A Note on the Capacity Region of the Multiple-Access Channel
Monika Bierbaum, Hans-Martin Wallmeier · 1979
be Let %, 9, and E be finite sets and let (w(z~x,Y)),~~~~~,.~~* the transmission matrix of a discrete memoryless multipleaccess channel. Ahlswede ([l], [2]) has shown that the capacity region of this channel equals the convex hull %* of the set 3,. Here 3 is the set of pairs (R,,R,) with the properties: R, Pr { Y=~}wtzlx,y) for zE%. At the European Meeting of Statisticians in Leuven, 1977, Cover asked whether ‘3 is already convex. We show by an example that this is in general not the case. Thus time-sharing is necessary to achieve some of the points in the capacity region.