Encoding Scheme Comparisons

Figure 8.10 shows an example of the waveform written to store the ASCII character X on a hard disk drive by using three different encoding schemes.

In each of these encoding scheme examples, the top line shows the individual data bits (01011000b, for example) in their bit cells separated in time by the clock signal, which is shown as a period (.). Below that line is the actual write waveform, showing the positive and negative voltages as well as head voltage transitions that result in the recording of flux transitions. The bottom line shows the transition cells, with T representing a transition cell that contains a flux transition and N representing a transition cell that is empty.

The FM encoding example shown in Figure 8.10 is easy to explain. Each bit cell has two transition cells: one for the clock information and one for the data itself. All the clock transition cells contain flux transitions, and the data transition cells contain a flux transition only if the data is a 1 bit. No transition is present when the data is a 0 bit. Starting from the left, the first data bit is 0, which decodes as a flux transition pattern of TN. The next bit is a 1, which decodes as TT. The next bit is 0, which decodes as TN, and so on.

The MFM encoding scheme also has clock and data transition cells for each data bit to be recorded. As you can see, however, the clock transition cells carry a flux transition only when a 0 bit is stored after another 0 bit. Starting from the left, the first bit is a 0, and the preceding bit is unknown (assume 0), so the flux transition pattern is TN for that bit. The next bit is a 1, which always decodes to a transition-cell pattern of NT. The next bit is 0, which was preceded by 1, so the pattern stored is NN. By using Table 8.2 (shown earlier), you easily can trace the MFM encoding pattern to the end of the byte. You can see that the minimum and maximum numbers of transition cells between any two flux transitions are one and three, respectively, which explains why MFM encoding can also be called RLL 1,3.

The RLL 2,7 pattern is more difficult to see because it encodes groups of bits rather than individual bits. Starting from the left, the first group that matches the groups listed in Table 8.3 is the first three bits, 010. These bits are translated into a flux transition pattern of TNNTNN. The next two bits, 11, are translated as a group to TNNN; and the final group, 000 bits, is translated to NNNTNN to complete the byte. As you can see in this example, no additional bits are needed to finish the last group.

Notice that the minimum and maximum numbers of empty transition cells between any two flux transitions in this example are 2 and 6, although a different example could show a maximum of seven empty transition cells. This is where the RLL 2,7 designation comes from. Because even fewer transitions are recorded than in MFM, the clock rate can be increased to three times that of FM or 1.5 times that of MFM, thus storing more data in the same space. Notice, however, that the resulting write waveform itself looks exactly like a typical FM or MFM waveform in terms of the number and separation of the flux transitions for a given physical portion of the disk. In other words, the physical minimum and maximum distances between any two flux transitions remain the same in all three of these encoding scheme examples.