Capacity Region of Vector Gaussian Interference Channels with Generally Strong Interference

An interference channel is said to have strong interference if for all input distributions, the receivers can fully decode the interference. This definition of strong interference applies to discrete memoryless, scalar and vector Gaussian interference channels. However, there exist vector Gaussian interference channels that may not satisfy the strong interference condition but for which the capacity can still be achieved by jointly decoding the signal and the interference. This kind of interference is called generally strong interference. Sufficient conditions for a vector Gaussian interference channel to have generally strong interference are derived. The sum-rate capacity and the boundary points of the capacity region are also determined.Comment: 50 pages, 11 figures, submitted to IEEE trans. on Information Theor

The structure, energy, and electronic states of vacancies in Ge nanocrystals

The atomic structure, energy of formation, and electronic states of vacancies in H-passivated Ge nanocrystals are studied by density functional theory (DFT) methods. The competition between quantum self-purification and the free surface relaxations is investigated. The free surfaces of crystals smaller than 2 nm distort the Jahn-Teller relaxation and enhance the reconstruction bonds. This increases the energy splitting of the quantum states and reduces the energy of formation to as low as 1 eV per defect in the smallest nanocrystals. In crystals larger than 2 nm the observed symmetry of the Jahn-Teller distortion matches the symmetry expected for bulk Ge crystals. Near the nanocrystal's surface the vacancy is found to have an energy of formation no larger than 0.5 to 1.4 eV per defect, but a vacancy more than 0.7 nm inside the surface has an energy of formation that is the same as in bulk Ge. No evidence of the self-purification effect is observed; the dominant effect is the free surface relaxations, which allow for the enhanced reconstruction. From the evidence in this paper, it is predicted that for moderate sized Ge nanocrystals a vacancy inside the crystal will behave bulk-like and not interact strongly with the surface, except when it is within 0.7 nm of the surface.Comment: In Press at Phys. Rev.

Capacity Regions and Sum-Rate Capacities of Vector Gaussian Interference Channels

The capacity regions of vector, or multiple-input multiple-output, Gaussian interference channels are established for very strong interference and aligned strong interference. Furthermore, the sum-rate capacities are established for Z interference, noisy interference, and mixed (aligned weak/intermediate and aligned strong) interference. These results generalize known results for scalar Gaussian interference channels.Comment: 33 pages, 1 figure, submitted to IEEE trans. on Information theor