In Information theory, and in particular, Data transmission, a finite state channel (FSC) is a discrete-time channel where the distribution of the channel output depends on both the channel input and the underlying channel state. This allows the channel output to depend implicitly on previous inputs and outputs via the channel state.
The channel can be modelled as a stochastic Finite-state transducer.
See here for more: http://pfister.ee.duke.edu/thesis/chap4.pdf
Entropy and Mutual Information for Markov Channels with General Inputs
Blackwell, Breiman, and Thomasian introduced indecomposable FSC (IFSC) in [7] and proved the natural analogue of the channel coding theorem for them. Birch discusses the achievable information rates of IFSCs in [5], and computes bounds for a few simple examples.
Examples of finite state channels
- Discrete-time Linear filter channels with AWGN
- Dicode erasure channel
- Finite state Z-channel
Trellis diagrams
Similar to the mapping between Boolean lattices and directed percolation. See Relations between the stability of Boolean networks and percolation.
Definitions and basic properties of FSCs
See Markov chain
In the thesis he considers a Markov input process as Information source
Combining the Markov Input Process and the Finite State Channel, gives a new Markov process over the states given by the cross product of the states of the channel and of the input. They label this new set of states by integers too. This combined process is what they call a Finite state process (FSP).
Entropy rate of a finite state process
Capacity of finite state markov channels with general inputs
A Randomized Approach to the Capacity of Finite-State Channels
Capacity, mutual information, and coding for finite-state Markov channels