Reduction of Bit Errors Due to Inter-Track Interference ... - Google Sites

> THIS MANUSCRIPT HAS BEEN ACCEPTED FOR FINAL PUBLICATION ON IEEE TRANSACTION ON MAGNETICS
THIS MANUSCRIPT HAS BEEN ACCEPTED FOR FINAL PUBLICATION ON IEEE TRANSACTION ON MAGNETICS < neighboring tracks (1 and 3) is defined as α and β. The size of the magnetic head is normalized to 1. Each state now has 8 branches. (c) ITI from a single neighboring track with a phase shift This corresponds to a conventional medium. The track shift parameters α and β are functions of the phase shift between the main track (track 1) and the neighboring tracks (2 and 3). The other conditions are the same as those in (a) and (b).

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One example of an improvement to the bit error rate for ITI from a single neighboring track is shown in Fig. 3. This simulation reproduces a signal with a track shift α = 0.2 and generates a main track signal ratio β = 0.8. This result was evaluated for a signal-to-noise ratio (SNR) of 10 dB. When the track shift is estimated correctly, according to (8), the bit error rate is improved by approximately two orders of magnitude by using the LLRs of a neighboring track signal as extrinsic information, independent of errors included in the neighboring track signal. 10

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Bit error rate

Extrinsic information without crosstalk error Extrinsic information with crosstalk error

(a) Signal sequence (b) Trellis diagram Fig. 1. Model of ITI from a single neighboring track.

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0

0.05

0.1

0.15 0.2 0.25 Track shift estimation

0.3

0.35

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Fig. 3. Bit error rate improvement for ITI from a single neighboring track.

B. ITI from Both Neighboring Tracks

(a) Signal sequence (b) Trellis diagram Fig. 2. Model of ITI from both neighboring tracks.

III. PERFORMANCE EVALUATION FOR BPM It is assumed that ITI of reproduced signals from BPM is neglected and ISI is treated as PR1after equalization when the head position is on track. A. ITI from a Single Neighboring Track We assume additive white Gaussian noise (AWGN). The signal-to-noise ratio (S/N) is defined as 10 log (2/N0), where N0 = 2σ2 and σ2 is the AWGN variance. The branch metric value (BM) is given by (5), where γ is the track shift estimation. The optimal value of γ is defined by (6). After simplifying yk' as shown in (7), the estimated value  * based on the LMS algorithm is represented as (8). Δ is the step size for adaptation. 2

where y  ' k

2

y 1

k

y

' k



2

1

 h

m 1 n 1

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With LLRS Without LLRS

,

' m ,n m ,n  k

x

  and H  1    0 '



0 1   0  . 0 0 

Bit error rate

BM  

1

In this case, the MIMO model has 3 inputs, 3 outputs (effectively 1 output), and 8 states. The signal detection ratio between the main track (track 2) and the neighboring tracks (1 and 3) is defined in Fig. 2. The size of the magnetic head is normalized to 1. Each state has 8 branches. In the decoding process,  and  can be estimated with an LMS algorithm based on the reproduced signals mixed with those of both neighboring tracks. Moreover, LLRs of both neighboring tracks are used as extrinsic information in the decoding process. Figure 4 shows one example of improvement to the bit error rate: this was achieved by using both neighboring LLRs that were generated from binary decision data, including errors at a bit error rate of 10-2. This figure plots the bit error rate performance as a function of the estimated error in the track shift. This result was evaluated with SNR of 10 dB and 20% track shift of both sides. Namely,  and  are selected as 0.2, respectively.

(5)

 opt  min arg ( yk'  yk )2

(6)

yk  (1   )( x0,k 1  x0,k ) *

 *   *  E{( yk'  yk )( x0,k 1  x0,k )}

(7)

0

0.05

0.1

0.15 0.2 0.25 Track shift estimation

0.3

0.35

. (8)

Fig. 4. Bit error rate improvement for ITI from both neighboring tracks.

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> THIS MANUSCRIPT HAS BEEN ACCEPTED FOR FINAL PUBLICATION ON IEEE TRANSACTION ON MAGNETICS
THIS MANUSCRIPT HAS BEEN ACCEPTED FOR FINAL PUBLICATION ON IEEE TRANSACTION ON MAGNETICS < The simulation results for signals from the VDGM are shown in Fig. 8, with the SNR of the training data indicated in parentheses in the curve labels. For SNR values larger than 23 dB, the bit error rate for the 32-state trellis structure is superior. In order to isolate the influence of noise coming from the Voronoi model, a bit error rate for each detection method is shown in Fig. 9. No AWGN is added to the retrieved signals. The horizontal axis shows SD. For SD values under 0.5, the bit error rate for the 32-state trellis is poorer than those of the ITI and the 8 × 8 trellis structures. Figures 8 and 9 clearly show that the detecting capability depends on the relation between the variance (VN) of noise coming from VDGM and the variance of AWGN. When the VN is larger than AWGN, the performance of the 32-state trellis structure is superior. Otherwise, the three detectors except BCJR have nearly the same performance

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(c) The proposed method with LDPC code The proposed decoding method with LDPC code was applied to SWR. We used PG-LDPC with a code rate of 0.95. Results are shown in Fig. 10. By using the PG-LDPC code, signals from VDGM with a low SD and a high SNR were decoded completely. However, the BCJR algorithm with the LDPC code did not work well in this case.

Fig. 10. Bit error rate performance for various detection methods with PG-LDPC code for SD = 1.

Ⅴ. CONCLUSIONS

(a) SD = 075

We have proposed novel iterative data-detection methods based on an adaptive estimation for ITI and also the log likelihood ratios for decoding reproduced signals, including both ITI and ISI for BPM and SWR. We have confirmed the possibility of correcting bit errors due to 2 neighboring track shifts of approximately 20%. ACKNOWLEDGMENTS This study was supported by the Japan Society for the Promotion of Science (JSPS) for Scientific Research KAKENHI (21560418), the Storage Research Consortium (SRC), and the NEDO project. REFERENCES

(b) SD = 1 Fig. 8. Bit error rate performance for various detection methods vs. AWGN.

Fig. 9. Bit error rate performance vs. SD.

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