Computing information rates of finite state models with application to magnetic recording

The topics of this thesis are the mathematical models of the magnetic recording channel and their ultimate information-theoretic limit, the capacity. Source and channel of a magnetic recording system can be represented by a single finitestate model (FSM). The joint source/channel FSM is fully specified by the state-transition probabilities of the source model and the output probability distribution. In our case, this distribution is a parameterized Gaussian mixture density. We focus on aperiodic and irreducible FSMs whose state and observation process are stationary and ergodic. Thus, by the ShannonMcMillan-Breiman theorem, the entropy rates of the state and the observation process are determined by the probability of a typical sequence of those processes. A new and practical method is presented for computing estimates of lower and upper bounds (information rates) on the capacity of FSMs. The pivotal observation behind the method is that the entropy rate of the channel output can be computed by standard forward sum-product trellis processing of simulated or (in principle) measured channel output data. The method is applied to various FSMs representing the magnetic recording channel. These models are (generalized) partial-response polynomials with additive white Gaussian noise (AWGN), sources with run-length limit constraints observed through AWGN, FSMs that are trained on synthetically generated waveforms (microtrack model) with continuous mixture noise including medium noise, and the binary jitter channel with discrete-valued data-dependent noise.