Secrecy capacity region of Gaussian broadcast channel

Abstract

1 Abstract-In this paper, we first consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-taper also receives the transmitted signal. We assume that the signals are transmitted over additive white Gaussian noise channels. We characterize the secrecy capacity region of this channel. Our achievable coding scheme is based on superposition coding and the random binning. We refer to this scheme as Secret Superposition Coding. The converse proof combines the converse proof for the conventional Gaussian broadcast channel and the perfect secrecy constraint. This capacity region matches the capacity region of the broadcast channel without security constraint. It also matches the secrecy capacity of the wire-tap channel. Based on the rate characterization of the secure Gaussian broadcast channel, we then use a multilevel coding approach for the slowly fading wire-tap. We assume that the transmitter only knows the eavesdropper's channel. In this approach, source node sends secure layered coding and the receiver viewed as a continuum ordered users. We derive optimum power allocation for the layers which maximizes the total average rate.

The secrecy capacity of the semi-deterministic broadcast channel

“…where (26) follows from (19) and (21), and (27) follows from the fact that the random variables satisfy (6).…”

On the MISO compound wiretap channel

“…In recent times that has been a significant interest in applying this model to wireless communication systems. Some recent works include secure communications over fading channels [2]- [4], multi-antenna wiretap channels [5]- [13] and several multiuser channels.…”

“…In addition we provide lower bounds based on time-sharing and noise transmission strategies and show that in some special cases these bounds can be further improved using signal alignment and multilevel coding strategies. While our analysis is restricted to the MISO wiretap channel, we expect techniques developed in deriving upper and lower bounds to be applicable to related problems such as the compund extension of the MIMO wiretap channel, the two receiver broadcast channel with mutually confidential messages [9] and the multi-receiver broadcast channel with an external wiretapper [12], [13]. We note that recently signal and interference alignment schemes have been used in the wiretap channel literature in e.g.…”

Secrecy capacity region of the Gaussian multi-receiver wiretap channel

“…As we will show in the sequel, any Gaussian multi-receiver wiretap channel can be regarded as a degraded multi-receiver wiretap channel, whose secrecy capacity region is known in a single-letter form [4]- [6]. This single-letter expression involves auxiliary random variables which need to be identified to establish the secrecy capacity region.…”