On 2-D Non-Adjacent-Error Channel Models

In this work, we consider two-dimensional (2-D) binary channels in which the 2-D error patterns are constrained so that errors cannot occur in adjacent horizontal or vertical positions. We consider probabilistic and combinatorial models for such channels. A probabilistic model is obtained from a 2-D random field defined by Roth, Siegel and Wolf (2001). Based on the conjectured ergodicity of this random field, we obtain an expression for the capacity of the 2-D non-adjacent-errors channel. We also derive an upper bound for the asymptotic coding rate in the combinatorial model.