Capacity of Binary State Symmetric Channel with and without feedback and transmission cost

We consider a unit memory channel, called Binary State Symmetric Channel (BSSC), in which the channel state is the modulo2 addition of the current channel input and the previous channel output. We derive closed form expressions for the capacity and corresponding channel input distribution for the BSSC with and without feedback and transmission cost. We also show that the capacity of the BSSC, with or without feedback, is achieved by a first order symmetric Markov process.