AbstractâTurbo codes, with potential 4 to 5 dB coding gain over the conventional Viterbi detection schemes, are good candidates for the next generation ...
IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 5, SEPTEMBER 2000
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Performance of Timing Recovery Methods in Turbo Coded Magnetic Recording Channels Yifei Yuan, Erozan Kurtas, and B. V. K. Vijaya Kumar
Abstract—Turbo codes, with potential 4 to 5 dB coding gain over the conventional Viterbi detection schemes, are good candidates for the next generation detection/decoding schemes for magnetic recording systems. In this paper, timing recovery is included in the evaluation of Turbo codes. Three timing recovery methods, namely voltage control oscillator (VCO) method, interpolated timing recovery (ITR) method and adaptive filter timing recovery (AFTR) method are examined for two turbo decoder architectures, full turbo and serial turbo. Bit error rate (BER) results from simulations suggest that full turbo decoder is more robust than the serial turbo decoder. For serial turbo decoder, error floor is seen earlier in VCO and ITR methods than AFTR method. Using s-random interleaver seems to be able to remove such error floor. Index Terms—Adaptive filter, concatenated coding, partial response signaling, timing recovery, turbo codes.
I. INTRODUCTION
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URBO codes, proposed by Berrou et al. [1], have gained much interest recently in magnetic recording systems due to the potential 4 to 5 dB coding/performance gain over the conventional partial response maximum likelihood (PRML) system. Earlier analyzes of turbo codes modeled recording channels as ideal partial response (PR) outputs corrupted by additive white Gaussian noise (AWGN) [2], [3]. Equalized Lorentzian pulse channel was studied in [2], [4] where BER performance degradation was observed when compared to the ideal PR plus AWGN channel. Such degradation is due to the mismatch between the ideal PR target and the actual equalized pulse response. In [4] and [5], it was shown that turbo decoders are quite insensitive to colored noise. All these studies assumed perfect timing. However, in real systems, timing recovery must be included to track unknown time variations due to speed fluctuations and other sources of timing disturbances. Even with timing recovery, sampling instants are often not perfect because of noise. Thus certain performance degradation is expected, especially when signal to noise ratio (SNR) is low. Three timing recovery methods suitable for magnetic recording channels are examined in this paper. The first one, called voltage control oscillator (VCO) method, is widely applied in current commercial hard drives. This method uses an analog VCO to control sampling of continuous-time readback signals. The second method is the interpolated timing recovery (ITR) where a digital interpolation filter adjusts phase
Manuscript received February 14, 2000. This work was supported in part by NSF 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 rate clock [6], [7]. Both these methods take the form of a phaselocked loop (PLL) and use Muller & Mueller timing error detector [8] to estimate timing errors. The third method, called adaptive filter timing recovery (AFTR) [9], uses an adaptive filter to do both timing recovery and equalization simultaneously so that a PLL is not needed. We consider two turbo decoder architectures [3], [4]. The first one called full turbo includes a channel a posterior probability (APP) detector and two convolutional code APP decoders. The second architecture called the serial turbo [3] includes a channel APP detector serially concatenated with a single outer convolutional code APP detector. Serial turbo method is more appealing than the full turbo method because of its simpler algorithm. In this paper, we present the BER as a function of input signal-to-noise ratio (SNR) for selected cases of timing recovery methods and turbo decoders. SNR is defined as the ratio of PR (code rate is included). target energy to the white noise level The rest of paper is organized as follows. In Section II, simulation parameters will be discussed. Simulation results will be provided in Section III. We will provide our conclusions in the summary section. II. SIMULATION PARAMETERS A. System Diagram Fig. 1 explicitly shows the timing recovery stage in the turbo coded magnetic recording channel. Readback signal suffers from timing variations due to speed fluctuations. The readback signal is first input to a low pass filter where out-of band noise is filtered out and preliminary equalization (in the form of a passband edge boost) is performed. The filtered signal is processed to extract timing information and equalization is performed. Finally, the equalized and timing-adjusted signal samples are detected and decoded by the turbo decoder block. B. Turbo Coding Parameters The block size of interleavers is 5120 bits. We apply two interleavers: pseudo-random and -random. -random interleaver
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 5, SEPTEMBER 2000
ensures minimum separation of bits = 20 in our simulations) after interleaving. The recursive systematic convolutional (RSC) encoder is described by generator polynomials in octal . The precoder is . Puncform 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 response plus additive white Gaussian noise (AWGN) is assumed. The normalized recording density is 2.5. To mimic continuous readback signals, we oversample by 20 so that the time resolution is 5% of channel bit interval. 200-bit long preamble sequence is added at the beginning of channel bits to facilitate the PLL to acquire the clock. Preamble sequence is: 1, 1, 1, 1, 1, 1, 1, 1, . Timing variability is modeled by two-stage integration of an AWGN sequence [10]. The outputs of the first integrator and the second integrator are frequency disturbance and phase disturbance (timing variability), respectively. In the simulations, frequency disturbance can be as high as 0.1%, which means that timing variability can be as large as 5 in a block (5120 bits).
Fig. 2. Bit error rate vs. SNR for full turbo decoder.
