This paper studies a variant of the rate-distortion problem motivated by task-oriented semantic communication and distributed learning problems, where $M$ correlated sources are independently encoded for a central decoder. The decoder has access to a correlated side information in addition to the messages received from the encoders, and aims to recover a latent random variable correlated with the sources observed by the encoders within a given distortion constraint rather than recovering the sources themselves. We provide bounds on the rate-distortion region for this scenario in general, and characterize the rate-distortion function exactly when the sources are conditionally independent given the side information.

翻译：本文研究一种受任务导向语义通信和分布式学习问题启发的率失真问题变体，其中$M$个相关信源被独立编码并传输至中央解码器。解码器除了接收来自编码器的消息外，还可获取相关边信息，其目标是在给定失真约束下恢复与编码器观测信源相关的隐随机变量，而非直接恢复信源本身。我们针对该场景给出了率失真区域的一般界，并在信源给定边信息条件下独立时精确刻画了率失真函数。