The Wiretap Channel with Feedback: Encryption over the Channel

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 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. 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 perfect secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.Comment: Submitted to IEEE Transactions on Information Theor

Studying the Dynamical Properties of 20 Nearby Galaxy Clusters

Using SDSS-DR7, we construct a sample of 42382 galaxies with redshifts in the region of 20 galaxy clusters. Using two successive iterative methods, the adaptive kernel method and the spherical infall model, we obtained 3396 galaxies as members belonging to the studied sample. The 2D projected map for the distribution of the clusters members is introduced using the 2D adaptive kernel method to get the clusters centers. The cumulative surface number density profile for each cluster is fitted well with the generalized King model. The core radii of the clusters' sample are found to vary from 0.18 Mpc \mbox{h}^{-1} (A1459) to 0.47 Mpc \mbox{h}^{-1} (A2670) with mean value of 0.295 Mpc \mbox{h}^{-1}. The infall velocity profile is determined using two different models, Yahil approximation and Praton model. Yahil approximation is matched with the distribution of galaxies only in the outskirts (infall regions) of many clusters of the sample, while it is not matched with the distribution within the inner core of the clusters. Both Yahil approximation and Praton model are matched together in the infall region for about 9 clusters in the sample but they are completely unmatched for the clusters characterized by high central density. For these cluster, Yahil approximation is not matched with the distribution of galaxies, while Praton model can describe well the infall pattern of such clusters.Comment: 16 pages, 8 figure

Cognitive Medium Access: Exploration, Exploitation and Competition

This paper establishes the equivalence between cognitive medium access and the competitive multi-armed bandit problem. First, the scenario in which a single cognitive user wishes to opportunistically exploit the availability of empty frequency bands in the spectrum with multiple bands is considered. In this scenario, the availability probability of each channel is unknown to the cognitive user a priori. Hence efficient medium access strategies must strike a balance between exploring the availability of other free channels and exploiting the opportunities identified thus far. By adopting a Bayesian approach for this classical bandit problem, the optimal medium access strategy is derived and its underlying recursive structure is illustrated via examples. To avoid the prohibitive computational complexity of the optimal strategy, a low complexity asymptotically optimal strategy is developed. The proposed strategy does not require any prior statistical knowledge about the traffic pattern on the different channels. Next, the multi-cognitive user scenario is considered and low complexity medium access protocols, which strike the optimal balance between exploration and exploitation in such competitive environments, are developed. Finally, this formalism is extended to the case in which each cognitive user is capable of sensing and using multiple channels simultaneously.Comment: Submitted to IEEE/ACM Trans. on Networking, 14 pages, 2 figure

The Deterministic Capacity of Relay Networks with Relay Private Messages

We study the capacity region of a deterministic 4-node network, where 3 nodes can only communicate via the fourth one. However, the fourth node is not merely a relay since it can exchange private messages with all other nodes. This situation resembles the case where a base station relays messages between users and delivers messages between the backbone system and the users. We assume an asymmetric scenario where the channel between any two nodes is not reciprocal. First, an upper bound on the capacity region is obtained based on the notion of single sided genie. Subsequently, we construct an achievable scheme that achieves this upper bound using a superposition of broadcasting node 4 messages and an achievable "detour" scheme for a reduced 3-user relay network.Comment: 3 figures, accepted at ITW 201

Effect of some nucleating agents on thermal expansion behaviour of Li2O-BaO-Al2O3-SiO2 glasses and glass-ceramics

The thermal expansion behaviour of some glasses and glass-ceramics within the system spodumence (LiAlSi2O6)-celsian (BaAl2Si2O8) containing LiF, TiO2 and Cr2O3 as nucleation catalysts was described. LiF and TiO2 were found to increase the thermal expansion of the glasses investigated, whereas Cr2O3 slightly lowered the expansion coefficient. The dilatometric transition and softening points of the glasses showed the reverse behaviour. The thermal expansion of the glass-ceramics was a function of type and amount of nucleating agent and heat treatment which greatly affected the mineralogical constitution of the materials