In this paper, three noise correlation-aided iterative decoding schemes are proposed for magnetic recording channels, where the correlation is imposed by the equalizer's spectral shaping effect. The first approach exploits the noise' correlation in the form of linear prediction-aided detection by increasing the number of detector trellis states invoked by the Bahl, Cocke, Jelinek, and Raviv (BCJR) detection algorithm. In the second approach, we have extended the first technique by employing both previous and future correlated noise samples in order to attain noise estimates. In order to achieve this objective, the classic BCJR algorithm has to be modified for the sake of additionally exploiting future noise samples. The third approach is designed for reducing the decoding complexity by applying the Viterbi Algorithm (VA) to assist the detector in finding the encoded sequences associated with the survivor paths in the detector's trellis, without increasing the number of trellis states. We will demonstrate that for the classic PR4-equalized Lorentzian channel, the proposed schemes are capable of offering a performance gain in the range of 1.1-3.7 dB over that of a benchmark turbo decoding system at the BER of 10-5 and at a recording density of 2.86. Keywords-magnetic recording, noise prediction, turbo codes.