Some New Results on the Gaussian Wiretap Feedback Channel

Chenxu Wei,Linman Yu,Bin Dai

doi:10.3390/e21090817

Abstract

In this paper, the Gaussian wiretap feedback channel is revisited, and some new results on its secrecy capacity are obtained. To be specific, first, we show that the Schalkwijk–Kailath (SK) feedback scheme, which achieves the secrecy capacity of the degraded Gaussian wiretap feedback channel, also achieves the secrecy capacity of the non-degraded Gaussian wiretap feedback channel. Second, applying the existing secret key-based feedback schemes to Gaussian wiretap feedback channels, we derive some new lower bounds on the secrecy capacities of these models. Finally, we compare the performances of the above feedback schemes in the degraded and non-degraded Gaussian wiretap feedback channels and show which feedback scheme performs better for these channel models.

Highlights

In recent years, mobile wireless communication has been widely used and has become an essential part in people’s daily life
The research on Physical layer security (PLS) in communication systems started from Wyner’s outstanding work on the degraded wiretap channel (DWTC) [1], where a transmitter broadcasts its message M over N channel uses to a legitimate receiver and an eavesdropper via a degraded broadcast channel, and the perfect secrecy is guaranteed if the information leakage rate N1 I ( M; Z N ), where Z N denotes the received output at the eavesdropper, vanishes as the transmitted codeword length N tends to infinity
Another definition of the perfect secrecy is strong secrecy, which is defined as the information leakage I ( M; Z N ) at the wiretapper vanishes as N tends to infinity.).The secrecy capacity, defined as the channel capacity under the weak secrecy constraint, was established in [1]

Summary

Introduction

Mobile wireless communication has been widely used and has become an essential part in people’s daily life. Since the transmitter knows the legitimate receiver’s channel output via the noiseless feedback channel, the work in [8] showed that generating the secret key from the legitimate receiver’s channel output and using it to encrypt the transmitted message help to increase the secrecy capacity of the WTC. The work in [10] extended the WTC with rate-limited feedback [9] to a broadcast case, where one secret message is sent to two legitimate receivers via a general broadcast wiretap channel, and two legitimate receivers independently send their secret keys to the transmitter via two noiseless feedback channels. The work in [17] showed that for feedback communication systems, a better use of the channel output feedback is to produce a secret key, and a helping message from it, and such a helping message improves the legitimate receiver’s decoding performance.

The Non-Degraded Gaussian Wiretap Feedback Channel

Comparison of the Already Existing Feedback Schemes for the Gaussian Wiretap

Conclusions