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In this paper, we consider the problem of modeling the timing error process in magnetic recording systems. We propose a discrete- valued Markov model for the timing error process, and design two methods (data-aided and nondata-aided), based on the Baum-Welch algorithm, to extract the model parameters from the readback waveforms. The channel model we consider is an intersymbol interference (ISI) channel with additive Gaussian noise. The continuous-time readback signal at the output of the channel is sampled at baud-rate. Simulation results show that the estimated parameters are close to the actual values and the convergence is attained in a few iterations of the Baum-Welch algorithm. We also demonstrate the usefulness of the accurate model extraction by comparing a fine-tuned Markov timing recovery loop to the standard Mueller and Muller detector with a tuned second-order loop filter. [ABSTRACT FROM AUTHOR]

High-rate low-density parity-check (LDPC) codes are the focus of intense research in magnetic recording because, when decoded by the iterative sum-product algorithm, they show decoding performance close to the Shannon capacity. However, cycles, especially short cycles, are harmful to LDPC codes. The paper describes the partition-and-shift LDPC (PS-LDPC) codes, a new class of regular, structured LDPC codes that can be designed with large girth and arbitrary large minimum distance. Large girth leads to more efficient iterative decoding and codes with better error-floor properties than random LDPC codes. PS-LDPC codes can be designed for any desired column weight and with flexible code rates. The paper details the girth and distance properties of the codes and their systematic construction and presents analytical and simulation performance results that show that, in the high signal-to-noise ratio region, PS-LDPC codes out- perform random codes, alleviating the error floor phenomenon. [ABSTRACT FROM AUTHOR]