On the achievability of the degrees of freedom for the three-cell MIMO interfering broadcast channel with minimum spatial dimensions

2013 ◽  
Author(s):  
Ahmed Medra ◽  
Timothy N. Davidson
Keyword(s):  
Degrees Of Freedom ◽  
Broadcast Channel ◽  
Spatial Dimensions

scholarly journals Degrees of Freedom of Time Correlated MISO Broadcast Channel With Delayed CSIT

2013 ◽  
Vol 59 (1) ◽  
pp. 315-328 ◽  
Author(s):  
Sheng Yang ◽  
Mari Kobayashi ◽  
David Gesbert ◽  
Xinping Yi
Keyword(s):  
Degrees Of Freedom ◽  
Broadcast Channel

scholarly journals Partition Function in One, Two, and Three Spatial Dimensions from Effective Lagrangian Field Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Christoph P. Hofmann
Keyword(s):  
Partition Function ◽  
Degrees Of Freedom ◽  
Spatial Dimension ◽  
Lagrangian Method ◽  
Point Of View ◽  
Low Energy ◽  
Effective Theory ◽  
Goldstone Bosons ◽  
Effective Lagrangian ◽  
Spatial Dimensions

The systematic effective Lagrangian method was first formulated in the context of the strong interaction; chiral perturbation theory (CHPT) is the effective theory of quantum chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain—in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension (ds=1), it perfectly works for nonrelativistic systems in ds=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films, and ferromagnetic crystals up to three loops in the perturbative expansion—an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in ds=1, 2, 3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

scholarly journals Secure Degrees of Freedom in Networks with User Misbehavior

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 945
Author(s):  
Karim Banawan ◽  
Sennur Ulukus
Keyword(s):  
Secure Communication ◽  
Multiple Access ◽  
Degrees Of Freedom ◽  
Broadcast Channel ◽  
Interference Channel ◽  
Extensive Form ◽  
Wiretap Channel ◽  
Form Game ◽  
Cooperative Jamming ◽  
Extensive Form Game

We investigate the secure degrees of freedom (s.d.o.f.) of three new channel models: broadcast channel with combating helpers, interference channel with selfish users, and multiple access wiretap channel with deviating users. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. That is in contrast with the common assumption in the literature that the users follow a certain protocol altruistically and transmit both message-carrying and cooperative jamming signals in an optimum manner. In the first model, over a classical broadcast channel with confidential messages (BCCM), there are two helpers, each associated with one of the receivers. In the second model, over a classical interference channel with confidential messages (ICCM), there is a helper and users are selfish. By casting each problem as an extensive-form game and applying recursive real interference alignment, we show that, for the first model, the combating intentions of the helpers are neutralized and the full s.d.o.f. is retained; for the second model, selfishness precludes secure communication and no s.d.o.f. is achieved. In the third model, we consider the multiple access wiretap channel (MAC-WTC), where multiple legitimate users wish to have secure communication with a legitimate receiver in the presence of an eavesdropper. We consider the case when a subset of users deviate from the optimum protocol that attains the exact s.d.o.f. of this channel. We consider two kinds of deviation: when some of the users stop transmitting cooperative jamming signals, and when a user starts sending intentional jamming signals. For the first scenario, we investigate possible responses of the remaining users to counteract such deviation. For the second scenario, we use an extensive-form game formulation for the interactions of the deviating and well-behaving users. We prove that a deviating user can drive the s.d.o.f. to zero; however, the remaining users can exploit its intentional jamming signals as cooperative jamming signals against the eavesdropper and achieve an optimum s.d.o.f.

scholarly journals Secure Degrees of Freedom Region of the Two-User MISO Broadcast Channel With Alternating CSIT

2017 ◽  
Vol 63 (6) ◽  
pp. 3823-3853 ◽  
Author(s):  
Pritam Mukherjee ◽  
Ravi Tandon ◽  
Sennur Ulukus
Keyword(s):  
Degrees Of Freedom ◽  
Broadcast Channel
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