Year: 2025
Type: article
Abstract: 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$S = \varphi (X) + W$, where X is the observable source with alphabet$\mathcal {X}$,$\varphi (\cdot)$is a deterministic function, and W is a random variable independent of X, satisfying$\mathbb {E}[W] = 0$,$\mathbb {E}[W^{2}] \gt 0$,$\mathbb {E}[W^{3}] = 0$, and$\mathbb {E}[W^{6}] \lt \infty $. Additionally, both the set$\{\varphi (x):\ x \in \mathcal {X} \}$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.
Authors: Huiyuan Yang, Xiaojun Yuan
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408145155