Error event characterization on 2-D ISI channels

For one-dimensional (1-D) recording channels, the detector performance can be assessed by the distance properties of the channel, which are defined in terms of the maximum-likelihood decoding trellis. Error events with minimum and near minimum distances play an important role in the performance of the recording system particularly at moderate to high signal-to-noise ratio (SNR). In this paper, we analyze the distance properties of two-dimensional (2-D) inter-symbol interference channels, in particular the 2-D PR1 channel which is an extension of the 1-D PR1 channel. The minimum distance of this channel is proved to be 2 and a complete characterization of the distance-2 error events is provided. Also, the error events with squared-Euclidean distance 6 are partially characterized. Analogous to 1-D channels, error-state diagrams for 2-D channels can be constructed to characterize the error events. We propose an efficient error event search algorithm operating on the error-state diagram that is applicable to any 2-D channel.