Constrained coding and detection for magnetic recording channels

In this dissertation, a series of problems which arise in communicating over a magnetic recording channel are addressed. The topics, most of which address areas more general than magnetic recording, are all linked by a common thread: applying constrained codes to communication channels.; The first chapter contains a brief introduction to the magnetic recording channel, or, rather, to a simplified model of the recording channel. Well known results describing the performance of a detector for the channel are reviewed. Explicit expressions for equalizer values and noise-correlation functions are presented.; In the second chapter, we address identifying the dominant sources of error, i.e., error events, in a discrete channel model corrupted by additive white Gaussian noise. An algorithm is presented for characterizing the set of dominant error events. The algorithm uses a novel ‘localized splitting’ and re-labeling of the error state diagram which enables a finite-depth search. A simplified error-state diagram utilizing a differential notation is introduced and it is shown that the reduced complexity diagram may be used to generate the set of dominant error events. Lists of error events are tabulated for discrete partial-response targets of interest in digital recording.; The third chapter extends the error-event characterization to channels with colored noise. This is accomplished by bounding the effective distance by a function of the Euclidean distance and converting the search to a Euclidean distance search. Constrained codes whose design is based on the knowledge of the dominant errors are discussed. It is shown by simulation and analysis that such codes may improve the overall system performance.; In the fourth chapter we extend the error-event characterization and constrained coding to noise-predictive maximum-likelihood (NPML) detectors. Using performance analysis of reduced-state sequence estimators (RSSE), the dominant error events for NPML detectors are characterized. The error event characterization is used to determine distance enhancing constraints that improve the reliability of NPML/RSSE detection. Several sample constraints are illustrated and evaluated.; The fifth chapter addresses a natural question which arose from searching for distance-enhancing codes. Namely, what is the bound on the rate of a code which avoids a set of error events, or difference-sequences. To that end, we study the largest number of sequences whose differences exclude a given set of disallowed patterns. We show that the number of such sequences increases exponentially with their length, and define the exponent as the capacity of the difference set. We show that the capacity of a difference set is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We introduce new algorithms for determining the joint spectral radius of sets of non-negative matrices and combine them with existing algorithms to determine the capacity of several sets of disallowed differences that arise in practice. As a by-product, the algorithms yield constraints which achieve the capacity of the difference set.; The sixth and final chapter investigates properties of the time-varying constraints which arise as solutions to the problem presented in chapter five. They are the subclass of shift spaces defined by a finite set of periodically forbidden words. We discuss some properties of the class and present a technique to construct labeled graphs which present periodic-finite-type shift spaces.