Sentence examples for an inner bound from inspiring English sources

For the Gaussian case, we also derived an inner bound using GDPC and an outer bound by providing the channel state to the decoder also.

The following theorem provides an inner bound for the DM case.

The following definition and theorem give an inner bound for the Gaussian MAC with one informed encoder.

We derived an inner bound for the DM case and specialized to a noiseless binary case using generalized binary DPC.

One way to find an inner bound is to use a monomial to approximate the objective in (23a)–(23a).

We derive an inner bound for the capacity region in the general discrete memoryless case and specialize to a binary noiseless case.

In Section 3, we study a general inner bound for the capacity region of the model in Figure 1 for a DM MAC and also specialize to a binary noiseless case.

In order to investigate the tightness of the proposed inner and outer bounds on the set of SPCGS achievable rates, in Figure 4 we provide a comparison between the inner bound proposed in Section 4.2, which is obtained via signomial programming and bisection search, and the outer bound proposed in Section 4.1.1, which is obtained via a geometric program.

If the binary channel state is a Bernoulli random variable with, we compare the inner bound with a trivial outer bound obtained by providing the channel state to the decoder, and the bounds do not meet.

By evaluating the inner bound 1 of Proposition 3 in [16] (and replacing S → a S, b → a, c → 1 a ), we can see that this inner bound when the channel gain tends to zero vanishes, and thus, we cannot achieve any positive rate region by such scheme.

First, we consider a class of degraded MA-CIFC and derive conditions under which the inner bound in Theorem 1 achieves the outer bound of Theorem 4. Next, we investigate the strong interference regime by deriving two sets of strong interference conditions under which the region of Theorem 3 achieves capacity.