COEN
180


Magnetic Codes 
Figure 1: Write currents for NRZ and NRZI binary coding
The principal drawback of NRZI is the clocking difficulties for a long string of zeroes (NRZ has the problem for long strings of ones as well). Furthermore, repeating ones in NRZI lead to a sequence of flux changes. As we have seen, flux changes in close proximity interfere with each other when read.
Phase encoding (PE) alleviates the clocking problem and is being used for 1/2 inch tapes. PE has a up transition for a one, a down transition for a zero. If there are two or more ones or zeroes in a row, then extra transitions occur at the bit cell boundary. PE can have twice as many flux transitions than there are bit changes in the original data. FM (Frequency Modulation) has a transition to delimit each clock window. A transition in the middle of the clock cell indicates a one, the absence of one a zero. In the worst case, FM also has twice as many transitions as bits. MFM (delay modulation / Miller Code) is an extremely popular variant of FM where the flux changes at the clock window boundaries are suppressed if they do not serve to adjust the clock timing. Thus, in MFM, we have a transition in the middle of the clock window, if the bit is a one. We have a transition at the boundary of the clock window if the data bits encoded in the two windows are both zeroes. The number of flux changes is now equal to the number of changes between bits.
Figure 2: Write currents for PE, FM, and MFM.
We can represent MFM as a state diagram. The data bits determine the transitions (the number next to the arrows) and the two bits within the state the bits emitted. In the emitted bit stream, a 1 stands for a transition, a 0 for a lack of a transition. The first bit indicates the changing of the clock window, the second one the transition or lack thereof in the middle of the clock window.
Figure 3: MFM (Miller Code) State Diagram.
Data  Code Word 
10 
0100 
11 
1000 
000 
000100 
010 
100100 
011 
001000 
0010 
00100100 
0011 
00001000 
© 2003 Thomas Schwarz, S.J., COEN, SCU SCU COEN T. Schwarz COEN 180 