Finite-blocklength information theory

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.