We propose a biometric identification system where the chosen- and generated-secret keys are used simultaneously, and investigate its fundamental limits from information theoretic perspectives. The system consists of two phases: enrollment and identification phases. In the enrollment phase, for each user, the encoder uses a secret key, which is chosen independently, and the biometric identifier to generate another secret key and a helper data. In the identification phase, observing the biometric sequence of the identified user, the decoder estimates index, chosen- and generated-secret keys of the identified user based on the helper data stored in the system database. In this study, the capacity region of such system is characterized. In the problem settings, we allow chosen- and generated-secret keys to be correlated. As a result, by permitting the correlation of the two secret keys, the sum rate of the identification, chosen- and generated-secret key rates can achieve a larger value compared to the case where the keys do not correlate. Moreover, the minimum amount of the storage rate changes in accordance with both the identification and chosen-secret key rates, but that of the privacy-leakage rate depends only on the identification rate.

This letter presents numerical results of lossy source coding for non-uniformly distributed binary source with trellis codes. The results show how the performance of trellis codes approaches the rate-distortion function in terms of the number of states.

This letter reveals that linear lossy codes cannot attain the rate-distortion function in general, even if the source is binary i.i.d. and the distortion is measured by the Hamming distortion measure.