Communication Over Discrete Channels Subject to State Obfuscation

We consider communication over a state-dependent discrete memoryless channel subject to a constraint that the output sequence must be nearly independent of the state sequence. We consider both cases where the transmitter knows (causally or noncausally) and where it does not know the states. When it does not know the states, we show that capacity can increase when the encoder uses some source of randomness that is not shared with the decoder. We consider three different cases for the state sequence: where it is independent and identically distributed across channel uses, where it is quasi-static, and where it has memory but is not quasi-static. We present single-letter capacity formulas for most combinations of the above scenarios, and also provide some illustrative examples.