I will present two results in this talk.


Capacity region of a sequence of less noisy receivers was open for k >= 3 receivers. We solve the capacity region for k=3 receivers. More generally, we establish the capacity region (show the optimality of superposition coding) for a class of k-receiver broadcast channels, which contains the afore mentioned 3 receiver less noisy case.


The second result is the following: For any five tuple (U,V,X,Y,Z) such that
(U,V) - X - (Y,Z) is Markov and |X|=2, we show that
I(U;Y) + I(V;Z) - I(U;V) \leq \max I(X;Y), I(X;Z).
In the context of broadcast channels this inequality implies that the sum-rate of Marton's coding strategy for binary input broadcast channels can be explicitly evaluated.


The first result is joint with my advisor Chandra Nair. The second result is joint with Yanlin Geng and my advisor Chandra Nair.