Detection and modeling of 2-dimensional signals

"2-D or not 2-D that is the question" - M. Marrow, 2004.; Efficient decoding techniques for the one dimensional inter-symbol interference problem, such as Viterbi equalization and decision-feedback equalization (DFE) have been well understood for almost 30 years and are in widespread use in communications devices. For channels with more that one dimension, optimal decoding has exponential complexity and is thus not realizable in practice. In the future, as high density page and volume oriented storage becomes viable, there will be an increasing need to develop low complexity methods. In this work we present a number of iterative techniques which try to approach optimal performance on a 2-dimensional ISI channel with additive white Gaussian noise. It is shown that unlike turbo product codes, straightforward application of turbo equalization to the 2-D ISI problem performs poorly. The source of the poor performance is shown to be attributable to the constituent detectors treating ISI from adjacent rows/columns as noise and thus performing badly both in isolation and as part of an iterative equalizer. Some low-complexity ad-hoc enhancements are presented, culminating in an iterative multi-strip (IMS) detector which for certain models approaches maximum likelihood detection to within 0.5dB yet having constant per-bit complexity. The detector is shown to perform well in a larger iterative system comprising equalization and channel coding.; We also developed a software simulator for high-density perpendicular recording based on the microtrack model that enables high-speed realistic waveform generation.; Thin film magnetic media utilized in high performance disk drives are comprised of fine grains which give rise to a stationary or DC noise in addition to transition noise. We introduce a numerical model of granular media which permits control of grain size variance, orientation distributions and packing fraction. Using this model, we determined by Monte Carlo simulation, the DC noise 2-D spatial correlation function. Of particular interest is the area under the correlation function, which gives a measure of the noise spectral density near DC. A mathematical model is developed to approximate this quantity for perfectly oriented media. The resulting expression produces a good approximation to the simulation results for a range of typical parameters. The model is also used to explain recent experiments of media noise which have shown DC noise amplification after the application of a partial reversal field.