Non-Asymptotic Achievable Rate-Distortion Region for Indirect Wyner-Ziv Source Coding

In the Wyner-Ziv source coding problem, a source $X$ has to be encoded while the decoder has access to side information $Y$. This paper investigates the indirect setup, in which a latent source $S$, unobserved by both the encoder and the decoder, must also be reconstructed at the decoder. This scenario is increasingly relevant in the context of goal-oriented communications, where $S$ can represent semantic information obtained from $X$. This paper derives the indirect Wyner-Ziv rate-distortion function in asymptotic regime and provides an achievable region in finite block-length. Furthermore, a Blahut-Arimoto algorithm tailored for the indirect Wyner-Ziv setup, is proposed. This algorithm is then used to give a numerical evaluation of the achievable indirect rate-distortion region when $S$ is treated as a classification label.