CIF: Small: Collaborative Research: Communications in Ultra-Low-Rate Regime: Fundamental Limits, Code Constructions, and Applications

无线网络通过连接全球数十亿用户，已经成为我们社会不可分割的一部分。下一代无线网络，即5G，预计将为越来越多的设备提供更高数量级的数据速率。网络能在多大程度上实现这些进步的根本限制取决于可用无线频带的数量。为此，无线通信的两个极端，即窄带和宽带变得越来越重要。使用小频段频率的窄带通信可以将数千个设备（例如物联网（IoT）网络中的日常物品）连接到单个蜂窝塔。在极高频率下使用大量频率的宽带通信是向5G移动用户提供超高数据速率的关键支持技术。在这两种情况下，单个信息位被分配极低的通信功率，导致低容量的逐位无线信道。这在低容量信道上的通信方面带来了一系列新的基本问题，而这正是本项目的重点。该项目的成果将有助于信息和编码理论的基础，以及能够实现窄带和宽带通信极限的无线网络的发展。最近，无线标准实体3GPP在标准中引入了新的协议，以便将物联网集成到蜂窝网络中。这些协议的一个主要特点是部署超低速率通信，以满足物联网网络的各种需求。这种低速率通信在标准中是通过简单地允许大量的块重复来实现的，从信道编码的角度来看，这可能是非常不理想的。在宽带场景中也会出现类似的情况。宽带信道基本上可以提供高数据速率，以每秒比特数计算。然而，由于有限的信号功率和较高频率下较大的衰减，单个编码比特的信噪比极低。鉴于这两种极端无线通信的新应用，研究人员旨在对低容量体制下的信道编码进行全面研究。该项目的具体目标如下：(1)为低容量信道编码提供一个精确的框架，并表征该体制下信道编码的基本非渐近规律；(2)开发无线宽带和毫米波系统的非渐近分析技术；(3)研究最先进的代码，包括其结构、性能和有效解码，以适应低速率制度；(4)根据低容量应用的不同需求，构建高效的串联编码方案，包括编码重复和低速率代数编码的串联。因此，该项目在信息理论、编码理论和无线通信之间建立了正式的联系，从而在这些领域之间建立了数学上精确的接口，以解决窄带和宽带无线系统的挑战。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Wireless networks have become an integral part of our society by connecting billions of users around the globe. The next generation wireless networks, known as 5G, are expected to deliver orders of magnitude higher data rates to an ever-increasing number of devices. The fundamental limits on how much networks can be pushed towards these advancements are determined by the amount of available wireless bands. To this end, two extremes of wireless communications have become increasingly important, namely, narrowband and wideband. The narrowband communication, using a small band of frequencies, enables connectivity of thousands of devices, such as everyday objects in Internet-of-Things (IoT) networks, to a single cell tower. Wideband communications, using large swaths of frequencies, at extremely high frequencies is the key enabling technology for delivering ultra-high data rates to 5G mobile users. In both of these scenarios, individual bits of information are assigned extremely low power for communication resulting in bit-wise wireless channels with low capacity. This introduces a new array of fundamental problems with respect to communications over low-capacity channels that is the focus of this project. The results of this project will contribute to the foundation of information and coding theory as well as the development of wireless networks that can achieve the ultimate limits of narrowband and wideband communications.Recently, the wireless standards entity, 3GPP, has introduced new protocols into the standard in order to integrate IoT into the cellular network. A major feature of these protocols is to deploy ultra-low-rate communications in order to address diverse requirements of IoT networks. Such low-rate communication is enabled in the standard by simply allowing a large number of block repetitions, which could be extremely suboptimal from the channel coding perspective. A similar situation arises in wideband scenarios. Wideband channels can essentially provide high data rates, in terms of bits per second. However, individual coded bits experience extremely low signal-to-noise ratios, due to limited signal power and larger attenuations in higher frequencies. In light of the emerging applications in these two extremes of wireless communications, the investigators aim at a comprehensive investigation of channel coding in the low-capacity regime. The specific objectives in this project are as follows: (1) Provide a precise framework for channel coding at low capacity, and characterize fundamental non-asymptotic laws for channel coding in this regime; (2) Develop techniques for the non-asymptotic analysis of wireless wideband and millimeter wave systems; (3) Investigate state-of-the-art codes, including their construction, performance, and efficient decoding, for adaptation to low-rate regimes; (4) Construct efficient concatenated coding schemes including coded repetition and concatenation with low-rate algebraic codes, given diverse requirements of low-capacity applications. Consequently, this project develops a formal connection between information theory, coding theory, and wireless communications resulting in a mathematically precise interface between these areas to address the challenges of narrowband and wideband wireless systems.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.