Traditional asymptotic information-theoretic studies of the fundamental limits of wireless communication systems primarily rely on some ideal assumptions, such as infinite blocklength and vanishing error probability. While these assumptions enable tractable mathematical characterizations, they fail to capture the stringent requirements of some emerging next-generation wireless applications, such as ultra-reliable low latency communication and ultra-massive machine type communication, in which it is required to support a much wider range of features including short-packet communication, extremely low latency, and/or low energy consumption. To better support such applications, it is important to consider finite-blocklength information theory. In this paper, we present a comprehensive review of the advances in this field, followed by a discussion on the open questions. Specifically, we commence with the fundamental limits of source coding in the non-asymptotic regime, with a particular focus on lossless and lossy compression in point-to-point~(P2P) and multiterminal cases. Next, we discuss the fundamental limits of channel coding in P2P channels, multiple access channels, and emerging massive access channels. We further introduce recent advances in joint source and channel coding, highlighting its considerable performance advantage over separate source and channel coding in the non-asymptotic regime. In each part, we review various non-asymptotic achievability bounds, converse bounds, and approximations, as well as key ideas behind them, which are essential for providing engineering insights into the design of future wireless communication systems.

翻译：传统的无线通信系统基本极限的渐近信息论研究主要依赖于一些理想假设，例如无限块长和趋于零的错误概率。虽然这些假设使得数学刻画易于处理，但它们未能捕捉到某些新兴的下一代无线应用的严格要求，例如超可靠低时延通信和超大规模机器类通信，这些应用需要支持更广泛的特性，包括短包通信、极低时延和/或低能耗。为了更好地支持此类应用，考虑有限块长信息论至关重要。本文对该领域的进展进行了全面综述，并对开放性问题进行了讨论。具体而言，我们从非渐近域中源编码的基本极限入手，特别关注点对点（P2P）和多终端情况下的无损与有损压缩。接着，我们讨论了P2P信道、多址信道以及新兴的大规模接入信道中信道编码的基本极限。我们进一步介绍了联合信源信道编码的最新进展，强调了其在非渐近域中相较于分离信源信道编码的显著性能优势。在每一部分中，我们回顾了各种非渐近可达界、逆界及其近似，以及它们背后的关键思想，这些对于为未来无线通信系统的设计提供工程洞见至关重要。