One-pairs codes for partial response magnetic recording

We consider a new constraint on stored data in partial response digital magnetic recording. The one-pairs constraint is an upper bound on the maximum number of symbols between pairs of ones in a coded sequence and can be considered as an alternative to the widely used (0, G/I) constraint, The constraint limits quasi-catastrophic error propagation and guarantees the occurrence of superior timing corrections in partial response class IV (PR4) and extended PR4 (EPR4) magnetic recording systems. In this paper we give low complexity rate 8/9, 16/17, and 24/25 block codes, derive the capacity of this constraint, and compute the power spectral density for maxentropic codes. The codes achieve greater than 95% of channel capacity and the 24/25 code has smaller than expected error propagation.