Unified Expression of Achievable Region in Privacy-Constrained Source Coding

Privacy-constrained source coding problems have become increasingly important recently, and the utility-privacy trade-off has been investigated for various systems. As pioneering work, Yamamoto (1983) found theoretical limits of the coding rate, privacy and utility in two cases; (i) both public and private information is encoded and (ii) only public information is encoded. However, the theoretical limit has not been characterized in a more general case; (iii) encoded messages consist of public information and a part of private information. Then in this paper, we characterize the trade-off relation in case (iii). The obtained expression of the achievable region is a "unified expression" because it includes the ones in case (i) and (ii) as special cases. Through the numerical results, we clarify the significance of the choice of the encoded set.