In this paper we study the nonasymptotic bounds of a special Joint Source-Channel Coding system with hierarchical source, where an observable source and an unobservable indirect source are required to be reconstructed. Namely, we focus on the achievable and converse bounds of the excess distortion probability in the finite blocklength regime. The main challenge arises from the hierarchical source structure, which requires simultaneous reconstruction of both sources. This setup demands a coding scheme which satisfy the demand of encoding both source for the achievability bound, and a method to characterize the joint excess-distortion probability of two correlated events for the converse bound.

翻译：本文研究一种具有分层信源的特定联合信源信道编码系统的非渐近界，该系统要求重构一个可观测信源和一个不可观测的间接信源。具体而言，我们关注有限码长下超额失真概率的可达界与逆界。主要挑战源于分层信源结构，该结构要求同时重构两个信源。此设置需要一种编码方案以满足可达界中对两个信源进行编码的要求，以及一种刻画逆界中两个相关事件的联合超额失真概率的方法。