The state-dependent interference channel with states available at a cribbing encoder and one receiver

The two-user discrete memoryless state-dependent interference channel models a scenario in which two encoders transmit a pair of independent messages to two receivers where the signal intended for one receiver causes interference at the other receiver. Message 1 sent by Encoder 1 should be decoded by both receivers while Message 2 sent by Encoder 2 should be decoded by Decoder 2. The channel law is governed by an i.i.d. state process and the state sequence is available non-causally to both Encoder 2 and Decoder 2. It is further assumed that Encoder 2 cribs causally from Encoder 1. We derive an achievable rate-region for this model and show that it is tight when the output at Decoder 1 is degraded w.r.t. the output at Decoder 2 conditionally on the state and the input of Encoder 1.