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This paper introduces the application of a factor graph (FG)-based detector on a one-dimensional (1D) intersymbol interference (ISI) magnetic recording channel. The conventional Bahl-Cocke-Jelinek-Raviv (BCJR) detection algorithm operates on a trellis, which defines an equivalence between a bit sequence and a path through the trellis, as well as all possible time evolutions of states of the channel. The BCJR algorithm outputs soft information which corresponds to the a-posteriori channel bit probabilities. Unlike the BCJR, the FG-based detector employs the use of the sum product algorithm (SPA) on a FG with the objective of calculating the same a-posteriori probabilities. Employing the binary SPA to this FG detector gives rise to a suboptimal performance due to the presence of short cycles within the channel factor graph. A nonbinary implementation of the same algorithm mitigates the effect of these cycles and thereby results in an improved performance as compared to the binary implementation. In this paper we also propose an alternative method that can be used to reduce the number of these cycles for performance enhancement. This method involves using an equalizer with a generalized partial response (GPR) target.