IEEE TRANSACTIONS ON MAGNETICS, VOL. 33, NO. 5 , SEPTEMBER 1997 3265

Multi-channel equalization for PWM channels in magneto-optical recording

Srinivasan Gopalaswamy Data Storage Institute, NUS, 10 Kent Ridge Crescent, Singapore 119260

B.V.K. Vijaya Kumar Data Storage Systems Center, Carnegie Mellon University, Pittsburgh PA 15213, USA

Abstract --- We show by modeling and simulations that multi- track readback and equalization can lead to significant increases in the track density in magneto-optical recording without performance degradation due to two-dimensional interference. We assume an architecture in which an isolated set of closely spaced tracks is read simultaneously. In an earlier paper, we described a multi-channel zero-forcing equalizer and a two- dimensional decision-feedback equalizer for this architecture, and presented their performance for PPM (pulse position modulation) optical recording channels. Since PWM (pulse width modulation) recording is more popular in magneto-optic (MO) disks, we model the PWM channel in this paper and show simulation results for the performance improvement obtained by using multi-channel equalization for data recorded in PWM format.

I. INTRODUCTION

Higher track density can be achieved in magneto-optic (MO) disks by using both land and groove recording, thus eliminating the guard space between data tracks, and by reducing the track pitch. Efficient use of the disk space is made by decreasing the track pitch to such levels that results in significant inter-track interference (ITI). This IT1 can be handled by improved readback methods. One approach to decrease cross-talk is to optimize the depth of the groove [ 11. The resulting cross-talk reduction is, however, very sensitive to non-idealities like defocus, tracking error and disk tilt. Further more, the grooving process is known to cause increased media noise, and could be expensive. Mitigation of the inter-track interference can also be achieved by reading several adjacent tracks and performing simultaneous two- dimensional equalization on the multi-track readback signals (multi-channel equalization). This approach addresses both inter-track interference and inter-symbol interference (within the track) together, and can possibly yield higher data rates with well designed readback electronics.

Multi-track readback in MO disks using a 3-beam head has been reported [2]. In this scheme, the central beam reads the main track of interest, and the other two beams read the adjacent tracks the signals from which are used to remove the interference from the data in those tracks. In our work, we assume that a finite set of adjacent tracks is read simultaneou-

Manuscript received January 22, 1997. Snnivasan Gopalaswamy, (65)-771-5220, fax (65)-776-6527, dsigopal@leonis.nus.sg; B. V. K. Vijaya Kumar, 412-268-3026, fax 412- 268-2860, kumar@previa.ece.cmu.edu.

This work was supported in part by the National Science Foundation under Grant ECD-8907068.

sly by a multi-beam head. It is assumed that this set of tracks is isolated, so that the signals from this set of tracks suffer no interference from another such set of adjacent tracks. This architecture allows for readback of data in all the tracks within the set simultaneously. This architecture also allows development of an efficient two-dimensional decision feedback equalizer (DE) [3]. This multi-channel DFE removes both IT1 and inter-symbol interference (ISI) by use of non-linear decision feedback. At every bit-period, the decisions from the tracks below are used to remove interference from those tracks. In this paper, we present the performance improvements obtained at a high track density for the magneto-optic PWM channel, by the use of the multi- channel zero-forcing equalizer and the decision feedback equalizer.

11. MULTI-CHANNEL READBACK MODEL FOR PWM RECORDING

In our model, the read laser spot focussed on the media is represented with a Gaussian intensity profile with a standard deviation of 0.251iJNA [4] where ?L = 780nm and NA = 0.5 are the wavelength and numerical aperture assumed for the readback optics. The light reflected off the media is obtained by a point-by-point multiplication of the spot intensity function with a “disk function” [5], that represents the change in phase of the beam on reflection due to the magnetization pattern on the MO media, The minimum mark width was assumed to be 390nm (which is also 0.25&,,lNAw where &,, = 780nm and NA, = 0.5 are parameters of the write optics - such small mark size has been reported [6] ) . The readback optical path from the media to the photo-detector array is treated as an imaging system, so that its effect is assumed to be essentially spatial low-pass filtering with cutoff frequency 2NAn [7]. The optical transfer function is obtained by convolution of a pupil function of radius NAIL with itself. Incoherent illumination is assumed, so that the optical system is linear in intensity. The multi-channel model was developed with these parameter values, for the case of a set of four tracks simultaneously read by four sensors,

