Secrecy Capacity of Independent Parallel Channels

Yingbin Liang, H. Vincent Poor, Shlomo Shitz Shamai

The parallel broadcast channel with confidential messages (BCC) is investigated, where a source node transmits to two receivers (receivers 1 and 2) over multiple independent subchannels. The source node has common information for both receivers, and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The secrecy capacity region of the parallel BCC is established. It is shown that independent input distribution for each subchannel is optimal. It is also shown that the secrecy capacity region of the parallel BCC can be larger than the sum of the secrecy capacity regions of the subchannels. The secrecy capacity region is further derived for the parallel BCC with degraded subchannels. Applications of these results to the fading BCC are also discussed.

Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets +3 more

Nir Shlezinger, Daniel Zahavi, Yonathan Murin +1 more

In this paper, we study the secrecy capacity of Gaussian multiple-input multiple-output (MIMO) wiretap channels (WTCs) with a finite memory, subject to a per-symbol average power constraint on the MIMO channel input. MIMO channels with finite memory are very common in wireless communications as well as in wireline communications (e.g., in communications over power lines). To derive the secrecy capacity of the Gaussian MIMO WTC with finite memory, we first construct an asymptotically equivalent block-memoryless MIMO WTC, which is then transformed into a set of parallel, independent, memoryless MIMO WTCs in the frequency domain. The secrecy capacity of the Gaussian MIMO WTC with finite memory is obtained as the secrecy capacity of the set of parallel, independent, memoryless MIMO WTCs, and is expressed as maximization over the input covariance matrices in the frequency domain. Finally, we detail two applications of our result: First, we show that the secrecy capacity of the Gaussian scalar WTC with finite memory can be achieved by waterfilling, and obtain a closed-form expression for this secrecy capacity. Then, we use our result to characterize the secrecy capacity of narrowband powerline channels, thereby resolving one of the major open issues for this channel model.

Ersen Ekrem, Şennur Ulukuş

Elloá B. Guedes, Francisco de Assis, Rex A. C. Medeiros

Nir Shlezinger, Daniel Zahavi, Yonathan Murin +1 more

In this work we study the secrecy capacity of Gaussian multiple-input multiple-output (MIMO) wiretap channels (WTCs) with a finite memory, subject to a per-symbol average power constraint on the MIMO channel input. MIMO channels with finite memory are very common in wireless communications as well as in wireline communications (e.g., in communications over power lines). To derive the secrecy capacity of the Gaussian MIMO WTC with finite memory we first construct an asymptotically-equivalent block-memoryless MIMO WTC, which is then transformed into a set of parallel, independent, memoryless MIMO WTCs in the frequency domain. The secrecy capacity of the Gaussian MIMO WTC with finite memory is obtained as the secrecy capacity of the set of parallel independent memoryless MIMO WTCs, and is expressed as a maximization over the input covariance matrices in the frequency domain. Lastly, we detail two applications of our result: First, we show that the secrecy capacity of the Gaussian scalar WTC with finite memory can be achieved by waterfilling, and obtain a closed-form expression for this secrecy capacity. Then, we use our result to characterize the secrecy capacity of narrowband powerline channels, thereby resolving one of the major open issues for this channel model.