Two Dimensional Magnetic Recording (TDMR) is a promising technology for next generation magnetic storage systems based on a systems level framework involving sophisticated signal processing at the core. The TDMR channel suffers from severe jitter noise along with electronic noise that needs to be mitigated during signal detection and recovery. Recently, we developed noise prediction based techniques coupled with advanced signal detectors to work with these systems. However, it is important to understand the role of harmful patterns that can be avoided during the encoding process. In this paper, we investigate into the Voronoi based media model to study the harmful patterns over multi-track shingled recording systems. Through realistic quasi micromagnetic simulations studies, we identify 2D data patterns that contribute to high media noise. We look into the generic Voronoi model and present our analysis on multi-track detection with constrained coded data. We show that two dimensional (2D) constraints imposed on input patterns result in an order of magnitude improvement in the bit error rate for TDMR systems. The use of constrained codes can reduce the complexity of 2D intersymbol interference (ISI) signal detection since lesser 2D ISI span can be accommodated at the cost of a nominal code rate loss. However, a system must be designed carefully so that the rate loss incurred by a 2D constraint does not offset the detector performance gain due to more distinguishable readback signals.Index Terms-TDMR systems, 2D no isolated bit constraint, multi-track detection, bit error rate, GBP algorithm.

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Abstract-In this paper, we present an algorithm to find all low-weight codewords in a given quasi-cyclic (QC) low-density parity-check (LDPC) code with a fixed column-weight and girth. The main idea is to view a low-weight codeword as an (a, 0) trapping sets, and then show that each topologically different (a, 0) trapping set can be dissected into smaller trapping sets. The proposed search method relies on the knowledge of possible topologies of such smaller trapping sets present in a code ensemble, which enables an efficient search. Combined with the high-rate QC LDPC code construction which successively adds blocks of permutation matrices, the algorithm ensures that in the code construction procedure all codewords up to a certain weight are avoided, which leads to a code with the desired minimum distance. The algorithm can be also used to determine the multiplicity of the low-weight codewords with different trapping set structure.

Two dimensional magnetic recording (TDMR) is a novel scheme which envisions reaching 10 Tb/in 2 density in magnetic recording systems. The feasibility of this density relies largely on sophisticated two-dimensional (2-D) signal processing algorithms. This paper gives a survey on TDMR channel models and 2-D detectors. Our discussion on channel models places an special emphasis on the suitability of the read channel models for the purpose of detector design. Furthermore, a comprehensive review on 2-D detection is given focusing on compatibility of the detectors for the TDMR channel models.