A System Level Study of Two-Dimensional Magnetic Recording (TDMR)

Non-Binary Constrained Codes for Two-Dimensional Magnetic Recording

“…In the setup we propose, after the wide read head finishes reading 3 tracks, it continues on reading the following 3 tracks, e.g., (T 0 , T 1 , T 2 ) then (T 3 , T 4 , T 5 ). Consequently, the ITI between the tracks at the bottom of the 3-tuple and the top of the next 3-tuple is negligible as demonstrated in [4]. This property enables us to design our TD-LOCO codes as non-binary LOCO codes that are used to write the bits on each group of 3 tracks together as we will illustrate shortly.…”

“…In TDMR, the number of tracks and the number of bits per track depend on properties of the magnetic substrate. A wide read head makes it possible to read multiple tracks at the same time [4]. In this paper, we focus on the scenario in which 3 of these tracks are read simultaneously.…”

“…1, 𝛽 , 𝛽 2 , 𝛽 3 , 𝛽 4 , 𝛽 5 1, 𝛽 , 𝛽 2 , 𝛽 3 , 𝛽 4 , 𝛽 5 1, 𝛽 , 𝛽 2 , 𝛽 3 , 𝛽 4 1, 𝛽 2 , 𝛽 3 , 𝛽 4 , 𝛽 5 1, 𝛽, 𝛽 2 , 𝛽 3 , 𝛽 5 The capacity C of these codes can be obtained from statetransition matrix, which is the adjacency matrix of the FSTD [13]. The state-transition matrix T of this FSTD is given by:…”

“…In TDMR devices, interference comes from the adjacent bits in the same track, which is called inter-symbol interference (ISI), in addition to nearby bits in the adjacent tracks, which is called inter-track interference (ITI) [4], [5]. Equalization, if applied, is assumed to have a target that mimics the channel impulse response [6], [16].…”

“…We call this pattern a square isolation (SIS) pattern. Here, we consider the case where a wide head is used to read the bits from three tracks at the same time as shown in [4] and [5]. Only SIS patterns with their centers aligned with the positions where the wide head will be centered (in middle tracks for each group of non-overlapping three) should be forbidden [4].…”