Capacity and Coding Techniques for Channels with Memory and Feedback

摘要：分布式网络与计算领域正处于一场技术革命的边缘。在国家安全、交通、通信和商业领域的新兴应用要求分布式网络能够多用户通信和协作信号和信息处理。这些网络的一个非常重要的组成部分是底层通信通道。这些通道具有内存，通常是时变的，并且通常建模不良。此外，在许多这样的网络中，节点的功率是有限的，只有适度的计算资源。反馈是现代通信系统的一个非常重要的特征，尽管人们对它知之甚少。反馈是有用的，因为它可以增加给定信道的内存容量；它可以增加误差指数，从而减少延迟；它通常会导致更简单的编码方案；它允许编码器适应未知的信道变化。本研究包括：(1)确定信道反馈质量与由此产生的信道香农容量之间的基本限制和权衡；(2)发展了联合信源信道编码的序贯率失真理论；(3)分析了一般消息传递算法的收敛性和准确性；(4)开发专门用于具有记忆和反馈的信道的消息传递、纠错码。研究者使用图形模型研究的工具来共同处理通信复杂性和计算复杂性。

Abstract:The field of distributed networking and computation is on the verge of a technological revolution. Emerging applications in national security, transportation, communication, and commerce require distributed networks to be capable of multi-user communication and collaborative signal and information processing. One very important component of these networks is the underlying communication channel. These channels have memory, are often time-varying, and are often poorly modeled. Furthermore, in many of these networks, the nodes are power limited and only have modest computational resources. Feedback is a very important, though poorly understood, feature of modern communication systems. Feedback is useful because it can increase the capacity of a given channel with memory; it can increase the error exponent and hence decrease latency; it often leads to simpler coding schemes; and it allows the encoder to adapt to unknown channel variations.This research involves: (1) determining the fundamental limits and tradeoffs between the quality of channel feedback and the resulting Shannon capacity of the channel; (2) developing the sequential rate distortion theory for joint-source channel coding; (3) analyzing the convergence and accuracy of message-passing algorithms in general; and (4) developing message-passing, error-correcting codes specialized for channels with memory and feedback. The investigators use tools from the study of graphical models to jointly treat communication complexity and computational complexity.