The minimum description length principle for modeling recording channels

Modeling the magnetic recording channel has long been a challenging research problem. Typically, the tradeoff has been simplicity of the model for its accuracy. For a given family of channel models, the accuracy will grow with the model size, at a price of a more complex model. In this paper, we develop a formalism that strikes a balance between these opposing criteria, The formalism is based on Rissanen's notion of minimum required complexity - the minimum description length (MDL). The family of channel models in this study is the family of signal-dependent autoregressive channel models chosen for its simplicity of description and experimentally verified modeling accuracy. For this family of models, the minimum description complexity is directly linked to the minimum required complexity of a detector. Furthermore, the minimum description principle for autoregressive models lends itself for an intuitively pleasing interpretation. The description complexity is the sum of two terms: 1) the entropy of the sequence of uncorrelated Gaussian random variables driving the autoregressive filters, which decreases with the model order (i.e., model size), and 2) a penalty term proportional to the model size. We exploit this interpretation to formulate the minimum description length criterion for the magnetic recording channel corrupted by nonlinearities and signal-dependent noise. Results on synthetically generated data are presented to validate the method. We then apply the method to data collected from the spin stand to establish the model's size and parameters that strike a balance between complexity and accuracy.