Markov Random Field Detection on Two-Dimensional Intersymbol Interference Channels

We present a novel iterative algorithm for detection of binary Markov random fields (MRFs) corrupted by 2-D intersymbol interference (ISI) and additive white Gaussian noise. We assume a first-order binary MRF as a simple model for correlated images. We assume a 2-D digital storage channel, where the MRF is interleaved before being written and then read by a 2-D transducer; such channels occur in recently proposed optical disk storage systems. The detection algorithm is a concatenation of two soft-input/soft-output (SISO) detectors: an iterative row-column soft-decision feedback (IRCSDF) ISI detector, and a MRF detector. The MRF detector is a SISO version of the stochastic relaxation algorithm by Geman and Geman. On the 2times2 averaging-mask ISI channel, at a bit error rate of 10^-4, the concatenated algorithm achieves SNR savings of between 0.2 and 2.0 dB over the IRCSDF detector alone; the savings increase as the MRFs become more correlated, or as the SNR decreases. The algorithm is also fairly robust to mismatches between the assumed and actual MRF parameters.