The Approximate Capacity of the MIMO Relay Channel

Capacity bounds are studied for the multiple-antenna complex Gaussian relay channel with t1 transmitting antennas at the sender, r2 receiving and t2 transmitting antennas at the relay, and r3 receiving antennas at the receiver. It is shown that the partial decode-forward coding scheme achieves within min(t1,r2) bits from the cutset bound and at least one half of the cutset bound, establishing a good approximate expression of the capacity. A similar additive gap of min(t1 + t2, r3) + r2 bits is shown to be achieved by the compress-forward coding scheme.Comment: 8 pages, 5 figures, submitted to the IEEE Transactions on Information Theor

On a New Approach for Constructing Wormholes in Einstein-Born-Infeld Gravity

We study a new approach for the wormhole construction in Einstein-Born-Infeld gravity, which does not require exotic matters in the Einstein equation. The Born-Infeld field equation is not modified from "coordinate independent" conditions of continuous metric tensor and its derivatives, even though the Born-Infeld fields have discontinuities in their derivatives at the throat in general. We study the relation of the newly introduced conditions with the usual continuity equation for the energy-momentum tensor and the gravitational Bianchi identity. We find that there is no violation of energy conditions for the Born-Infeld fields contrary to the usual approaches. The exoticity of energy-momentum tensor is not essential for sustaining wormholes. Some open problems are discussed.Comment: Minor revision to improve the clarity, Corrected typos, Added reference and footnot