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The paper considers the issue of channel a posteriori probability (APP) computation for equalized Lorentzian magnetic recording channels with colored noise. Most work on the application of turbo codes to magnetic recording channels has focused on ideal partial response (PR) channels with additive white Gaussian noise (AWGN). Since the channel APP detector assumes uncorrelated Gaussian noise, the performance of turbo codes on the more realistic equalized Lorentzian channel with correlated noise is much worse than on an ideal PR channel. To deal with the colored noise, we consider modifications to the computation of the channel APP tuned to the colored noise statistics of the equalized channel. We first apply the soft-output detector (SOD) for Markov noise from Kavcic (1999) with some modification in the branch metric computation. We then propose a new forward extended detector (FED) for Gaussian colored noise. Simulations of a rate 8/9 turbo code on a PR4-equalized Lorentzian channel with colored noise for both detectors are conducted. With FED, we observe a gain of 1.1 dB at a bit error rate of 10-5 relative to the conventional APP channel detector for user density of 2.0 and a gain of 1.8 dB for user density of 2.5.