CIF: Small: Fundamental limits of interactive communications

该研究旨在了解交互如何影响通信系统的基本性能。“交互”表示当前的决策（例如向通道输入什么）何时可以基于过去的决策（例如通过反馈或对通道输出的访问）而改变。 为了评估交互的影响，该项目使用了信息理论的技术独立形式主义，它量化了数据压缩和传输的基本限制。 这为交互式通信系统的实际性能提供了上限和基准，这将比考虑反馈的理想化概念的当前界限更现实。本文将从三个信息理论的角度来研究在有噪声反馈的单向信道和双向信道中交互的作用：1）比较粗糙的容量观点; 2）更精确的误差指数角度;以及最后3）甚至更精细的二阶编码/有限块长度上下文。 具有噪声反馈的单向通道突出了使当前输入适应过去的噪声通道输出的潜在效用或无用性，从而扩展了对大部分考虑无噪声/完美输出反馈的现有技术的理解。 双向通道，其中两个用户希望在公共通道上交换消息，并且交互地这样做，通过捕获不仅交互/反馈的影响，而且使用公共通道在一个方向上发送数据与在另一个方向上发送反馈之间的张力，进一步理解这种理解。建议的研究成果将提供一个更现实的和相对未开发的互动settings.This奖项反映了NSF的法定使命的相互作用的全面理解，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

The proposed research aims to understand how interaction affects the fundamental performance of communication systems. "Interaction" denotes when current decisions such as what to input to the channel may be altered based on past decisions, for example through feedback or access to channel outputs. To assess the impact of interaction, this project uses the technology-independent formalism of information theory, which quantifies the fundamental limits of data compression and transmission. This provides upper bounds and benchmarks for real-world performance of interactive communication systems, which will be more realistic than current bounds which consider idealized notions of feedback. This is expected to refine the design of communication systems in the noisy feedback and two-way settings of relevance in many existing and future communication paradigms.The role of interaction in one-way channels with noisy feedback and two-way channels will be looked at using three information theoretic metrics: 1) the somewhat crude capacity viewpoint; 2) a more refined error exponents angle; and finally 3) the even more refined second order coding / finite-blocklength context. One-way channels with noisy feedback highlight the potential utility or futility of adapting current inputs to past noisy channel outputs, extending the understanding from the current state of the art which for the most part considers noiseless / perfect output feedback. Two-way channels where two users wish to exchange messages over a common channel and do so interactively take this understanding one step further by capturing not only the impact of interaction / feedback, but also the tension between using a common channel to send data in one direction versus feedback in the other. The outcomes of the proposed research will provide a comprehensive understanding of interaction in two more realistic and relatively unexplored interactive settings.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.