The minimum description length principle for modeling recording channels

Modeling the magnetic recording channel has long been a challenging researc h problem. Typically, the tradeoff has been simplicity of the model for its accuracy. For a given family of channel models, the accuracy will grow wit h the model size, at a price of a more complex model. In this paper, we dev elop a formalism that strikes a balance between these opposing criteria, Th e 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 chose n for its simplicity of description and experimentally verified modeling ac curacy. For this family of models, the minimum description complexity is di rectly 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 t he sum of two terms: 1) the entropy of the sequence of uncorrelated Gaussia n 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 des cription length criterion for the magnetic recording channel corrupted by n onlinearities and signal-dependent noise. Results on synthetically generate d data are presented to validate the method. We then apply the method to da ta collected from the spin stand to establish the model's size and paramete rs that strike a balance between complexity and accuracy.