A Lower Bound on the Second-Order RDP Function

The rate-distortion-perception (RDP) problem is investigated in a general context. In recent years, the RDP problem has attracted significant attention from both theoretical and practical standpoints. Various researchers have explored this problem, seeking to better understand its implications and applications. Recently, Nomura [1] explored the self-random number generation (SRNG) problem using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f$</tex>-divergence, which serves as a subproblem within the larger RDP framework. This paper builds upon the work of [1], extending the analysis to the second-order setting and deriving the optimal rate. Furthermore, we apply our findings to the RDP problem, obtaining a lower bound for the second-order RDP function.