  We study a special class of the cognitive radio channel in which the receiver
of the cognitive pair does not suffer interference from the primary user.
Previously developed general encoding schemes for this channel are complex as
they attempt to cope with arbitrary channel conditions, which leads to rate
regions that are difficult to evaluate. The focus of our work is to derive
simple rate regions that are easily computable, thereby providing more insights
into achievable rates and good coding strategies under different channel
conditions. We first present several explicit achievable regions for the
general discrete memoryless case. We also present an improved outer bound on
the capacity region for the case of high interference. We then extend these
regions to Gaussian channels. With a simple outer bound we establish a new
capacity region in the high-interference regime. Lastly, we provide numerical
comparisons between the derived achievable rate regions and the outer bounds.
