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

无线网络通过连接地球仪上的数十亿用户，已经成为我们社会不可或缺的一部分。被称为5G的下一代无线网络预计将为越来越多的设备提供数量级更高的数据速率。网络能够向这些进步推进多少的基本限制取决于可用无线频段的数量。为此，无线通信的两个极端，即窄带和宽带变得越来越重要。窄带通信使用一个小频段，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。宽带通信使用极高频率的大范围频率，是向5G移动的用户提供超高数据速率的关键技术。在这两种情况下，信息的各个比特被分配极低的功率用于通信，从而导致具有低容量的逐比特无线信道。这就引入了一系列新的基本问题，关于低容量信道的通信，这是本项目的重点。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开发。最近，无线标准实体3GPP在标准中引入了新协议，以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通过简单地允许大量的块重复来实现，从信道编码的角度来看，这可能是非常次优的。类似的情况出现在宽带场景中。宽带信道基本上可以提供高数据速率（以每秒比特数计）。然而，由于有限的信号功率和较高频率下的较大衰减，各个编码比特经历极低的信噪比。在这两个极端的无线通信中的新兴应用，调查人员的目的是在低容量制度的信道编码的全面调查。本项目的具体目标如下：（1）为低容量下的信道编码提供一个精确的框架，并描述这种情况下信道编码的基本非渐近规律：（2）发展无线宽带和毫米波系统的非渐近分析技术;（3）研究最先进的编码，包括它们的构造、性能和有效解码，以适应低速率机制;（4）针对低容量应用的不同需求，构造高效的级联编码方案，包括编码重复和与低速率代数码的级联。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，以应对窄带和宽带无线系统的挑战。该奖项反映了NSF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.