We consider the following communication task in the multi-party setting, which involves joint random variables $XYZMN$ with the property that $M$ is independent of $YZN$ conditioned on $X$ , and $N$ is independent of $XZM$ conditioned on $Y$ . Three parties Alice, Bob and Charlie, respectively, observe samples $x,y$ and $z$ from $XYZ$ . Alice and Bob communicate messages to Charlie with the goal that Charlie can output a sample ${ \left ({m,n }\right) }$ such that the distribution of ${ \left ({x,y,z,m,n }\right) }$ is close to $XYZMN$ . This task reflects the simultaneous message passing communication complexity. Furthermore, it is a generalization of some well studied problems in information theory, such as distributed source coding, source coding with a helper and one sender and one receiver message compression. It is also closely related to the lossy distributed source coding task. Our main result is an achievable communication region for this task in the one-shot setting, through which we obtain a nearly optimal characterization using auxiliary random variables of bounded size. We employ our achievability result to provide a nearly optimal one-shot communication region for the task of lossy distributed source coding, in terms of auxiliary random variables of bounded size. Finally, we show that interactions are necessary to achieve the optimal expected communication cost.

中文翻译：

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关于多方设置中的消息压缩

我们在多方设置中考虑以下通信任务，其中涉及联合随机变量 $XYZMN$ 与财产 百万美元 独立于 $YZN$ 以 $X$ ， 和 $N$ 独立于 $XZM$ 以 $Y$ . 三方 Alice、Bob 和 Charlie 分别观察样本 $x,y$ 和 $z$ 从 $XYZ$ . Alice 和 Bob 向 Charlie 传达消息，目的是让 Charlie 可以输出样本 ${ \left ({m,n }\right) }$ 使得分布 ${ \left ({x,y,z,m,n }\right) }$ 接近 $XYZMN$ . 该任务反映了同步消息传递通信复杂性。此外，它是对信息论中一些经过充分研究的问题的概括，例如分布式源编码、具有帮助器和一发送一接收器消息压缩的源编码。它也与有损分布式源编码任务密切相关。我们的主要结果是在一次性设置中为该任务提供了一个可实现的通信区域，通过该区域，我们使用有界大小的辅助随机变量获得了近乎最佳的表征。我们利用我们的可实现性结果为有损分布式源编码任务提供近乎最优的一次性通信区域，就有限大小的辅助随机变量而言。最后，我们表明交互是实现最佳预期通信成本所必需的。