Integrated Communication and Binary State Detection Under Unequal Error Constraints

2025-01-31

IEEE Transactions on Communications

AI Summary

This paper addresses binary state detection in integrated sensing and communication (ISAC), introducing, for the first time within an information-theoretic framework, a decoupled treatment of asymmetric error types—false alarms and missed detections—and jointly optimizes communication rate alongside their respective error exponents. We establish a “ternary tradeoff theory” characterizing the optimal frontier among communication rate, false-alarm exponent, and miss-detection exponent. For both static (state-constant) and i.i.d. time-varying state models, we derive asymptotically optimal characterizations: a complete characterization of the optimal ternary tradeoff region for the static case, and an exact achievable region parameterized by the receiver operating characteristic (ROC) curve for the time-varying case. Our approach integrates log-likelihood ratio moment-generating function analysis, broadcast channel coding, and hypothesis testing theory. The results provide the first information-theoretic benchmark for ISAC systems under asymmetric error constraints.

Technology Category

• Machine Learning: Information Theory
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search

Abstract

This work considers a problem of integrated sensing and communication (ISAC) in which the goal of sensing is to detect a binary state. Unlike most approaches that minimize the total detection error probability, in our work, we disaggregate the error probability into false alarm and missed detection probabilities and investigate their information-theoretic three-way tradeoff including communication data rate. We consider a broadcast channel that consists of a transmitter, a communication receiver, and a detector where the receiver's and the detector's channels are affected by an unknown binary state. We consider and present results on two different state-dependent models. In the first setting, the state is fixed throughout the entire transmission, for which we fully characterize the optimal three-way tradeoff between the coding rate for communication and the two possibly nonidentical error exponents for sensing in the asymptotic regime. The achievability and converse proofs rely on the analysis of the cumulant-generating function of the log-likelihood ratio. In the second setting, the state changes every symbol in an independently and identically distributed (i.i.d.) manner, for which we characterize the optimal tradeoff region based on the analysis of the receiver operating characteristic (ROC) curves.

Problem

• Optimal Trade-off
• Communication Speed
• State Detection Errors

Innovation

• Error-rate constrained communication
• False alarm and miss detection
• Optimal trade-off between communication speed and error rates