This paper deals with the H∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results. ; This work was supported in part by the Royal Society of the UK, the Research Fund for the Taishan Scholar Project of Shandong Province of China, National Natural Science Foundation of China under Grants 61403420, 61573377 and 61329301, Fundamental Research Fund for the Central Universities of China under Grant 15CX08014A, the Project for the Applied Basic Research of Qingdao of China under Grant 16-5-1-3-jch, and the Alexander von Humboldt Foundation of Germany.