Sentence examples for establish an outer bound from inspiring English sources
In this section, we establish an outer bound on the capacity region of the restricted half-duplex Gaussian MIMO two-way relay channel and, as our main contribution, propose an efficient method to evaluate it.
Thus, the only step remaining in the converse is to establish an outer bound on the sum degrees-of-freedom which coincides with (d_{mathsf {sum}}^{mathsf {max}}), the sum-degrees-of-freedom constraint on the achievable region, (mathcal {D}_{mathsf {FD}}), given in (16).
To establish the converse part of Theorem 1, we must show that the region (mathcal {D}_{mathsf {FD}}), which we have already shown is achievable, is also an outer bound on the degrees-of-freedom, i.e., we want to show that if an arbitrary degree-of-freedom pair (d 1,d 2) is achievable, then ((d_{1},d_{2}) in mathcal {D}_{mathsf {FD}}).
In [10], an outer bound for the capacity of a general IFC-CR was first derived.
We now present an outer bound on the Gaussian orthogonal relay eavesdropper channel using Lemma 15.
For comparison, an outer bound on the capacity region of the G-CICS is provided.
In order to derive an outer bound on the rate region, we use the transformation.
Next, an outer bound on the capacity region for full parameter regime is provided.
The following proposition gives an outer bound for the Gaussian MAC with one informed encoder as.
