In this work, the role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is investigated. A model is considered in which the feed-forward and feedback signals share the same noisy channel. More specifically, a discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that a judicious use of feedback increases the perfect secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. Then a half-duplex system is considered, for which a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source.
In this work, the role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is investigated. A model is considered in which the feed-forward and feedback signals share the same noisy channel. More specifically, a discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that a judicious use of feedback increases the perfect secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. Then a half-duplex system is considered, for which a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source.
In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-Lambda channel where it is shown that the secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.
Most practical communication links are bidirectional. In these models, since the source node also receives signals, its encoder has the option of computing its output based on the signals it received in the past. On the other hand, from a practical point of view, it would also be desirable to identify the cases where such an encoder design may not improve communication rates. This question is particularly interesting for the case where the transmitted messages and the feedback signals are subject to eavesdropping. In this paper, we investigate the question of how much impact the feedback has on the secrecy capacity by studying two fundamental models. First, we consider the Gaussian two-way wiretap channel and derive an outer bound for its secrecy capacity region. We show that the secrecy rate loss can be unbounded when feedback signals are not utilized except for a special case we identify, and thus conclude that utilizing feedback can be highly beneficial in general. Second, we consider a half-duplex Gaussian two-way relay channel where the relay node is also an eavesdropper, and find that the impact of feedback is less pronounced compared to the previous scenario. Specifically, the loss in secrecy rate, when ignoring the feedback, is quantified to be less than 0.5 bit per channel use when the relay power goes to infinity. This achievable rate region is obtained with simple time sharing along with cooperative jamming, which, with its simplicity and near optimum performance, is a viable alternative to an encoder that utilizes feedback signals.
It is well-known that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this work, an achievable scheme for the wiretap channel with generalized feedback -based on joint source-channel coding- is presented. This scheme recovers previous results, thus it can be seen as a generalization and unification of several results in the field. Additionally, the Gaussian wiretap channel with noisy feedback is analyzed, and the scheme achieves positive secrecy rates even in unfavorable situations where the eavesdropper experiences a much better channel than the legitimate user.
The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)
A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not larger than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively broadcast random keys over insecure channels is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with log SNR. The pre-log factor of the secrecy rate, i.e. the secure degree of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes.
In this paper, the k-th order autoregressive moving average (ARMA(k)) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that a variant of the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. As the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.