Information rates for a discrete-time Gaussian channel with intersymbol interference and stationary inputs

Bounds are presented on I_i.i.d.-the achievable information rate for a discrete Gaussian Channel with intersymbol interference (ISI) present and i.i.d. channel input symbols governed by an arbitrary predetermined distribution p_x(x). The lower and upper bounds on I _i.i.d. and I are formulated. The bounds on I_i.i.d. are calculated for independent equiprobably binary channel symbols and for causal channels with ISI memory of degree one and two. The bounds on I_i.i.d. are compared to the approximated (by Monte Carlo methods) known value of I_i.i.d. and their tightness is considered. An application of the new lower bound on I_i.i.d. yields an improvement on previously reported lower bounds for the capacity of the continuous-time strictly bandlimited (or bandpass) Gaussian channel with either peak or simultaneously peak power and bandlimiting constraints imposed on the channel´s input waveform