Achievable Rates of Attack Detection Strategies in Echo-Assisted Communication

We consider an echo-assisted communication model wherein block-coded messages, when transmitted across several frames, reach the destination as multiple noisy copies. We address adversarial attacks on such models wherein a subset of the noisy copies are vulnerable to manipulation by an adversary. Particularly, we study a non-persistent attack model with the adversary attacking 50% of the frames on the vulnerable copies in an i.i.d. fashion. We show that this adversarial model drives the destination to detect the attack locally within every frame, thereby resulting in degraded performance due to false-positives and miss-detection. Our main objective is to characterize the mutual information of this adversarial echo-assisted channel by incorporating the performance of attack-detection strategies. With the use of an imperfect detector, we show that the compound channel comprising the adversarial echo-assisted channel and the attack detector exhibits memory-property, and as a result, obtaining closed-form expressions on mutual information is intractable. To circumvent this problem, we present a new framework to approximate the mutual information by deriving sufficient conditions on the channel parameters and also the performance of the attack detectors. Finally, we propose two attack-detectors, which are inspired by traditional as well as neural-network ideas, and show that the mutual information offered by these detectors is close to that of the Genie detector for short frame-lengths.