This paper studies the performance of a serial turbo code on two simplified rectangular-grain models of recording media for two dimensional magnetic recording at a density of more than 0.5 bits/grain. We derive one-dimensional (1D) and two-dimensional (2D) rectangular-grain media models and from these present finite-state-machine (FSM) representations. From the FSM for the 1D model we computed achievable information rates assuming independent and uniformly distributed (i.u.d.) binary inputs. From the (approximate) FSM for the 2D 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 1D model and 65\% of the average of published upper and lower bounds on capacity for the 2D model.