On the generalized symmetric cut-off rate for finite state channels

The main results are demonstrated for three interesting examples of binary input finite state (FS) Gaussian additive channels. Specializing to the additive Gaussian channel and using the assertion for a maximum likelihood metric yields a relation in a general setting between the symmetric cut-off rate and the minimum Euclidean distance of an uncoded system operating over the channel. We examine also the familiar case of a simple linear ISI Gaussian channel and move on to investigate a nonlinear ISI Gaussian channel. The last example addresses a concatenated coding scheme where the simple inner 4-state amplitude modulated (4-AM), Ungerboeck rate 1/2 trellis code combined with the memoryless additive Gaussian channel is interpreted as a FS-channel