U. Glaeser

In the above example, we see that sample “1” is suppressed by “−1” from the next transition. It is a simple
matter to check that all possible linear combinations of the samples result in only three possible values
{−1, 0, +1} (naturally, it is that all parts of the system are working properly, i.e., equalization, gain, and
timing recovery, and that the signal is noise free). A positive pulse of voltage is always followed by a
negative pulse and vice versa, so that the system can be regarded as an alternative mark inversion (AMI)
code.
The higher bit capacity of the PR4 channel can best be understood from Fig. 34.48. It is observed that
PR4 channel provides a 50% enhancement in the recording density as compared with the peak detection
(fully equalized) one, since the latter requires isolation of single bits from each other. In the next figure,
we see that the EPR4 channel (explained later) adds another 33% to this packing density. PR4 has another
advantage over all the other PR systems; since H(D) = 1 − D 2 , the current symbol is correlated to the
second previous one, allowing the system to be modeled as two interleaved dicode channels, implying
the use of simple dicode detectors for even and odd readback samples. RLL coding is necessary in this
case, since nonideal tracking and timing errors result in a residual intermediate term (linear in D) that
induces correlation between two interleaved sequences, and thus degrades systems that rely on decoupled
detection of each of them.
RLL codes are widely used in conjunction with PR equalization in order to eliminate certain data
strings that would render tracking and synchronization difficult. If PR4 target is used, a special type of
RLL coding is used, characterized by (0,G/I). Here, G and I denote the maximum number of consecutive
zeros in the overall data string, and in the odd/even substrings, respectively. The latter parameter ensures
proper functioning of the clock recovery mechanism if deinterleaving of the PR4 channel into two
independent dicode channels is performed. The most popular is the (0,4/4) code, whose data rate is 7/8,
i.e., whose data loss is limited to 12.5%.
Other PR targets are used besides PR4. The criterion of how to select the appropriate PR target is
based on spectral matching, to avoid introducing too much equalization noise. For instance, for PW50/T
≈ 2.25, it is better to model ISI pattern as the so-called EPR4 (i.e. extended class-4 partial response)
channel with H(D) = (1 + D) 2 (1 − D) = 1 + D − D 2 − D 3 . As the packing density goes up, more low
frequency components are being introduced (low compared to 1/T, that also increases as T is shortened,
in reality those frequencies are higher than those met for lower recording densities, respectively greater
T). This is the consequence of the fact that intersymbol interference blurs the boundary between individual
pulses, flattening the overall response (in time domain). The additional 1 + D term in the target
PR effectively suppresses the unwanted high frequencies. EPR4 enables even higher capacities of the
magnetic recording systems than PRIV, observing the difference of 33% in the recording density displayed
in Fig. 34.49; however, a practical implementation of EPR4 is much more complex than is the case with
PR4. First, the deinterleaving idea used for PR4 cannot be implemented. Second, the corresponding state
diagram (and consequently trellis) now has eight states instead of four (two if deinterleaving is used).
Furthermore, its output is five-leveled, instead of ternary for the PR4 and the dicode channel, so that a
4.4 dB degradation is to be expected with a threshold detector. Naturally, if sequence detector is used,
such as Viterbi algorithm (VA), this loss does not exist, but its elimination is obtained at the expense of
a significantly increased complexity of the detector. Furthermore, if such a detector can be used, EPR4
has a performance advantage over PR4 due to less equalization noise enhancement, cf. Fig. 34.50.
Let us reconsider the PR equalizer shown in Fig. 34.47. Following the approach from Reference 44,
its aim is to transform the input spectrum Y′(e j2πΩ ) into a spectrum Y(e j2πΩ ) = Y′(e j2πΩ )|C(e j2πΩ )| 2 , where
C(e j2πΩ ) is the transfer function of the equalizer. The spectrum Y(e j2πΩ ) = I(e j2πΩ )|H(e j2πΩ )| 2 + N(e j2πΩ )
where H (D) is the PR target. For instance, duobinary PR target (H(D) = 1 + D) enhances low frequencies
and suppresses those near the Nyquist frequency Ω = 0.5, whereas dicode H(D) = (1 − D) does the
opposite: it suppresses low frequencies and enhances those near Ω = 0.5.
In principle, the spectral zeros of H(e j2πΩ ) can be undone via a linear (recursive) filter, but this would
excessively enhance any noise components added. The schemes for tracking the input sequence to the
system based on the PR target equalized one will be reviewed later in this chapter section. For instance,
© 2002 by CRC Press LLC