Bounds on the Ergodic Secret-Key Capacity for Dependent Fading Channels.

L. Srividya, Pattipati Naga Sudha

Matthieu R. Bloch, J. Nicholas Laneman

In this paper, we investigate the effect of partial channel state information on the achievable secure communication rates and secret-key generation rates over ergodic fading channels. In particular, we establish the strong secret-key capacity as well as lower bounds for the strong secrecy capacity of ergodic and block-ergodic fading channels with partial Channel State Information at the Transmitter(CSIT). Our analysis sheds light on the usefulness of CSIT to harness the benefits of fading for secrecy and allows us to quantify the penalty incurred by the lack of full CSIT. In particular, we numerically illustrate situations in which little CSIT is required to recover most of the benefits of fading and in which the legitimate terminals have an incentive to precisely characterize their channel.

Dengke Guo, Dongtang Ma, Jun Xiong +2 more

Secret-key generation (SKG) at physical layer is considered as a promising solution for lightweight key distribution. On the analysis of the secret-key capacity over multipath fading channels, existing studies generally neglect the channel observation method, which has a direct impact on the secret-key capacity. Moreover, there is a lack of concise and interpretable expressions for the secret-key capacity based on the channel state information. Motivated by the above, we analyze the performance of SKG based on MMSE estimation of channel impulse response over multipath fading channels. The general expression of secret-key capacity is derived. We find that the secret-key capacity depends on the estimation signal-to-noise ratios (SNRs) of channel-tap gains. Then, the condensed-parameter expressions of exact secret-key capacity and the expressions of asymptotic secret-key capacity at high SNR are derived in two specific PDP cases. We show that the bandwidth and the transmission SNR determine the upper bound of secret-key capacity over channels with different degrees of freedom for the flat PDP case. In addition, we find that the asymptotic secret-key capacities under these two PDPs follow a uniform form, which is a linear function of the channel estimation SNR (in dB). Finally, we simulate the channel probing process under different transmission and channel parameters and exploit the simulated channel estimates to estimate the secret-key capacity through numerical methods. The simulation results demonstrate the theoretical analysis and conclusions.

隆太郎 松本, Ryutaroh Matsumoto

友彦 植松, Tomohiko Uyematsu

Zouheir Rezki, Ashish J. Khisti, Mohamed‐Slim Alouini

We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers. We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free feedback channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q = 1. We also show that the lower and the upper bounds coincide asymptotically as q → ∞. Finally, asymptotic analysis at high Signal-to-Noise Ratio (SNR) are presented where it is found that the capacity is bounded at high-SNR and present a simple suboptimal scalar quantizer that is capacity achieving, without the need of any numerical optimization, as q → ∞. When applied to Rayleigh fading channels, we show that, at high-SNR, a 4-bit feedback achieves 90% of the secrecy capacity when perfect main CSI is available at the transmitter.