IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 5, SEPTEMBER 2000 2187

Performance of Timing Recovery Methods in TurboCoded Magnetic Recording Channels

Yifei Yuan, Erozan Kurtas, and B. V. K. Vijaya Kumar

Abstract—Turbo codes, with potential 4 to 5 dB coding gain overthe conventional Viterbi detection schemes, are good candidatesfor the next generation detection/decoding schemes for magneticrecording systems. In this paper, timing recovery is included inthe evaluation of Turbo codes. Three timing recovery methods,namely voltage control oscillator (VCO) method, interpolatedtiming recovery (ITR) method and adaptive filter timing recovery(AFTR) method are examined for two turbo decoder architec-tures, full turbo and serial turbo. Bit error rate (BER) results fromsimulations suggest that full turbo decoder is more robust thanthe serial turbo decoder. For serial turbo decoder, error floor isseen earlier in VCO and ITR methods than AFTR method. Usings-random interleaver seems to be able to remove such error floor.

Index Terms—Adaptive filter, concatenated coding, partial re-sponse signaling, timing recovery, turbo codes.

I. INTRODUCTION

T URBO codes, proposed by Berrouet al. [1], have gainedmuch interest recently in magnetic recording systems due

to the potential 4 to 5 dB coding/performance gain over theconventional partial response maximum likelihood (PRML)system. Earlier analyzes of turbo codes modeled recordingchannels as ideal partial response (PR) outputs corrupted byadditive white Gaussian noise (AWGN) [2], [3]. EqualizedLorentzian pulse channel was studied in [2], [4] where BERperformance degradation was observed when compared to theideal PR plus AWGN channel. Such degradation is due to themismatch between the ideal PR target and the actual equalizedpulse response. In [4] and [5], it was shown that turbo decodersare quite insensitive to colored noise.

All these studies assumed perfect timing. However, in realsystems, timing recovery must be included to track unknowntime variations due to speed fluctuations and other sources oftiming disturbances. Even with timing recovery, sampling in-stants are often not perfect because of noise. Thus certain per-formance degradation is expected, especially when signal tonoise ratio (SNR) is low. Three timing recovery methods suit-able for magnetic recording channels are examined in this paper.The first one, called voltage control oscillator (VCO) method, iswidely applied in current commercial hard drives. This methoduses an analog VCO to control sampling of continuous-timereadback signals. The second method is the interpolated timingrecovery (ITR) where a digital interpolation filter adjusts phase

Manuscript received February 14, 2000. This work was supported in part byNSF Grant ECD-8907068.

Y. Yuan and B. V. K. Vijaya Kumar are with the Data Storage Systems Center(DSSC), Carnegie Mellon University, Pittsburgh, PA 15213 USA.

E. Kurtas is with Seagate Technology, Pittsburgh, PA 15203 USA.Publisher Item Identifier S 0018-9464(00)08403-X.

Fig. 1. Block diagram of the turbo coded magnetic recording system.

offsets in asynchronous signal samples obtained via a fixed rateclock [6], [7]. Both these methods take the form of a phase-locked loop (PLL) and use Muller & Mueller timing error de-tector [8] to estimate timing errors. The third method, calledadaptive filter timing recovery (AFTR) [9], uses an adaptivefilter to do both timing recovery and equalization simultane-ously so that a PLL is not needed.

We consider two turbo decoder architectures [3], [4]. The firstone called full turbo includes a channela posteriorprobability(APP) detector and two convolutional code APP decoders. Thesecond architecture called the serial turbo [3] includes a channelAPP detector serially concatenated with a single outer convo-lutional code APP detector. Serial turbo method is more ap-pealing than the full turbo method because of its simpler algo-rithm. In this paper, we present the BER as a function of inputsignal-to-noise ratio (SNR) for selected cases of timing recoverymethods and turbo decoders. SNR is defined as the ratio of PRtarget energy to the white noise level (code rate is included).The rest of paper is organized as follows. In Section II, simu-lation parameters will be discussed. Simulation results will beprovided in Section III. We will provide our conclusions in thesummary section.

