- Trellis diagrams are basically state diagrams stretched out in time. For example let us consider two states
*S*_{0}and*S*_{1}. At time*t*= 0 the states as nodes are depicted as ◯ on the other hand at time*t*= 1 the states as nodes are depicted as ⬤.

For example for various cases of relation - If knowledge of
*x̅*(i.e,*S*(*t*= 0)) lets us know all possible output (generated) sequence*y̅*, then this channel with memory is called non-catastrophic or conditionally catastrophic. - If a channel does not incorporate a noise channel but there is still information loss, then such channels are called noise-less channels.
- Channel capacity can be used to determine maximum information rate for class of inofrmation channel which are
- a noise-less channel that is non-catastrophic,
- either states
*S*(*t*= 0) or*S*(*t*=*t*) is known, and_{final} - output sequence
*y̅*is also known.

- The channel capacity or maximum information rate or maximum mutual information between
*X*and*Y*for such class of channels with memory is*t*steps reaching all*S*_{j} - It is hard to compute the channel capacity by the approach of determining . An easier approach is to diagonalize
**D**(). Thus*C*are constants because they are derived from_{j}**U**^{−1},**U**and their constants. - In general you do not need to compute all
*C*, just_{j}*C*. The maximum channel capacity is_{m}*λ*is the largest eigenvalue; ._{m}