Turbo Equalization for Two Dimensional Magnetic Recording Using Voronoi Model Averaged Statistics

This paper considers turbo equalization for 2-D magnetic recording. Magnetic grains are modeled as Voronoi regions of randomly distributed nuclei. Bits read from the magnetic grain model flow into a 2-D intersymbol interference (2D-ISI) model including additive white Gaussian noise. At high bit densities, some bits are not written on any grain, and hence are effectively "overwritten" by surrounding bits. The proposed system iteratively exchanges log-likelihood ratios (LLRs) between a 2D-ISI equalizer based on the forward-backward algorithm and an irregular repeat-accumulate (IRA) decoder. To combat bit overwrites, the system employs a non-linear function to map 2D-ISI extrinsic output LLRs to IRA decoder input LLRs. To pass back LLRs from the IRA decoder to the 2D-ISI equalizer, we design a simple likelihood-ratio-based LLR estimator. Simulations of the proposed system that employ the perturbed-bit-centers grain model proposed in a 2010 IEEE Transactions on Magnetics paper show a 6.5% increase in user bits per grain (U/G) and a 16.4 dB signal-to-noise ratio (SNR) gain compared with the previous paper, without iterative turbo equalization. Utilizing the LLR estimator to do iterative detection results in SNR gains of up to 1.7 dB compared with non-iterative detection. The random Voronoi model employed in this paper appears to be more difficult to equalize than the grain model in the 2010 paper. The proposed system with random Voronoi model achieves 0.4422 U/G at SNR =11.6 dB, i.e., about 8.8 Tb/in 2 at (typically assumed future grain density) 20 Tgr/in 2 ; this is almost ten times the density of current systems at 10 Tgr/in 2 .