We design a network-based H-infinity filter for a parabolic system governed by a vector semilinear N-D diffusion equation over a rectangular domain Omega under distributed in space measurements. The sampled in time measurements are sent to the observer over a communication network according to Round-Robin scheduling protocol (one after another in a periodic manner). The objective is to enlarge the sampling time intervals and, thus, to reduce the amount of communications, while preserving a satisfactory error system performance. We suggest to divide Omega into a finite number of rectangular sub-domains N-s, where stationary or mobile sensing devices provide spatially averaged state measurements to be transmitted through communication network. Sufficient conditions in terms of Linear Matrix Inequalities (LMIs) for the internal exponential stability and L-2-gain analysis of the estimation error are derived via the time-delay approach to networked control systems. By solving these LMIs, the filter gain along with the upper bounds on the sampling time intervals, on the network induced time-delays, and on the diameters of the sub-domains can be found that preserve the internal stability of the error system and achieve a given L-2-gain. Numerical examples illustrate the efficiency of the method. (C) 2014 Elsevier Ltd. All rights reserved.