This fact is readily obtained from the alternative achievability proof given in Section 4. We note that [25, 26] consider the problem key generation from common randomness over wiretap channels and exploit a Wyner-Ziv coding scheme to limit the amount of information conveyed from the source to the destination via the wiretap channel.
The achievability proof can be given on similar lines as in [9].
To show the achievability of the region given by (30), first we need to note that the boundary of this region can be decomposed into three surfaces as follows [26].
To show the achievability of the region given in Theorem 9, we use Theorem 7. First, we group subchannels into two sets where contains the subchannels in which user has the best observation.
Thus we seek to prove the achievability of the tuple (d1′,d2′) given in 17-188).
The achievability part of Theorem 1 is given in Section 3.1, and the converse is given in Section 3.2.
For general classes of channels, they have obtained new achievability and converse bounds on the coding rate for a given finite blocklength and error probability.
Corollary 2 proves Theorem 2 by contradiction; if it is easy to find D s for a given SFM, then we can easily decide the achievability of (D_{mathcal {S}_{p}}) by comparing D s with (D_{mathcal {S}_{p}}), as (D_{s}=D_{mathcal {S}_{p}}) means that (D_{mathcal {S}_{p}}) is achievable, and (D_{s}>D_{mathcal {S}_{p}}) means that (D_{mathcal {S}_{p}}) is not achievable.
We start Section 3 by stating the theorem which characterizes the degrees-of-freedom region and then give the achievability and converse arguments in Sections 3.1 and 3.2, respectively.
We briefly discuss the transmission scheme that attains the rate (8) and point out some implications of this result, leaving the details of the proof of achievability to Appendix B. Again, to fix the ideas, consider the set of active MSs at a given time, one per cell, which employ a fraction of time of both the uplink and the conferencing channels.
