Finite Blocklength Approach and Its Security Analysis for the Dirty-Tape Channel With Noiseless/Noisy Feedback

The classical Schalkwijk-Kailath (SK) scheme, which achieves the capacity of the additive white Gaussian noise (AWGN) channel with noiseless feedback, is also shown to be an excellent secure finite blocklength (FBL) coding scheme for the AWGN wiretap channel with noiseless feedback. In this paper, the dirty tape channel (AWGN channel with Gaussian state interference causally known by the transmitter) with noiseless/noisy feedback is investigated. First, SK-type feedback schemes are proposed for this model by introducing a lattice-based strategy into the classical SK scheme, and it is shown that this strategy helps to eliminate the impact of the state interference and the feedback channel noise on the performance of the SK scheme. Then, we analyze the security performance of the proposed schemes, in particular, for the dirty tape channel with noisy feedback and eavesdropper, we give a lower bound on the normalized eavesdropper’s equivocation by establishing a novel inequality about the differential entropy of the Gaussian modulo-lattice function. Finally, performances of our proposed schemes are further explained by numerical examples.