As a result, both the proposed sum-SDoF upper and lower bounds are tighter than the existing sum-SDoF upper and lower bounds, respectively. To eliminate the redundant equations in security analysis, this approach first identifies the constituent equations, and then analyzes the rank of assemble of them. For these two schemes, we propose the redundancy reduction approach for security analysis, by which the minimal duration of artificial noise transmission phase of the scheme is obtained. Then, for the sum-SDoF lower bound, we leverage the artificial noise transmission and interference re-transmission to design two transmission schemes, which have holistic and sequential higher-order symbol generation, respectively. Firstly, we derive the sum-SDoF upper bound by means of statistical equivalence property, security constraints, and permutations. Specifically, we obtain non-trivial sum-SDoF upper and lower bounds. This paper investigates the sum-secure degrees-of-freedom (SDoF) of three-user multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). To the best of our knowledge, this is the first result on the K-user interference channel with secrecy constrained models and delayed CSIT that achieves an SDoF which scales with K, square-root of number of users. We show that for the K-user IC-EE, 1 2 ( K - 3 ) SDoF is achievable, and for the K-user IC-CM-EE, 1 2 ( K - 6 ) is achievable. We present our achievable scheme for three models, namely: (1) K-user interference channel with confidential messages (IC-CM), and we show that 1 2 ( K - 6 ) SDoF is achievable (2) K-user interference channel with an external eavesdropper (IC-EE) and 3) K-user IC with confidential messages and an external eavesdropper (IC-CM-EE). These phases are designed to ensure the decodability of the desired messages while satisfying the secrecy constraints. In the next phase, each transmitter uses the delayed CSIT of the previous phase and sends a function of the net interference and artificial noises (generated in previous phase), which is simultaneously useful for all receivers. Our scheme works over two phases: Phase one, in which each transmitter sends information symbols mixed with artificial noises, and repeats such transmission over multiple rounds. Achieving positive secure degrees of freedom (SDoF) is challenging due to the delayed nature of CSIT, and the distributed nature of the transmitters. We propose a novel secure retrospective interference alignment scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality.
Many other features are provided, you can see most of them in the dedicated section.In this paper, the K-user interference channel with secrecy constraints is considered with delayed channel state information at transmitters (CSIT).
#Latexit alognment code#
Moreover, for the compatible formats, you can reopen the equation to modify it : the LaTeX code is kept inside. The result is automatically cropped and you can drag and drop it in any application, in the desired format (certainly PDF). With LaTeXiT, you only focus on your equation. This is to get rid of that burden that LaTeXiT was created. restart from the beginning if you want to modify a little thing in the equation.īalking is forgiven.delete or backup the files you have just used.But to be honest, you don't really want to go though all of the following steps just to illustrate a document : Then you are given a great power to compose equations, from the simplest to the most complex ones, with a perfect result. You are maybe familiar with the LaTeX language. However, its large set of features is a reason to see it as an editor this is the goal in fact. This is not the plain truth, since LaTeXiT is "simply" a graphical interface above a LaTeX engine. Should LaTeXiT be categorized, it would be an equation editor.
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