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In this paper, we analyze the distance properties of two-dimensional (2-D) intersymbol interference (ISI) channels, in particular the 2-D partial response class-1 (PR1) channel which is an extension of the one-dimensional (1-D) PR1 channel. The minimum squared-Euclidean distance of this channel is proved to be 4 and a complete characterization of the squared-Euclidean distance 4 error events is provided. As for 1-D channels, we can construct error-state diagrams for 2-D channels to help characterize error events. We propose an efficient error event search algorithm operating on the error-state diagram that is applicable to any 2-D channel.