The degrees of freedom (DoF) of the two-user Gaussian multiple-input and multiple-output (MIMO) broadcast channel with confidential message (BCC) is studied under the assumption that delayed channel state information (CSI) is available at the transmitter. We characterize the optimal secrecy DoF (SDoF) region and show that it can be achieved by a simple artificial noise alignment (ANA) scheme. The proposed scheme sends the confidential messages superposed with the artificial noise over several time slots. Exploiting delayed CSI, the transmitter aligns the transmit signal in such a way that the useful message can be extracted at the intended receiver but is completely drowned by the artificial noise at the unintended receiver. The proposed scheme can be interpreted as a non-trivial extension of Maddah-Ali Tse (MAT) scheme and enables us to quantify the resource overhead, or equivalently the DoF loss, to be paid for the secrecy communications. DRAFT 3 a general CSIT assumption. In other words, if the statistics of the underlying channels seen by both receivers are symmetrical, additional side information (not necessarily instantaneous CSIT) is essential to ensure a positive SDoF, by introducing some asymmetry at the encoder. As a matter of fact, this reveals one of the major limitations of the wiretap model whose performance strongly depends on the quality of the channel state information at the transmitter side. Evidently, theoretically addressing CSI issues is of fundamental impact for secrecy systems.Recently, in the context of multi-antenna broadcast channel, the pioneering work [1] showed that completely outdated channel state information at the transmitter is still very useful and increases the degrees of freedom of the multi-user channel. Motivated by this exciting result, the new assumption, commonly referred to as delayed CSIT, has since been applied to several multi-user settings, including the MIMO broadcast channel, X channel, and interference channel [12]- [15]. Non-trivial gain of degrees of freedom have been shown in all these settings with delayed CSIT. The main idea behind the utility of delayed CSIT can be best described with the term "retrospective interference alignment" introduced in[13] and [16]. That is, the knowledge of causal channel state is used to align the interference between users into a spatial/temporal subspace with a reduced dimension at each receiver.In this paper, we study the impact of delayed CSIT on the secrecy degrees of freedom in a MIMO broadcast channel. In our setting, delayed CSI of a given receiver is available both at the transmitter and the other receiver 2 , whereas each receiver knows its own instantaneous channel. Such a scenario is of practical interest since the receivers may send their channel states to the transmitter via delayed feedback links that may be overheard by the other receivers. We first characterize the optimal SDoF of the Gaussian MIMO wiretap channel with delayed CSIT. It is shown that delayed CSIT can significantly improve the SDoF, provided that ...

Caching is an efficient way to reduce network traffic congestion during peak hours, by storing some content at the user's local cache memory, even without knowledge of user's later demands. Maddah-Ali and Niesen proposed a two-phase (placement phase and delivery phase) coded caching strategy for broadcast channels with cache-aided users. This paper investigates the same model under the constraint that content is placed uncoded within the caches, that is, when bits of the files are simply copied within the caches. When the cache contents are uncoded and the users' demands are revealed, the caching problem can be connected to an index coding problem. This paper focuses on deriving fundamental performance limits for the caching problem by using tools for the index coding problem that were either known or are newly developed in this work.First, a converse bound for the caching problem under the constraint of uncoded cache placement is proposed based on the "acyclic index coding converse bound." This converse bound is proved to be achievable by the Maddah-Ali and Niesen's scheme when the number of files is not less than the number of users, and by a newly derived index coding achievable scheme otherwise. The proposed index coding achievable scheme is based on distributed source coding and strictly improves on the widely used "composite (index) coding" achievable bound and its improvements, and is of independent interest.An important consequence of the findings of this paper is that advancements on the coded caching problem posed by Maddah-Ali and Niesen are thus only possible by considering strategies with coded placement phase. A recent work by Yu et al has however shown that coded cache placement can at most half the network load compared to the results presented in this paper.Index Terms-Coded caching; uncoded cache placement; index coding; distributed source coding.The results of this paper were presented in parts at the following conferences: the IEEE