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This paper studies the performance of a serial turbo code on two simplified rectangular-grain models of recording media for two-dimensional (2-D) magnetic recording at a density of more than 0.5 bits/grain. We derive one-dimensional (1-D) and 2-D rectangular-grain media models and from these present finite-state-machine (FSM) representations. From the FSM for the 1-D model we computed achievable information rates assuming independent and uniformly distributed (i.u.d.) binary inputs. From the (approximate) FSM for the 2-D model, we present a detector. We then present a serial turbo code architecture with constituent convolutional codes that is capable of achieving 80% of i.u.d. capacity for the 1-D model and 65% of the average of published upper and lower bounds on capacity for the 2-D model. We also present schemes which combine the advantages of an (inner) repetition code and an (outer) serial turbo code. One such scheme cleverly arranges the three bits in each three-fold repetition into the shape of an “L”. This obviates the need for a sequence detector and converts the 2-D channel model into an equivalent binary symmetric channel.