I. Introduction
Present technologies in 1-D magnetic recording yield storage densities as high as . A thermodynamic limit for the magnetic storage density is shown to be close to [1]. With the need for higher areal densities, alternative technologies, such as heat-assisted-magnetic- recording and bit-patterned-media recording, have been proposed. However, these technologies require advancements in guided laser delivery over nano-scales and careful lithographic considerations, respectively. The timing recovery for 2-D magnetic recording (TDMR) is an alternative magnetic recording technology [2], where a greater emphasis is laid on advanced signal processing techniques for significantly enhancing the areal densities within the existing technological framework.