Converse Bounds for Finite-Length Joint Source-Channel Coding
Based on the hypothesis-testing method, the authors derive lower bounds on the average error probability of finite-length joint source-channel coding. The extension of the meta-converse bound of channel coding to joint source-channel coding depends on the codebook and the decoding rule and thus, it is a priori computationally challenging. Weaker versions of this general bound recover known converses in the literature and provide computationally feasible expressions. Reliable communication of messages in the finite block length regime can be characterized by upper and lower bounds on the average error probability of the best possible code.