In this paper we study the problem of half-duplex active eavesdropping in fast fading channels. The active eavesdropper is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping the transmission between the legitimate parties (Ex mode), and jamming it (Jx mode) -- the active eavesdropper cannot function in full duplex mode. We consider a conservative scenario, when the active eavesdropper can choose its strategy based on the legitimate transmitter-receiver pair's strategy -- and thus the transmitter and legitimate receiver have to plan for the worst. We show that conventional physical-layer secrecy approaches perform poorly (if at all), and we introduce a novel encoding scheme, based on very limited and unsecured feedback -- the Block-Markov Wyner (BMW) encoding scheme -- which outperforms any schemes currently available.
A great number of recent works have been fueled by the still growing interest in physical layer secrecy. Most of them attempt to overcome the limitations of the classical wiretapper/eavesdropper scenarios of [1] or [2] (namely that no secret message can be successfully transmitted if the eavesdropper's channel is less noisy than the legitimate receiver's channel) by using some form of diversity.
The benefits of the ergodic-fading diversity upon the achievable secrecy rates have been exposed by works like [3], [4], [5] or [6]. A fast-fading eavesdropper channel is studied in [3] under the assumption that the main channel is a fixed-SNR additive white Gaussian noise (AWGN) channel. Although the secrecy capacity for fast-fading eavesdropper channels is still unknown, [3] provides achievable secrecy rates and shows that sometimes noise injection at the transmitter can improve these rates.
The different approach of [4] models both the main and the eavesdropper channels as ergodicly-fading AWGN channels. However, the fading is assumed to be slow enough to be considered constant for infinitely long blocks of transmitted symbols. The secrecy capacity is derived for this model, and the achievability part is proved by using separate channel encoding for each of the blocks. A similar approach is taken in [5] and [6], where the fading broadcast channel with confidential messages (BCC) is considered equivalent to a parallel AWGN BCC.
However, the slow fading ergodic channel model is quite restrictive. Although the model can be artificially created by a multiplexing/demultiplexing architecture as in [7], it still requires either coarse quantization or long delays (e.g. under fine quantization, for a channel state with low probability it may take a very large number of transmitted symbols to enable almost-error-free decoding).
With these considerations, we focus instead on a more practical scenario where both the main and the eavesdropper’s channel are affected by fast stationary fading. However, unlike [3], we are concerned with a much stronger adversary: a halfduplex active eavesdropper.
In our channel model, depicted in Figure 1, the eavesdropper (Eve) has two options: either to jam the conversation between the legitimate transmitter (Alice) and the legitimate receiver (Bob) -Jx mode -or to eavesdrop -Ex mode -(our eavesdropper cannot function in full duplex mode, i.e. she cannot transmit and receive on the same frequency slot, at the same time). Both Alice and Eve (in Jx mode) are constrained by average (over each codeword) power budgets P and J , respectively. Eve’s purpose is to minimize the secrecy rate achievable by Alice, and to that extent she has to decide on the optimal alternation between the jamming mode and the eavesdropping mode. The state of each of the main and eavesdropper channels, i.e. the absolute squared channel coefficients (or simply “the channel coefficients” hence forth), which we denote by h M and h W , respectively, are assumed to be available to the respective receivers. However, Bob does not know the exact state of Eve’s channel, nor does Eve have any information about Bob’s channel, except its statistics. In addition to fading, each channel is further distorted by an independent additive white complex Gaussian noise of variance σ 2 N . There exists a low-rate, unprotected (i.e. public) feedback channel between Bob and Alice.
The present paper is limited to the following simplifying (although not uncommon) assumptions.
i) Rayleigh fading: h M and h W are exponentially distributed, with parameters λ M and λ W respectively.
ii) The channel that links Eve (when in Jx mode) and Bob is error free and does not experience fading [8], [9].
iii) Eve only uses white Gaussian noise for jamming [10], [8], since this is the most harmful uncorrelated jamming strategy [11]. iv) Eve’s exact jamming strategy (i.e. when and with what power she jams) is perfectly known to Bob (a posteriori) 1 so that Bob can employ coherent detection and communicate Eve’s strategy to Alice, via the low-rate feedback link.
v) The instantaneous state of the main channel cannot be known to the transmitter Alice non-causally.
vi) The codewords are long enough such that not only the channel fading, but also the combination of channel fluctuation and Eve’s alternation between jamming and eavesdropping display ergodic properties over the duration of a codeword.
vii) Eve employs an ergodic strategy, i.e. she uses the same statistics for alternating between Jx mode and Ex mode for every codeword.
viii) Eve has access to the exact value of h W only after she made her decision to eavesdrop (Ex mode), and has no information about the value(s) that h W might take while she is in Jx mode. This scenario models a situation where the training sequences, which are transmitted by Alice at a low rate, and are used by Bob to estimate the channel coefficient before the transmission of a block of symbols, are protected against eavesdro
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