II. SIMULATION PARAMETERS

A. System Diagram

Fig. 1 explicitly shows the timing recovery stage in the turbocoded magnetic recording channel. Readback signal suffersfrom timing variations due to speed fluctuations. The readbacksignal is first input to a low pass filter where out-of band noiseis filtered out and preliminary equalization (in the form ofa passband edge boost) is performed. The filtered signal isprocessed to extract timing information and equalization isperformed. Finally, the equalized and timing-adjusted signalsamples are detected and decoded by the turbo decoder block.

B. Turbo Coding Parameters

The block size of interleavers is 5120 bits. We apply two in-terleavers: pseudo-random and-random. -random interleaver

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2188 IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 5, SEPTEMBER 2000

ensures minimum separation ofbits = 20 in our simula-tions) after interleaving. The recursive systematic convolutional(RSC) encoder is described by generator polynomials in octalform . The precoder is . Punc-turing results in an overall code rate of 16/17. Bit error rates(BER) are collected after employing 15 decoding iterations.

C. Recording Model

Linear superposition model with Lorentzian step responseplus additive white Gaussian noise (AWGN) is assumed. Thenormalized recording density is 2.5. To mimic continuous read-back signals, we oversample by 20so that the time resolutionis 5% of channel bit interval. 200-bit long preamble sequence isadded at the beginning of channel bits to facilitate the PLL toacquire the clock. Preamble sequence is:1, 1, 1, 1, 1, 1,1, 1, .

Timing variability is modeled by two-stage integration of anAWGN sequence [10]. The outputs of the first integrator and thesecond integrator are frequency disturbance and phase distur-bance (timing variability), respectively. In the simulations, fre-quency disturbance can be as high as 0.1%, which means thattiming variability can be as large as 5 in a block (5120 bits).

D. Equalization and Timing Recovery

The low pass filter used is a 7th order linear phase equi-ripplefilter with two parameters optimized for BER.

The equalizer is a finite impulse response (FIR) filter with11 coefficients and their initial values are obtained via leastmean squares (LMS) training.

The PLL’s in both the VCO method and the ITR method areof second order. In simulations, VCO is assumed to exhibit idealvoltage-to-frequency characteristics. The interpolation filter inthe ITR method uses 11 precomputed coefficients stored in alook-up table. The table has 40 entries, therefore, the phase res-olution is (1/40)th of bit interval.

In the AFTR method, the LMS algorithm is used to update theadaptive filter’s coefficients “on-the-fly.” The adaptation stepsize is 0.018. The adaptive filter has 7 coefficients and works ina decision-directed mode.

All the simulation results shown (except PRML and idealtiming) include timing variations. Ideal timing refers tothe system with uniform sampling and without any timingvariation.

III. SIMULATION RESULTS

A. Bit Error Rate Comparisons

Fig. 2 shows the BER vs. SNR for the full turbo decoder. Itis seen that there is no sign of error floor. At BER = 10, theVCO and the ITR methods are better than the AFTR methodby about 0.2 dB and worse than the ideal timing case by 0.1 dB.The slightly worse performance of AFTR method is perhaps dueto the filter’s coefficients being updated at SNR less than 9 dBwhereas other methods use precomputed coefficients trained atSNR = 12 dB. From Fig. 2, it seems that the coding gain of thefull turbo decoder can still be around 3.5 dB over the PRMLsystem even with frequency disturbance of about 0.1%.

Fig. 2. Bit error rate vs. SNR for full turbo decoder.

Fig. 3. Bit error rate vs. SNR for serial turbo decoder.

Fig. 3 shows BER vs. SNR for the serial turbo decoder. Incontrast to Fig. 2, both VCO method and ITR method hint atan earlier error floor for pseudo-random interleaver. However,in the case of s-random interleaver, such early floor is removed.At BER = 10 level, VCO method and ITR method are closeto the ideal timing case and better than AFTR by 0.3 dB.

