Collaborative Research: Code Design and Analysis to Approach Capacity with Short Blocklengths Using Feedback

本研究描述了反馈在沟通中的好处，并开发了实现这些好处的技术。今天的通信系统力求尽可能快地将信息从发射机转移到接收机。这项研究涉及到使用反馈（从接收器发送回发射器的消息）来允许通信系统使用更少的传输时间（延迟）和更低复杂度的解码来接近最高可能的通信速率（信道容量）。这项研究的一个关键方面是开发新的错误控制代码和新技术，使用这些代码来促进传输，以比不使用反馈的系统低得多的延迟接近容量。更广泛的影响包括通过加州大学洛杉矶分校工程（HSSEAS）高中暑期研究项目培训高中生，通过加州大学洛杉矶分校工程本科研究项目培训本科生。传统的技术通过使用长块长度和复杂的解码来获得无反馈的容量。然而，信息理论表明，反馈允许用更短的块长度和更简单的解码来接近容量。本研究采用了一种速率兼容的球体填充分析，提供了一种反馈减少延迟的定量分析。该分析提供了解码错误轨迹，指导开发速率兼容的代码族，以接近具有反馈的容量。这些具有反馈的速率兼容码族的实际好处将在典型的工作在加性高斯白噪声中的无线通信系统的背景下进行描述。这些技术被扩展到衰落信道和高阶调制。这个研究项目的总体目标是开发和传播一种基本的理解，即应该如何设计代码族来与反馈一起工作，以实现非常短块长度的容量。

This research characterizes the benefits of feedback in communication and develops techniques to achieve those benefits. Today's communication systems seek to move information as rapidly as possible from transmitter to receiver. This research involves using feedback (messages sent from the receiver back to the transmitter) to allow communication systems to approach the highest possible communication rate (the channel capacity) using less transmission time (latency) and lower-complexity decoding. A key aspect of this research is the development of new error control codes and new techniques to use those codes to facilitate transmissions that approach capacity with much lower latency than systems that do not use feedback. Broader impacts include training high school students through the UCLA Engineering (HSSEAS) High School Summer Research program and training undergraduates through the UCLA Engineering undergraduate research program.Traditional techniques approach capacity without feedback by using long block lengths and complex decoding. However, information theory indicates that feedback permits capacity to be approached with shorter block lengths and simpler decoding. This research employs a rate-compatible sphere-packing analysis to provide a quantitative analysis of the latency reduction possible with feedback. This analysis provides decoding error trajectories that guide the development of rate-compatible code families needed to approach capacity with feedback. Practical benefits of these rate-compatible code families with feedback will be characterized in the context of a typical wireless communication system operating in additive white Gaussian noise. These techniques are extended to fading channels and higher-order modulations. The overall goal of this research project is the development and promulgation of a fundamental understanding of how code families should be designed to work with feedback to achieve capacity with very short block lengths.