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systems.Recently, in the context of multi-antenna broadcast channel, the pioneering work [1] showed that completely outdated channel state information at the transmitter is still very useful and increases the degrees of freedom of the multi-user channel.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

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate -average uncertainty-at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger-Tung and the secure source coding setups. Inner and outer bounds on the so called rates-distortion-equivocation region are derived. The inner region turns to be tight for two cases: (i) uncoded side information at Bob and (ii) lossless reconstruction of both sources at Bobsecure distributed lossless compression-. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (resp.) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a nonzero distortion at Bob can be fully exploited to guarantee secrecy.

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Caching appears to be an efficient way to reduce peak hour network traffic congestion by storing some content at the user's cache without knowledge of later demands. Recently, Maddah-Ali and Niesen proposed a two-phase, placement and delivery phase, coded caching strategy for centralized systems (where coordination among users is possible in the placement phase), and for decentralized systems. This paper investigates the same setup under the further assumption that the number of users is larger than the number of files. By using the same uncoded placement strategy of Maddah-Ali and Niesen, a novel coded delivery strategy is proposed to profit from the multicasting opportunities that arise because a file may be demanded by multiple users. The proposed delivery method is proved to be optimal under the constraint of uncoded placement for centralized systems with two files; moreover it is shown to outperform known caching strategies for both centralized and decentralized systems.

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In this work we consider incremental redundancy (IR) hybrid automatic repeat request (HARQ), where transmission rounds are carried out over independent block-fading channels. We propose the so-called multi-packet HARQ where the transmitter allows different packets to share the same channel block. In this way the resources (block) are optimally assigned throughout the transmission rounds.This stands in contrast with the conventional HARQ, where each transmission round occupies the entire block. We analyze superposition coding and time-sharing transmission strategies and we optimize the parameters to maximize the throughput. Besides the conventional one-bit feedback (ACK/NACK) we also consider the rich, multi-bit feedback. To solve the optimization problem we formulate it as a Markov decision process (MDP) problem where the decisions are taken using accumulated mutual information (AMI) obtained from the receiver via delayed feedback. When only one-bit feedback is used to inform the transmitter about the decoding success/failure (ACK/NACK), the Partial State Information Markov Decision Process (PSI-MDP) framework is used to obtain the optimal policies. Numerical examples obtained in a Rayleigh-fading channel indicate that, the proposed multi-packet HARQ outperforms the conventional one, by more than 5 dB for high spectral efficiencies.

The second-order coding rate of the multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channel is studied. We tackle this problem via an information-spectrum approach and statistical bounds based on recent random matrix theory techniques. We derive a central limit theorem (CLT) to analyze the information density in the regime where the block-length n and the number of transmit and receive antennas K and N , respectively, grow simultaneously large. This result leads to the characterization of closed-form upper and lower bounds on the optimal average error probability when the coding rate is within O(1/ √ nK) of the asymptotic capacity. Index Terms-Finite block-length, second-order coding rate, error probability, quasi-static fading channel, block-fading channel , MIMO, information spectrum, random matrix theory.