We study channel simulation under common randomness-assistance in the finite-blocklength regime and identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance. We show that this one-shot converse can be achieved exactly using no-signaling assisted codes, and approximately achieved using common randomness-assisted codes. Our one-shot converse thus takes on an analogous role to the celebrated meta-converse in the complementary problem of channel coding, and find tight relations between these two bounds. We asymptotically expand our bounds on the simulation cost for discrete memoryless channels, leading to the second-order as well as the moderate deviation rate expansion, which can be expressed in terms of the channel capacity and channel dispersion known from noisy channel coding. Our techniques extend to discrete memoryless broadcast channels. In stark contrast to the elusive broadcast channel capacity problem, we show that the reverse problem of broadcast channel simulation under common randomness-assistance allows for an efficiently computable single-letter characterization of the asymptotic rate region in terms of the broadcast channel's multi-partite mutual information. Finally, we present a Blahut-Arimoto type algorithm to compute the rate region efficiently.

翻译：我们在公共随机辅助下研究有限分组长度体制的信道模拟问题，并识别出光滑信道最大信息量作为固定误差容限下最小模拟代价的一个线性规划单次逆界。我们证明该单次逆界可通过无信号辅助码精确达到，并通过公共随机辅助码近似达到。因此，我们的单次逆界在信道编码的互补问题中扮演着与著名的元逆界类似角色，并且发现这两个界限之间存在紧密关联。我们渐近展开离散无记忆信道模拟代价的界限，导出二阶展开以及中等偏差率展开，这些展开可通过噪声信道编码中已知的信道容量和信道色散表示。我们的技术可推广至离散无记忆广播信道。与难以捉摸的广播信道容量问题截然不同的是，我们证明在公共随机辅助下广播信道模拟的反问题允许用广播信道的多部分互信息对渐近速率区域进行高效可计算的单字母刻画。最后，我们提出一种Blahut-Arimoto型算法以高效计算该速率区域。