Secrecy Capacity of a Gaussian Wiretap Channel with One-bit ADCs is Always Positive

摘要

We consider the Gaussian wiretap channel with onebit analog-to-digital converters (ADCs) at both the legitimate receiver and the eavesdropper. In this channel, we show that a positive secrecy rate is always achievable whenever the noise power n₁² at the legitimate receiver is not the same as the noise power n₂² at the eavesdropper. A binary phase-shift keying (BPSK) and an asymmetric BPSK are shown to achieve a positive secrecy rate for the cases of n₁ <; n₂ and n₁ > n₂, respectively. We partially justify the choice of these signalings by showing that the optimal input distribution that achieves R_s* := sup_PX:E[X2]≤P I(X; Y₁) - I(X; Y₂), where X is the channel input with power constraint of P, and Y₁ and Y₂ are the channel outputs at the legitimate receiver and the eavesdropper, respectively, should satisfy some symmetric and asymmetric properties for the cases of n₁ <; n₂ and n₁ > n₂, respectively. Moreover, for n₁ <; n₂ and sufficiently large P, it is shown that a BPSK using power smaller than P achieves R_s*.