We analyze the finite-blocklength performance of lossy joint source-channel codes (JSCC) in an unknown-channel framework, where the true channel is unknown but the source distribution is known. We establish achievability results for mismatched-design JSCC, where the code design is based on a channel $Q_{Y|X}$ but deployed over a different channel $P_{Y|X}$. Our mismatched-design achievability result allows nonstationary channel laws and arbitrary standard Borel alphabets for the source, reproduction, channel input and channel output. The achievability bound is given in terms of the rate-distortion and rate-dispersion functions, as well as two channel-dependent quantities that we call the mismatched-design rate and mismatched-design rate-dispersion. For block erasure channels, our result shows that channel mismatch incurs no penalty. We then show a second-order universal family of source-channel codes over the set of block erasure channels. Our code construction uses Poisson functional representations of suitable conditional probability measures to produce the encoder and decoder outputs. We use a parameterized family of Gibbs posteriors as the decoder-side kernels, whose envelope recovers the generalized mutual information.

翻译：我们分析了在未知信道框架下，有损联合信源信道编码的有限块长性能。在此框架中，真实信道未知但信源分布已知。我们建立了失配设计联合信源信道编码的可达性结果，其中编码设计基于信道 $Q_{Y|X}$，但部署在另一信道 $P_{Y|X}$ 上。我们的失配设计可达性结果允许非平稳信道律以及信源、再现、信道输入与信道输出的任意标准波莱尔字母表。可达性界由率失真函数与率色散函数，以及两个信道相关量（即失配设计速率与失配设计色散）给出。对于块擦除信道，我们的结果表明信道失配不会造成性能损失。随后，我们展示了在块擦除信道集合上的一类二阶通用信源信道码。我们的码构造利用适当条件概率测度的泊松函数表示来生成编码器与解码器输出。我们采用参数化的吉布斯后验族作为解码器侧核，其包络可恢复广义互信息。