On the Second-Order Achievabilities of Indirect Quadratic Lossy Source Coding

This paper studies the second-order achievabilities of indirect quadratic lossy source coding for a specific class of source models, where the term “quadratic” denotes that the reconstruction fidelity of the hidden source is quantified by a squared error distortion measure. Specifically, it is assumed that the hidden source S can be expressed as S=φ(X)+W, where X is the observable source with alphabet X, φ(∙) is a deterministic function, and W is a random variable independent of X, satisfying E[W]=0, E[W2]>0, E[W3]=0, and E[W6]<∞. Additionally, both the set {φ(x): x εX}and the reconstruction alphabet for S are assumed to be bounded. Under the above settings, a second-order achievability bound is established using techniques based on distortion-tilted information. This result is then generalized to the case of indirect quadratic lossy source coding with observed source reconstruction, where reconstruction is required for both the hidden source S and the observable source X, and the distortion measure for X is not necessarily quadratic. These obtained bounds are consistent in form with their finite-alphabet counterparts, which have been proven to be second-order tight.