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We propose a three-track detection system for two dimensional magnetic recording (TDMR) in which a local area influence probabilistic (LAIP) detector works with a trellis-based Bahl-Cocke-Jelinek-Raviv (BCJR) detector to remove intersymbol interference (ISI) and intertrack interference (ITI) among coded data bits as well as media noise due to magnetic grain-bit interactions. Two minimum mean-squared error (MMSE) linear equalizers with different response targets are employed before the LAIP and BCJR detectors. The LAIP detector considers local grain-bit interactions and passes coded bit log-likelihood ratios (LLRs) to the channel decoder, whose output LLRs serve as a priori information to the BCJR detector, which is followed by a second channel decoding pass. Simulation results under 1-shot decoding on a grain-flipping-probability (GFP) media model show that the proposed LAIP/BCJR detection system achieves density gains of 10.16% for center-track detection and 3.13% for three-track detection compared to a standard BCJR/1D-PDNP. The proposed system's BCJR detector bit error rates (BERs) are lower than those of a recently proposed two-track BCJR/2D-PDNP system by factors of (0.55, 0.08) for tracks 1 and 2 respectively. 

Trellis based detection with pattern dependent noise prediction (PDNP) has become standard practice in the HDD industry. In a typical single-track signal processing scheme, the received samples from the read head are first filtered by a linear equalizer with a 1D partial response (PR). The linear filter output flows into a trellis-based (e.g. BCJR) detector that employs a super-trellis based on the PR mask ISI channel and a 1D pattern dependent noise prediction (1D PDNP) algorithm. The effective channel model has a media noise term which models signal dependent noise due to, e.g., magnetic grains intersected by bit boundaries. The media noise can influence two or more bit readback values. The trellis detector sends soft estimates of the coded bits to a channel decoder, which outputs estimates of the user information bits. There are two problems with traditional PDNP. First, when the number of tracks Nt simultaneously processed is greater than one, e.g. in two-dimensional magnetic recording (TDMR), the number of trellis states can become impractically large; this is the state explosion problem. Second, the relatively simple autoregressive noise model and linear prediction used in PDNP is somewhat restrictive and may not accurately represent the media noise, especially at high storage densities; this is the modeling problem. To address the state explosion problem, we separate the ISI detection and media noise prediction into two separate detectors and use the turbo-principle to exchange information between them, thus avoiding use of a super-trellis. To address the modeling problem, we design and train deep neural network (DNN) based media noise predictors. As DNN models are much more general than autoregressive models, they give a more accurate model of magnetic media noise than PDNP; this more accurate modeling results in reduced detector BERs compared to PDNP.