# Exploring ISAC: Information-Theoretic Insights
## 1 Introduction  
Integrated sensing and communication (ISAC) represents a transformative paradigm that unifies sensing and communication functionalities into a single system, leveraging shared spectral, hardware, and computational resources. This integration is increasingly crucial in modern technological ecosystems, where efficient resource utilization and enhanced system performance are paramount. ISAC offers notable benefits in applications such as autonomous vehicles, industrial automation, smart cities, and wireless networks. By reducing latency, improving spectral efficiency, and enhancing situational awareness, ISAC is foundational to emerging technologies like 6G communication and the Internet of Things (IoT). Its dual-purpose design minimizes infrastructure costs while enabling seamless interaction between sensing and communication, paving the way for adaptive and intelligent systems. As an example of a practical ISAC system, we can consider Wi-Fi technology. Based on the IEEE 802.11 standards, it has delivered significant social and economic benefits. Recently, attention has turned to WLAN sensing--also known as Wi-Fi sensing--which leverages the widespread Wi-Fi infrastructure and ubiquitous signals in our environment to perform various sensing tasks. By employing advanced signal processing techniques, received Wi-Fi signals can be used to detect obstructions, monitor environmental changes, and interpret target movement. Despite these innovations and progress, several challenges remain in current standardization efforts, as evidenced by ongoing work towards IEEE 802.11 bf for WLAN sensing and ISAC [1]. In general, designing effective ISAC systems involves achieving simultaneous high-performance sensing and communication. Advanced configurations, such as bi-static radar or multi-terminal ISAC systems, require efficient exchange of sensing information between terminals to enhance collective sensing capabilities rather than relying solely on local data. Furthermore, modern ISAC applications impose additional constraints, such as privacy and security. Balancing these competing requirements necessitates an understanding of the tradeoffs and fundamental performance limits across various system criteria. Information theory has a rich history and provides a robust framework for analyzing such complex multi-purpose systems and revealing the inherent tensions and tradeoffs in the fundamental limits of the various performances of such systems. Fundamental results from the information theory literature for communication (e.g., data rate, capacity) [2; 3; 4; 5; 6; 7], detection and hypothesis testing [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20], estimation [21; 22; 23; 24], and compression [25; 26; 27; 28; 29; 30; 31] indeed can form the foundation for analyzing ISAC systems. Prior studies have explored tradeoffs between these performance measures in both distributed and non-distributed setups. Some ISAC scenarios, though not explicitly named as such, have been studied within the information-theoretic community under related contexts like \"simultaneous data communication and state estimation\". Other scenarios remain unexplored but can benefit from information-theoretic insights derived from analogous setups. This article aims to synthesize and present both established and emerging information-theoretic results relevant to ISAC systems. Compared to many existing overview ISAC articles that tackle the problem more from a communication and signal processing angle [32; 33; 34; 35; 36; 37; 38; 39; 40; 41], here we focus on information-theoretic results that are more closely aligned with [42; 43]. Specifically, we focus on the inherent tradeoffs and fundamental performance limits of ISAC systems, emphasizing coding techniques and proof strategies that enable optimal sensing-communication tradeoffs. We would like to point out that the information-theoretic models studied in this survey are very general, and can be specialized to different practical scenarios of interest.