Utility-Privacy Trade-Offs with Limited Leakage for Encoder

The utilization of database such as IoT has progressed. As pioneering work, Yamamoto (1983) assumed the source (database) which consists of public information and private information and found theoretical limits (first-order rate analysis) among the coding rate, privacy for the decoder and utility in two special cases. In this paper, we consider a more general case based on the work by Shinohara and Yagi (2022). Introducing a measure of privacy for the encoder, we investigate two problems as follows: The first problem is the first-order rate analysis among the coding rate, utility, privacy for the decoder, and privacy for the encoder in which utility is measured by the expected distortion or the excess-distortion probability. The second task is establishing the strong converse theorem for utility-privacy trade-offs in which utility is measured by the excess-distortion probability. These results may lead to a more refined analysis such as the second-order rate analysis.