminals observe two correlated biometric sequences. The first terminal selects a secret key, which is independent of the biometric data, binds this secret key to the observed biometric sequence and communicates it to the second terminal by sending a public message. This message should only contain a negligible amount of information about the secret key, but also leak as little as possible about the biometric data. Current approaches to realize such biometric systems use fuzzy commitment with codes that, given a secret-key rate, can only achieve the corresponding privacy-leakage rate equal to one minus this secret-key rate. However, the results in Willems and Ignatenko  indicate that lower privacy leakage can be achieved if vector quantization is used at the encoder. In this paper we study the use of convolutional and turbo codes applied in fuzzy commitment and its modifications that realize this.