AbstractThis paper provides an information‐theoretic study for the additive white impulsive noise channels by considering Gaussian mixture (GM) noise model, which includes Middleton class A andε‐mixture Gaussian models. First, three lower and two upper bounds are found for the differential entropy of complex multivariate GM distribution and these bounds are extended to the univariate GM noise of flat fading impulsive noise channels. Second, the instantaneous capacity of these channels is bounded using two lower and two upper bounds, and the ergodic capacity and outage probability of these bounds are investigated for the log‐normal fading model. Finally, the obtained bounds are numerically illustrated and their tightness is discussed for various realizations of the GM noise. The results demonstrate that the tight bounds are not the same for all considered realizations, but they are close enough and converge to each other for a specific realization.