B. Error Bit Location Comparisons

Fig. 4 shows the histograms of the cumulative number of er-rors that occurred at each bit position in a block for the full turbodecoder. The data is collected at BER’s around . Foreach plot, 500 blocks are considered. From block to block, wechange the pseudo-random user bit sequence while using thesame time base wander and pseudo-random interleavers. It isfound that the error bit locations for all three timing methods areuniformly distributed across entire blocks, similar to the idealtiming case. The absence of error burst may be due to the fact

YUAN et al.: TIMING RECOVERY METHODS IN TURBO CODED MAGNETIC RECORDING CHANNELS 2189

Fig. 4. Cumulative bit error locations for full turbo decoder.

that the full turbo decoder uses a second interleaver in the it-erative decoding process, where erroneous chunks of bits areshuffled further.

The cumulative error bit location counts for the serial turbodecoder are shown in Fig. 5 with BER around for allthree timing recovery methods. It is seen that the error bits tendto concentrate in a few locations for the three timing methods,while the error locations in ideal timing case are more evenlydistributed. Such difference may be due to the fact that the se-rial turbo decoder uses only a single pseudorandom interleaverin the iterative decoding process, where local chunks of bit er-rors cannot be thoroughly shuffled. Using-random interleaverseems to offer a solution that results in quite evenly distributederror bit locations.

IV. CONCLUSION

Timing recovery is considered in turbo coded magneticrecording channels. Three timing recovery methods are simu-lated for two types of turbo decoders: full turbo and serial turbo.BER results show that serial turbo decoder exhibits a significanterror floor for VCO and ITR methods. From the distribution oferror bit locations, full turbo decoder does not appear to leadto correlated errors. For serial turbo decoder, including timingrecovery appears to affect the error bit location distributions,especially for VCO and ITR methods when pseudo-random

Fig. 5. Cumulative bit error locations for serial turbo decoder.

interleaver is used. Such effect appears to be not significantwhen applying -random interleaver.

REFERENCES

[1] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limiterror-correcting coding and decoding: turbo codes,” inProc. 1993 Int.Conf. Commun., May 1993, pp. 1064–1070.

[2] W. Ryan, “Performance of high rate turbo codes on a PR-4 equalizedmagnetic recording channel,” inProc. 1998 Int. Conf. Commun., June1998, pp. 947–951.

[3] T. Souvignier, A. Friedmann, M. Oberg, P. Siegel, and J. K. Wolf, “Turbocodes for PR4: Parallel versus serial concatenation,” inProc. 1999 Int.Conf. Commun., June 1999, pp. 1638–1642.

[4] T. M. Duman and E. Kurtas, “Comprehensive performance investiga-tion of turbo codes over high density magnetic recording channels,” inGLOBECOM, 1999.

[5] T. Souvignier and J. K. Wolf, “Turbo decoding for partial response chan-nels with colored noise,”IEEE Trans. Magn., vol. 35, pp. 2322–2324,Sept. 1999.

[6] M. Spurbeck and R. T. Behrens, “Interpolated timing recovery for harddisk drive read channels,” inProc. 1997 Int. Conf. Commun., June 1997,pp. 1618–1624.

[7] Z. Wu and J. M. Cioffi, “A MMSE interpolated timing recovery schemefor the magnetic recording channel,” inProc. 1997 Int. Conf. Commun.,June 1997, pp. 1625–1629.

[8] K. H. Mueller and M. Muller, “Timing recovery in digital synchronousdata receivers,”IEEE Trans. Commun., vol. COM-24, pp. 516–530, May1976.

[9] Y. Yuan and B. V. K. Vijaya Kumar, “Use of adaptive filter for timingrecovery for data storage channels,” in 2000 Int. Conf. Commun., NewOrleans, LA, June 2000, to be published.

[10] A. Pataputian, “On phase-locked loops and Kalman filters,”IEEE Trans.Commun., vol. 47, pp. 670–672, May 1999.