Unified Expression of Achievable Region in Privacy-Constrained Source Coding
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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. The numerical results also imply that the optimal privacy in case (i) and (iii) is securer than the one in case (ii) whereas for the optimal privacy, the achievable coding rates in case (ii) and (iii) are smaller than the one in case (i).
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