In telepresence and teleaction systems the haptic communication channel plays a central role. As it closes a global control loop any introduced communication delay possibly destabilizes the system and impairs the performance. The scattering theory is known to solve these stability issues by transmitting wave variables instead of haptic signals, i.e. force and velocity, over the communication channel. For stability and performance additionally high packet rates are required stressing the underlying network resources. Perceptual coding techniques of haptic signals, such as the Weber-inspired deadband approach, are known to successfully reduce the packet rate on the haptic channel. However, as wave variables do not directly represent haptic information but a linear transformation of both signals, perceptual coding is not directly applicable anymore. In this paper, we present a novel control scheme as well as a modification of the deadband approach to take advantage of the stabilization ability of the wave variables while allowing perceptual coding on the communication channel. Simulation results and comparison with the wave variables architecture indicate improved data compression for same degree of transparency for purely stiff as well as free environments.