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Therefore, in Figures 3, 4, and 5 we will provide exemplary cross-sections of the rate region for different values of the common information rate,.
Indeed, for θ=0, we maximize the common information rate R2, and when θ=0.5, we maximize the rate achieved by user 1 (R1+R2).
In particular, Figure 4(a) shows a 3-dimensional plot of the inner and outer bounds on the rate triples when the common information rate is set at.
To achieve the maximum common information rate, the common message codebook cannot be broken into different codebooks for each channel, that is, joint encoding and joint decoding must be performed across all subchannels [23].
As an initial illustration of the proposed approach, in Figure 3 we show the regions of SPCGS achievable rate triples that are obtained via the signomial programming technique described in Section 4.2 for different values of the common information rate: and.
The maximum common information rate that can be supported by the channel is given by (2). with the variance of the input signal on channel, the power allocation among all subchannels, the total power constraint, and the SNR gap which measures the loss with respect to theoretically optimum performance [22].
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Moreover, (38 - 41) with condition (34) give the capacity region for a three-user MAC with common information where R1 and R2 are the common rates, R3 is the private rate for Tx3, and the private rates for Tx1 and Tx2 are zero.
From the capacity region of MAC with common information [30, page 102], we obtain the following rate requirements (A8).
However, as shown in (5) and the discussion thereafter, the number of constraints that characterize the rate region of multicarrier broadcast channels with common information grows very rapidly with the number of users.
Therefore, (R1, R2, R3) is contained in the capacity region of a three-user MAC with common information [19] at Rx1, where R1 and R2 are the common rates between Tx1-Tx3 and Tx2-Tx3, R3spectisely; R3 is the private rate for Tx3; and the private rates for Tx1 and Tx2 are zero.
We have a collective memory, a backlog of common information".
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