U. Glaeser

FIGURE 34.43 Two equivalent constraints: (a) F = {11} NRZI and (b) F = {101, 010} NRZ.
For high capacity constraints, graph transforming techniques, such as the state-splitting algorithm,
may result in encoder/decoder architectures with formidable complexity. Fortunately, a block encoder/
decoder architecture with acceptable implementation complexity for many constraints can be designed
by well-known enumerative [6], and other combinatorial [32] as well as heuristic techniques [25].
Translation of constrained sequences into the channel sequences depends on the modulation method.
Saturation recording of binary information on a magnetic medium is accomplished by converting an
input stream of data into a spatial stream of bit cells along a track where each cell is fully magnetized in
one of two possible directions, denoted by 0 and 1. Two important modulation methods are commonly
used on magnetic recording channels: non-return-to-zero (NRZ) and modified non-return-to-zero (NRZI).
In NRZ modulation, the binary digits 0 and 1 in the input data stream correspond to 0 and 1 directions
of cell magnetizations, respectively. In NRZI modulation, the binary digit 1 corresponds to a magnetic
transition between two bit cells, and the binary digit 0 corresponds to no transition. For example, the
channel constraint which forbids transitions in two neighboring bit cells, can be accomplished by either
F = {11} NRZI constraint or F = {101, 010} NRZ constraint. The graph representation of these two
constraints is shown in Fig. 34.43. The NRZI representation is, in this case, simpler.
Constraints for ISI Channels
This subsection discusses a class of codes known as codes, which avoid specified differences. This is the
only class of distance enhancing codes used in commercial magnetic recording systems. Two main reasons
for this are: these codes simplify the channel detectors relative to the uncoded channel and even high
rate codes in this class can be realized by low complexity encoders and decoders.
Requirements
A number of papers have proposed using constrained codes to provide coding gain on channels with
high ISI (see, for example, [4,10,20,28]). The main idea of this approach can be described as follows
[20]. Consider a discrete-time model for the magnetic recording channel with possibly constrained input
a = {an} C ∈� {0,1} ∞ , impulse response {hn}, and output y = {yn} given by
© 2002 by CRC Press LLC
∑
yn = amh n−m + ηn m
(34.32)
where h(D) = ∑ nh nD n = (1 − D)(1 + D) 3 (E 2 PR4) or h(D) = ∑ nh nD n = (1 − D)(1 + D) 4 (E 3 PR4), η n are
independent Gaussian random variables with zero mean and variance σ 2 . The quantity 1/σ 2 is referred
to as the signal-to-noise ratio (SNR). The minimum distance of the uncoded channel (34.32) is
2
d
min
min =
�( D)
0
≠ h( D)�(
D)
2