D. Equalization and Timing Recovery The low pass filter used is a 7th order linear phase equi-ripple filter with two parameters optimized for BER. The equalizer is a finite impulse response (FIR) filter with 11 coefficients and their initial values are obtained via least mean squares (LMS) training. The PLL’s in both the VCO method and the ITR method are of second order. In simulations, VCO is assumed to exhibit ideal voltage-to-frequency characteristics. The interpolation filter in the ITR method uses 11 precomputed coefficients stored in a look-up table. The table has 40 entries, therefore, the phase resolution is (1/40)th of bit interval. In the AFTR method, the LMS algorithm is used to update the adaptive filter’s coefficients “on-the-fly.” The adaptation step size is 0.018. The adaptive filter has 7 coefficients and works in a decision-directed mode. All the simulation results shown (except PRML and ideal timing) include timing variations. Ideal timing refers to the system with uniform sampling and without any timing variation. III. SIMULATION RESULTS
Fig. 3. Bit error rate vs. SNR for serial turbo decoder.
Fig. 3 shows BER vs. SNR for the serial turbo decoder. In contrast to Fig. 2, both VCO method and ITR method hint at an 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 close to the ideal timing case and better than AFTR by 0.3 dB.
A. Bit Error Rate Comparisons Fig. 2 shows the BER vs. SNR for the full turbo decoder. It is seen that there is no sign of error floor. At BER = 10 , the VCO and the ITR methods are better than the AFTR method by about 0.2 dB and worse than the ideal timing case by 0.1 dB. The slightly worse performance of AFTR method is perhaps due to the filter’s coefficients being updated at SNR less than 9 dB whereas other methods use precomputed coefficients trained at SNR = 12 dB. From Fig. 2, it seems that the coding gain of the full turbo decoder can still be around 3.5 dB over the PRML system even with frequency disturbance of about 0.1%.
B. Error Bit Location Comparisons Fig. 4 shows the histograms of the cumulative number of errors that occurred at each bit position in a block for the full turbo . For decoder. The data is collected at BER’s around each plot, 500 blocks are considered. From block to block, we change the pseudo-random user bit sequence while using the same time base wander and pseudo-random interleavers. It is found that the error bit locations for all three timing methods are uniformly distributed across entire blocks, similar to the ideal timing case. The absence of error burst may be due to the fact
YUAN et al.: TIMING RECOVERY METHODS IN TURBO CODED MAGNETIC RECORDING CHANNELS
Fig. 4. Cumulative bit error locations for full turbo decoder.
that the full turbo decoder uses a second interleaver in the iterative decoding process, where erroneous chunks of bits are shuffled further. The cumulative error bit location counts for the serial turbo for all decoder are shown in Fig. 5 with BER around three timing recovery methods. It is seen that the error bits tend to concentrate in a few locations for the three timing methods, while the error locations in ideal timing case are more evenly distributed. Such difference may be due to the fact that the serial turbo decoder uses only a single pseudorandom interleaver in the iterative decoding process, where local chunks of bit errors cannot be thoroughly shuffled. Using -random interleaver seems to offer a solution that results in quite evenly distributed error bit locations. IV. CONCLUSION Timing recovery is considered in turbo coded magnetic recording channels. Three timing recovery methods are simulated for two types of turbo decoders: full turbo and serial turbo. BER results show that serial turbo decoder exhibits a significant error floor for VCO and ITR methods. From the distribution of error bit locations, full turbo decoder does not appear to lead to correlated errors. For serial turbo decoder, including timing recovery appears to affect the error bit location distributions, especially for VCO and ITR methods when pseudo-random
Fig. 5.
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Cumulative bit error locations for serial turbo decoder.
interleaver is used. Such effect appears to be not significant when applying -random interleaver. REFERENCES [1] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo codes,” in Proc. 1993 Int. Conf. Commun., May 1993, pp. 1064–1070. [2] W. Ryan, “Performance of high rate turbo codes on a PR-4 equalized magnetic recording channel,” in Proc. 1998 Int. Conf. Commun., June 1998, pp. 947–951. [3] T. Souvignier, A. Friedmann, M. Oberg, P. Siegel, and J. K. Wolf, “Turbo codes for PR4: Parallel versus serial concatenation,” in Proc. 1999 Int. Conf. Commun., June 1999, pp. 1638–1642. [4] T. M. Duman and E. Kurtas, “Comprehensive performance investigation of turbo codes over high density magnetic recording channels,” in GLOBECOM, 1999. [5] T. Souvignier and J. K. Wolf, “Turbo decoding for partial response channels with colored noise,” IEEE Trans. Magn., vol. 35, pp. 2322–2324, Sept. 1999. [6] M. Spurbeck and R. T. Behrens, “Interpolated timing recovery for hard disk drive read channels,” in Proc. 1997 Int. Conf. Commun., June 1997, pp. 1618–1624. [7] Z. Wu and J. M. Cioffi, “A MMSE interpolated timing recovery scheme for the magnetic recording channel,” in Proc. 1997 Int. Conf. Commun., June 1997, pp. 1625–1629. [8] K. H. Mueller and M. Muller, “Timing recovery in digital synchronous data receivers,” IEEE Trans. Commun., vol. COM-24, pp. 516–530, May 1976. [9] Y. Yuan and B. V. K. Vijaya Kumar, “Use of adaptive filter for timing recovery for data storage channels,” in 2000 Int. Conf. Commun., New Orleans, 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.
