The effect on the probability of error from intersymbol interference caused by a repeated use of a continuous-time Gaussian channel is examined. The model assumes that signals that are power constrained are put through a linear filter after which Gaussian noise is added to produce the received signal. One can view the linear filter as a frequency constraint on the inputs. Because of the memory in the filter, past inputs affect the filter output for the current input. It is shown that this interference can be treated as an additional input whose reproducing kernel Hilbert space (RKHS) norm is upper bounded by a function that tends to 0 with increasing block length. Describing the channel in RKHS terms, we show that the exponential error bounds obtained by Gallager are unchanged if one takes intersymbol interference into account.

The generator matrices of(n, 2)codes which are optimum for the BSC with sufficiently small channel error probabilitypare given.