On the implementation of linear diffusion in transconductance-based cellular nonlinear networks

In theory, cellular nonlinear networks (CNN) are well capable of implementing discrete-space linear diffusion by means of the appropriate templates. In practice, good results have not been demonstrated with transconductance-based circuits. In this paper, we prove that inherent mismatch to very large scale integration implementation is the reason. Although previous works consider that the small perturbations of the network parameters lead to small deviations from the ideal behavior, we consider that this is over optimistic. When interactions between nodes are supported by unidirectional building blocks, originally balanced current paths are realized by mismatched elements. In the case of linear diffusion, the singular location of natural frequencies of the system implies that a small perturbation of balanced current paths renders qualitatively different network dynamics. We analyze and compare a set of linear templates performing unconstrained and constrained linear diffusion in transconductance-based CNN hardware. Several numerical examples are also presented to visualize the consequences of mismatch on the processing. Finally, in order to emphasize the importance of having balanced current paths, we tested the influence of mismatch in a grid built with MOS transistors. In spite of their nonlinearity, the resulting network is much more robust to mismatch. This last result coincides with previous studies. Copyright 2008 John Wiley & Sons, Ltd.