  In this paper, we investigate the sum-capacity of the two-user Gaussian
interference channel with Gaussian superposition coding and successive
decoding. We first examine an approximate deterministic formulation of the
problem, and introduce the complementarity conditions that capture the use of
Gaussian coding and successive decoding. In the deterministic channel problem,
we find the constrained sum-capacity and its achievable schemes with the
minimum number of messages, first in symmetric channels, and then in general
asymmetric channels. We show that the constrained sum-capacity oscillates as a
function of the cross link gain parameters between the information theoretic
sum-capacity and the sum-capacity with interference treated as noise.
Furthermore, we show that if the number of messages of either of the two users
is fewer than the minimum number required to achieve the constrained
sum-capacity, the maximum achievable sum-rate drops to that with interference
treated as noise. We provide two algorithms (a simple one and a finer one) to
translate the optimal schemes in the deterministic channel model to the
Gaussian channel model. We also derive two upper bounds on the sum-capacity of
the Gaussian Han-Kobayashi schemes, which automatically upper bound the
sum-capacity using successive decoding of Gaussian codewords. Numerical
evaluations show that, similar to the deterministic channel results, the
constrained sum-capacity in the Gaussian channels oscillates between the
sum-capacity with Han-Kobayashi schemes and that with single message schemes.
