Statistical properties of selected recording codes

Most recording systems encode their data using binary run-length-limited (RLL) codes. Statistics such as the density of 1s, the probabilities of specific code strings or run lengths, and the power spectrum are useful in analyzing the performance of RLL codes in these applications. These statistics are easy to compute for ideal run-length-limited codes, those whose only constraints are the run-length limits, but ideal RLL codes are not usable in practice because their code rates are irrational. Implemented RLL codes achieve rational rates by not using all code sequences which satisfy the run-length constraints, and their statistics are different from those of the ideal RLL codes. Little attention has been paid to the computation of statistics for these practical codes. In this paper a method is presented for computing statistics of implemented codes. The key step is to develop an exact description of the code sequences which are used. A consequence of the code having rational rate is that all the code-string and run-length probabilities are rational. The method is illustrated by applying it to three codes of practical importance: MFM, (2, 7), and (1, 7).