15.01.2013 Views

U. Glaeser

U. Glaeser

U. Glaeser

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

FIGURE 34.36 An example of two Gray-coded track addresses. The two addresses are different only in the third<br />

location.<br />

that specific track. As will be discussed shortly, such a constraint influences the ECC as well as sequence<br />

detection strategies.<br />

A related concern is the presence of radial incoherence, and the erase field introduced during servo<br />

writing that are present when the read head straddles two tracks. The detector performance will suffer<br />

from such impairments. Formats that tolerate such impairments are desired.<br />

Because the recorded address mark and wedge address does not vary from one track to the next, the<br />

emphasis is on track addresses. When the read head is in the middle of two adjacent tracks, with track<br />

addresses X and Y, the read waveform is the superposition of the waveforms generated from each of the<br />

respective addresses. In general, the resulting waveform cannot be decoded reliably to any one of the two<br />

track addresses. A common solution is the use of a Gray code to encode track addresses, as shown in<br />

Fig. 34.36, where any two adjacent tracks differ in their binary address representation in only one symbol<br />

value. Hence, for the moment ignoring ISI, when the head is midway between adjacent tracks, the detector<br />

will decode the address bits correctly except for the bit location where the two adjacent tracks differ, that<br />

is, for the two track addresses labeled as X and Y, the decoder will decode the waveform to either track<br />

address X or Y, introducing an error of at most one track. By designing a radially periodic servo burst<br />

field, with period of at least two track widths, track number ambiguity generated by track addresses is<br />

resolved; however, as will be discussed next, Gray codes complicate the use of ECC codes and sequence<br />

detectors.<br />

A Gray code restricts two adjacent tracks to differ in only a single position, or equivalently forcing the<br />

Hamming distance between two adjacent track addresses to be one. Adding an ECC field to the digital<br />

fields is desirable since reliable detection of track addresses is needed in the presence of miscellaneous<br />

impairments such as electronic and disk media noise, radial incoherence, erase bands, etc.; however, any<br />

ECC has a minimum Hamming distance larger than one. That is, it is not possible to have two adjacent<br />

track-addresses be Gray and ECC encoded simultaneously. If an ECC field is appended to each track<br />

address, it can be used only when the head is directly above a track. A possible alternative is to write the<br />

track addresses multiple times with varying radial shifts so that, at any position, the head is mostly directly<br />

above a track address [13]. Such a solution improves reliability at the expense of significant format<br />

efficiency loss.<br />

Another complication of introducing Gray codes results from the interaction of these codes with the<br />

ISI channel. Consider an ISI free channel where the magnetic transitions are written ideally and where<br />

the read head is allowed to be anywhere between two adjacent Gray coded track addresses X and Y. As<br />

was discussed earlier, the track address reliability, or the probability that the decoded address is neither<br />

X nor Y, is independent of the read head position. Next, it is shown that for an ISI channel the detector<br />

performance depends on the radial position. In particular, consider the simple ISI channel with pulse<br />

response 1 − D, which approximates a magnetic recording channel. For such a channel, events of length<br />

two are almost as probable as errors of length one (same distance but different number of neighbors).<br />

Now, as the head moves from track X to Y, the waveform modification introduced by addresses X and<br />

Y, at that one location where the two tracks differ, can trigger an error of length two. The detector may<br />

decode the received waveform to a different track address Z, which may lie far from addresses X or Y. In<br />

other words, in an ISI channel, whenever the head is between two tracks X and Y, the probability that<br />

the received waveform is decoded to some other address Z increases.<br />

© 2002 by CRC Press LLC<br />

X<br />

Y<br />

+ - + + + -<br />

+ - - + + -

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!