Lectures.13_and_14_-_Notes

Lectures.13_and_14_-_Notes - 1 Mapping User Data to...

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Mapping User Data to Magnetic Media Two different conventions are used to map a binary sequence, z 0 z 1 …, where z i =0,1 to a magnetization pattern, w 0 w 1 …, where w i =-1,+1. NRZ: z=1 >w=1 z=0 >w= 1 NRZ: z i =1 --> w i =1 , z i =0 --> w i =-1 NRZI: z i =1 represents a reversal of the direction of magnetization, while z i =0 represents no change. z i =1 --> w i -w i-1 =+2,-2 , z i =0 --> w i -w i-1 =0 NRZ NRZI 0 1 1 1 0 0 0 1 0 0 1 0 Translating between the two conventions: {NRZI} = (1+D){NRZ} or z i =x i +x i-1 (mod2 addition) {NRZ} = [1/(1+D)]{NRZI} or x i =x i-1 +z i (mod2 addition) ENC PRECODER 1/(1+D) User Data Constrained NRZI NRZ 2 1+D CHANNEL DEC NRZI NRZ
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Motivation Modulation codes are used to convert arbitrary binary data sequences (user data) to binary sequences that satisfy certain constraints or restrictions. The constrained sequences are written on the medium instead of the original user data. When reading, the constrained sequences are converted back in order to recover the user data. – This is done by encoding and decoding schemes. Modulation codes can improve the performance of the system by reducing the number of errors made by the detector. They also enable an increase in recording density as they alleviate problems that occur when bits are getting smaller smaller. We will mainly focus on Peak Detection systems, which gave rise to many constraints. However, modulation codes are also widely used in today’s PRML detectors 3 and serve the same purpose.
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Peak Detection A peak detector looks for peaks in the output waveform, whose magnitude exceeds some predetermined threshold. Each such peak is thought to be due to a transition in the input waveform. Peak detection errors may arise from shifts of the peak locations. This happens when 2 adjacent peaks are too close to each other such that they significantly overlap. This is called intersymbol interference (ISI). Some examples are given in the next few slides. Since a peak corresponds to a transition in magnetization, we want to keep transitions farther apart than data bits. Another source of errors is a drifting of the clock phase due to an inadequate number of peaks: – Clock accuracy is maintained by an adaptive timing recovery circuit, known as a phase-lock loop (PLL). It produces a clock of period T b seconds by which to identify seconds by which to identify bit cells. The clock generated by the PLL is adjusted such that, on average, the peaks occur in the centers of clock intervals. Adjustments are made whenever a peak is detected. Thus timing recovery can be improved by ensuring 4 Thus, timing recovery can be improved by ensuring some maximum distance between consecutive transitions.
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Modulation Constraints for Peak Detectors As a result of these problems, some of the sequences that are input to the channel will not be detected correctly, while some other sequences will. This means that some sequences are preferable to others. If we transmit only these preferred sequences, then we may experience fewer detection errors.
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This note was uploaded on 11/11/2009 for the course ECE 670377 taught by Professor Wolf during the Winter '07 term at UCSD.

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Lectures.13_and_14_-_Notes - 1 Mapping User Data to...

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