  This paper studies a class of stochastic and time-varying Gaussian
intersymbol interference (ISI) channels. The $i^{th}$ channel tap during time
slot $t$ is uniformly distributed over an interval of centre $c_i$ and radius $
r_{i}$. The array of channel taps is independent along both $t$ and $i$. The
channel state information is unavailable at both the transmitter and the
receiver. Lower and upper bounds are derived on the White-Gaussian-Input (WGI)
capacity $C_{\scriptscriptstyle{WGI}}$ for arbitrary values of the radii $
r_i$. It is shown that $C_{\scriptscriptstyle{WGI}}$ does not scale with the
average input power. The proposed lower bound is achieved by a joint-typicality
decoder that is tuned to a set of candidates for the channel matrix. This set
forms a net that covers the range of the random channel matrix and its
resolution is optimized in order to yield the largest achievable rate. Tools in
matrix analysis such as Weyl's inequality on perturbation of eigenvalues of
symmetric matrices are used in order to analyze the probability of error.
