Performance of an 8/9 rate matched spectral null code on the PR4 magnetic recording channel

The performance of an 8/9 rate matched spectral null (MSN) code is analyzed on the PR4 magnetic recording channel with additive white Gaussian noise (AWGN) at the sensor. The high rate is achieved with a fixed charge constraint code of block length N=27 on each of the PR4 channel's dicode interleaves. A simplified semi-analytic method for MSN codes that approximates the constants multiplying the Q function for certain error event types is introduced and validated by simulations. The 8/9 rate MSN/PR4 system was compared to a normal 16/17 rate code with PR4 and EPR4 detectors for a range of user densities. The MSN/PR4 system has less than 0.9 dB net coding gain for user densities above 2.25, and it's inferior to simple EPR4 at user densities above 1.9.