New Result on the Feedback Capacity of the Action-Dependent Dirty Paper Wiretap Channel

The Gaussian wiretap channel with noncausal state interference available at the transmitter, which is also called the dirty paper wiretap channel (DP-WTC), has been extensively studied in the literature. Recently, it has been shown that taking actions on the corrupted state interference of the DP-WTC (also called the action-dependent DP-WTC) helps to increase the secrecy capacity of the DP-WTC. Subsequently, it has been shown that channel feedback further increases the secrecy capacity of the action-dependent DP-WTC (AD-DP-WTC), and a sub-optimal feedback scheme is proposed for this feedback model. In this paper, a two-step hybrid scheme and a corresponding new lower bound on the secrecy capacity of the AD-DP-WTC with noiseless feedback are proposed. The proposed new lower bound is shown to be optimal (achieving the secrecy capacity) and tighter than the existing one in the literature for some cases, and the results of this paper are further explained via numerical examples.

A Capacity-Achieving Feedback Scheme of the Gaussian Multiple-Access Channel with Degraded Message Sets

The classical Schalkwijk–Kailath (SK) scheme for the point-to-point white Gaussian channel with noiseless feedback plays an important role in information theory due to the fact that it is capacity-achieving and the complexity of its encoding–decoding procedure is extremely low. In recent years, it has been shown that an extended SK feedback scheme also achieves the capacity region of the two-user Gaussian multiple-access channel with noiseless feedback (GMAC-NF), where two independent messages are, respectively, encoded by two intended transmitters. However, for the two-user GMAC-NF with degraded message sets (one common message for both users and one private message for an intended user), the capacity-achieving feedback scheme remains open. In this paper, we propose a novel two-step SK-type feedback scheme for the two-user GMAC-NF with degraded message sets and show that this scheme is capacity-achieving.

Feedback Schemes for the Action-Dependent Wiretap Channel with Noncausal State at the Transmitter

In this paper, we propose two feedback coding schemes for the action-dependent wiretap channel with noncausal state at the transmitter. The first scheme follows from the already existing secret key based feedback coding scheme for the wiretap channel. The second one follows from our recently proposed hybrid feedback scheme for the wiretap channel. We show that, for the action-dependent wiretap channel with noncausal state at the transmitter, the second feedback scheme performs better than the first one, and the capacity results of this paper are further explained via a Gaussian example, which we call the action-dependent dirty paper wiretap channel with noiseless feedback.