  We establish several new results on Marton's coding scheme and its
corresponding inner bound on the capacity region of the general broadcast
channel. We show that unlike the Gaussian case, Marton's coding scheme without
superposition coding is not optimal in general even for a degraded broadcast
channel with no common message. We then establish properties of Marton's inner
bound that help restrict the search space for computing the sum-rate. Next, we
show that the inner bound is optimal along certain directions. Finally, we
propose a coding scheme that may lead to a larger inner bound.
