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In this paper, we introduce a modulation code design problem where best selection of two-dimensional codewords are determined to reduce two-dimensional (2D) Intersymbol Interference (ISI) and Interpage Interference (IPI), while when these codewords are randomly arranged on the storage, isolated pixel cannot be formed. Codeword selection problem and isolated pixel detection problem are formulated as integer program models and we develop a cutting plane algorithm where a valid cut is generated to remove current feasible solution to avoid isolated pixel by solving the isolated pixel detection subproblem. Using the proposed method, 6/8 codewords with non-isolated pixel are found.

Cutting Plane Algorithm for the Selection of Non-Isolated Pixel Modulation Code