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Patterned magnetic media promises areal densities in excess of 1 Tbit/in2 for data storage. However, current imperfect patterning techniques result in a variation in the dimensions and distribution of the fabricated islands. As a result, this variation introduces jitter in the replay waveform that makes data recovery difficult. In this paper, we investigate the use of low-density parity-check (LDPC) codes and iterative decoding for mitigating the effects of lithography jitter and improving the read channel performance in patterned media storage systems. In addition, we show that the adoption of LDPC coding techniques permits an increase in the data storage capability of the medium to approximately 1.6 Tbit/in2 with acceptable bit-error-rate performance.