IEEE Transactions on Information Theory

A Broadcast Approach for Fading Wiretap Channels

Yingbin Liang, Lifeng Lai, H. Vincent Poor, Shlomo Shitz Shamai

Published Jan 24, 2014• 42 citations

Abstract

A (layered) broadcast approach is studied for the fading wiretap channel without the channel state information (CSI) at the transmitter. Two broadcast schemes, based on superposition coding and embedded coding, respectively, are developed to encode information into a number of layers and use stochastic encoding to keep the corresponding information secret from an eavesdropper. The layers that can be successfully and securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The advantage of these broadcast approaches is that the transmitter does not need to know the CSI to the legitimate receiver and the eavesdropper, but the scheme still adapts to the channel states of the legitimate receiver and the eavesdropper. Three scenarios of block fading wiretap channels with stringent delay constraints are studied, in which either the legitimate receiver's channel, the eavesdropper's channel, or both channels are fading. For each scenario, the secrecy rate that can be achieved via the broadcast approach developed in this paper is derived, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also characterized. A notion of probabilistic secrecy, which characterizes the probability that a certain secrecy rate of decoded messages is achieved during one block, is also introduced and studied for scenarios when the eavesdropper's channel is fading. Numerical examples are provided to demonstrate the impact of the CSI at the transmitter and the channel fluctuations of the eavesdropper on the average secrecy rate. These examples also demonstrate the advantage of the proposed broadcast approach over the compound channel approach.

DOI: 10.1109/tit.2013.2293756

Related papers

The broadcast approach over fading Gaussian wiretap channels

Yingbin Liang, Lifeng Lai, H. Vincent Poor +1 more

A (layered) broadcast approach is studied for fading wiretap channels. The basic idea is to employ superposition coding to encode information into a number of layers and use stochastic encoding for each layer to keep the corresponding information secret from an eavesdropper. The legitimate receiver successively decodes information one layer after another by canceling the interference caused by the layers that the receiver has already decoded. The advantage of this approach is that the transmitter does not need to know the channel states to the legitimate receiver and the eavesdropper, but can still securely transmit certain layers of information to the legitimate receiver. The layers that can be securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The Gaussian wiretap channel with fixed channel gains is first studied to illustrate the idea of the broadcast approach. Three cases of block fading wiretap channels with a stringent delay constraint are then studied, in which either the legitimate receiver's channel, the eavesdropper's channel, or both channels are fading. For each case, the secrecy rate that can be achieved by using the broadcast approach is obtained, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also derived.

IEEE Information Theory Workshop (ITW)Oct 1, 200917 citations

Broadcasting over fading wiretap channels

Yingbin Liang, Lifeng Lai, H. Vincent Poor +1 more

Broadcasting over the fading wiretap channel is investigated for the situation without the channel state information (CSI) at the transmitter and subject to a delay constraint. A new broadcast approach is developed, which integrates secure superposition coding studied in the authors' previous work and embedded coding in a hybrid fashion. This scheme outperforms the previous approaches for the cases when the eavesdropper's channel is fading. The secrecy rate achievable via the new broadcast approach is derived, and the structure of the optimal power allocation function across the secure coding layers is characterized via techniques for solving the problem of constrained calculus of variations. A notion of probabilistic secrecy is introduced and studied, which characterizes the probability that a certain secrecy rate is achieved for any given fading block. Numerical examples are provided to demonstrate the impact of CSI at the transmitter if not available and the channel fluctuation of the eavesdropper on the average secrecy rate.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 20124 citations

Comparison of coding strategies for the block fading erasure wiretap channel

Anuradha Wickramasooriya, Ingmar Land, R. Subramanian

In this paper we study the block fading binary erasure wiretap channel, where the transmitter sends secret messages to a legitimate receiver over a block fading erasure channel in the presence of an eavesdropper. The eavesdropper receives the transmitted secret message over a separate block fading binary erasure channel. It is assumed that the transmitter knows the instantaneous channel state information (CSI) of the main channel and knows only the probability distribution of the capacity of the wiretap channel. We mainly consider the case where the transmitter adapts the code based on the CSI of the main channel in order to achieve either a certain secrecy rate or a certain level of secrecy. We compare the two proposed scenarios for the adaptive coding method based on the probability of secrecy outage and the average throughput.

Australian Communications Theory WorkshopJan 1, 20131 citation

Secrecy capacity region of Gaussian broadcast channel

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

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.

Conference on Information Sciences and SystemsMar 1, 200929 citations

Securing Multi-User Broadcast Wiretap Channels With Finite CSI Feedback

Amal Hyadi, Zouheir Rezki, Mohamed‐Slim Alouini

In this work, we investigate the problem of secure broadcasting over block-fading wiretap channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having a finite rate feedback on the throughput of multi-user broadcast wiretap channels. We consider that the transmitter is only provided by a b -bits feedback of the main channel state information (CSI) sent by each legitimate receiver, at the beginning of each fading block, over error-free public links with limited capacity. Also, we assume that the transmitter is aware of the statistics of the eavesdropper's CSI but not of its channel's realizations. Under these assumptions of CSI uncertainty, we characterize the ergodic secrecy capacity of the system when a common message is broadcasted to all legitimate receivers, the ergodic secrecy sum-capacity when multiple independent messages are transmitted, and the ergodic secrecy capacity region for the broadcast channel with confidential messages (BCCM). In all three scenarios, we show that as long as the transmitter has some knowledge of the main CSI, obtained even through a 1-bit CSI feedback, a non-zero secrecy rate can still be achieved. The impact of having the feedback sent over a binary erasure channel (BEC) is also investigated for the BCCM case. Here again, and even with the possibility of having the feedback bits erased, a positive secrecy rate can still be achieved as long as the erasure event is not a probability-one event. An asymptotic analysis of the obtained results is provided for the high SNR regime, and the scaling law of the system, when the number of legitimate receivers is large, is also presented.

arXiv:2004.10023IEEE Transactions on Information TheoryApr 21, 20207 citations

Secrecy Rate Region of the Broadcast Channel with an Eavesdropper

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages to two receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with an eavesdropper. We present an inner bound on the secrecy capacity region for this model. This inner bound is based on a combination of random binning, and the Gelfand-Pinsker binning. We further study the situation in which the channels are degraded. For the degraded broadcast channel with an eavesdropper, we present the secrecy capacity region. Our achievable coding scheme is based on Covers superposition scheme and random binning. We refer to this scheme as the Secret Superposition Scheme. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar Lemma. We then assume that the channels are Additive White Gaussian Noise (AWGN) and show that the Secret Superposition Scheme with Gaussian codebook is optimal. The converse proof is based on Costas entropy power inequality. Finally, we use a broadcast strategy for the slowly fading wire-tap channel when only the eavesdroppers channel is fixed and known at the transmitter. We derive the optimum power allocation for the coding layers, which maximizes the total average rate.

arXiv:0910.3658Oct 19, 200913 citations