Sentence examples for outer bound with from inspiring English sources

The achievable sum rate and sum rate outer bound with different d for HBC and 2-CoMABC protocols are given in Fig. 3.

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.

Clearly, limiting the eavesdropper capabilities can only improve the secrecy rates, and thus, an outer bound for this channel with a constrained eavesdropper is also an outer bound for the original channel (with in both cases) with an unconstrained eavesdropper.

The following proposition gives an outer bound for the Gaussian MAC with one informed encoder as.

As we observe, for high SNRs, the achievable rate region by lattice codes coincides with the outer bound.

Since the Gaussian-distributed input is the optimal input for a given mean power constraint, (10) serves as an outer bound for the capacity region with a practically motivated input, i.e., finite constellation input as discussed in Section 3.1.

The inner bound using GDPC is compared with a trivial outer bound obtained by providing channel state to the decoder.

If the channel state is a Bernoulli random variable with, we compared the inner bound in the binary case with a trivial outer bound obtained by providing the channel state to only the decoder.

Their performance is compared with the cut-set outer bound.

In the high SNR regime, the proposed scheme coincided with the cut-set outer bound and thus the capacity region is achieved.

We compare the information rates achievable by the proposed strategies in Section 4 with the cut-set outer bound in [29].