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Suppressing intertrack interference (ITI) and intersymbol interference (ISI) is crucial for achieving high-density magnetic recording beyond 10 Tera bits/inch2. We propose a novel iterative method for reducing errors caused by ITI and ISI involving the adaptive estimation of ITI and the log likelihood ratios obtained from signals of neighboring tracks. This method is useful for decoding signals recorded by bit-patterned media and conventional media. Moreover, the method is extended to decode signals from the Voronoi-based discrete grain model for shingled write recording (SWR), accounting for four neighboring bits. Bit errors due to both neighboring track shifts of approximately 20% can be canceled for BPM and SWR.