A Separate Quantization and Privatization Is Strictly Sub optimal

First let us recap the subset selection (SS) scheme proposed by [51]. In the achievability part of Theorem 2.1, our proposed scheme SQKR randomly and independently samples We summarize it in the following corollary: Corollary B.2 The achievability parts of Corollary B.1 and Corollary B.2 follow directly from the analysis of SQKR Note that the red line in Figure 3 can be achieved by RHR. A scheme is consistent if it has vanishing estimation error as n!1 . O (min ( d " e log d, d)) bits of communication to achieve r Similarly, the estimation error of private-coin RHR is characterized below: Corollary B.4 (Private-coin RHR) We implement our mean estimation scheme Subsampled and Quantized Kashin's Response (SQKR) We construct the tight frame by using the random partial Fourier matrices in [36]. It can be shown that the tight frame based on U has Kashin's level K = O (1) . Compare to optimal " -LDP scheme [13] Figure 4: ` SQKR achieves similar performance with significantly communication budgets.