Distance-enhancing codes for digital recording

We review recent progress in the design of high-rate, distance-enhancing codes that achieve the matched-filter-bound (MFB) on the E²PR4 channel, h(D)=(1-D)(1+D)³, including a rate 8/9 block code satisfying a time-varying maximum-transition-run (TMTR) constraint. We then prove that these TMTR codes also achieve the MFB on the E³PR4 channel, h(D)=(1-D)(1+D)⁴. Finally, we describe a TMTR constraint that achieves the MFB on the PR2 channel, h(D)=(1+D)², and the EPR2 channel, h(D)=(1+D)³ , both of which are of interest as channel models in optical recording, and we present a new, rate 3/4 block code that satisfies this constraint. Computer simulation results confirm that the codes provide substantial performance improvement in additive, white, Gaussian noise (AWGN)