This paper studies a class of stochastic and time-varying Gaussian intersymbol interference~(ISI) channels. The probability law for the~$i^{th}$ channel tap during time slot~$t$ is supported over an interval of centre $c_i$ and radius~$ r_{i}$. The transmitter and the receiver only know the centres $c_i$ and the radii $r_i$. The joint distribution for the array of channel taps and their realizations are unknown to both the transmitter and the receiver. A lower bound (achievability result) is presented on the channel capacity which results in an upper bound on the capacity loss compared to when all radii are zeros. The lower bound on the channel capacity saturates at a positive value as the maximum average input power $P$ increases beyond what is referred to as the saturation power $P_{sat}$. Roughly speaking, $P_{sat}$ is inversely proportional to the sum of the squares of the radii $r_i$. A partial converse result is provided in the worst-case scenario where the array of channel taps varies independently along both indices $t$ and $i$ with uniform marginals. It is shown that for every sequence of codebooks with vanishing probability of error, if the size of each symbol in every codeword is bounded away from zero by an amount proportional to $\sqrt{P}$, then the rate of that sequence of codebooks does not scale with~$P$. Tools in matrix analysis such as matrix norms and Weyl's inequality on perturbation of eigenvalues of symmetric matrices are used in order to analyze the probability of error.

翻译：本文研究的是一组随机和时间变化的 Gaussian intersymbol 干扰 ~( ISI) 频道。 频道容量较低( 可实现性结果) 显示在频道能力上, 导致能力损失的上限, 与所有弧度为零时相比。 频道容量较低的约束值为正值, 最大平均输入力为 $P$, 超过所谓的饱和力 $P$ 美元。 粗略地说, $Psat} 与当时的正方对数成反比。 频道容量较低的约束值( 可实现性结果) 显示在频道能力上导致能力损失的上限, 相对于所有正值为零时, 美元 。 频道容量的下限值为正值, 最大平均输入力为 $P$, 超过所谓的饱和度 $Pr_ 美元 美元 。 粗略地说, 美元与当时的美元正数之正数之正数之和偏差值分析结果, 在每张正数的折数序列中, 每个正数的正数序列中, 它的偏差值为正数的正数, 以每平数的正数的正数值 的正数的正数的直值 。