In PWM recording, a binary “1” is represented by a transition from region of one magnetization direction to the other. Thus the magnetization of the medium cannot be expressed simply as a sum of elements of magnetization corresponding to the input binary “1”s themselves. However, ignoring the curvature of the transition boundaries, the medium magnetization can be represented as a sum of rectangular magnetization patterns corresponding to a coded version of the input data. Fig. 1 illustrates this representation.

0018-9464/97$10.00 0 1997 IEEE

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' I . ' 7 ' I

1 0 1 1 0 0 1 1 1 (a)INPLiTDATA

(b) PWM FORMAT a, 0.4- c ._ -

(c) APPROXIMATE E" 0.2

INPUT DATA 2 -0.2

REPRESENTATION a P o

1 1 -1 1 1 1 -1 1 -1 (d)CODED - b Z -0.4

._

Fig. 1.Representation of PWM marks as a sum of rectangular elements

The effect of the curvature of the mark edges can be made -ol- -0.8

-1 I negligible by slightly widening the marks by a fixed amount while writing [ 81. -2000 -1500 -1000 -500 0 500 1000 1500 2000

Distance (nm)

Defining a sequence c [k] by

cJ[k] = cj[k - 13 0 aJ[k], (1)

where 0 denotes the XOR-operation and a J [k] is the original input bit stream in the j* track (shown in part (a) of Fig. 1),

the coded bit stream bJ[k] (shown in Part (d) of Fig. 1) in the

j" track is obtained from cJ[k] by replacing 0 by -1. This representation is similar to the NRZI representation in magnetic recording. The multi-track readback signals can now be related to the coded input bit streams by a linear time- invariant model. The readback signals are assumed to be passed through an analog front-end and synchronously sampled at bit-rate. The front-end used in the following results was the optimal multiple matched filter [SI, the outputs of which sampled at the bit-rate give a sufficient statistic for the estimation of the input bits. However the front-end could also be easily implementable simple low-pass filters.

Fig. 2. Response of isolated transition on-track and on adjacent track for two different track densities

[k] corresponds to a 1 in a[k], and no transition in b[k] denotes a 0 in a[k]). In the worst case, this decoding can give rise to twice the number of errors in the estimate for a[k], as in the estimate for b[k]. This happens when all the errors in the estimate for b[k] are single errors. In our numerical results we present this worst case.

To show the level of inter-track interference in the foregoing model, we show the transition response (readback signal due to an isolated transition) on the correct track and one track away, in Fig. 2. The solid line represents the normalized signal in the correct track and the broken lines represent the IT1 on the central head signal due to a transition in the adjacent track. The line with alternating dots and dashes and the dotted line represent IT1 at track densities of 32564 and 43419 trackshnch respectively. At the higher track density, the IT1 from a transition in the adjacent track is about 15% of on-track maximum response.

Collecting the bit streams bj[k] in the different tracks into the bit-vector stream b[k], we can arrive at a discrete-time equivalent model that relates the sampled output vector sequence r[k] to b[k], through the discrete-time response matrix sequence V[k]:

Fig. 2 shows that for the on-track response, the transition extends over a distance of 1500nm. For the minimum bit- interval of 390nm (highest linear density), the transition thus spreads over about 3.8 bits. Thus, it is clear that simple threshold detection would be a poor performer at higher densities of interest, unless RLL codes with d>O constraint are

(2) where n[k] is the additive noise after the sampler, and 8 denotes matrix convolution defined as follows. The (ij)" element of the convolution of the matrix (or vector) sequences A[k] (of size N X M) and [k] (of size M X P) is given by

....

where the * in the right-hand side of (3) denotes the regular 1-D convolution. The development of above is similar to the case of PPM recording format, which is detailed in [3]. We note that the equalization and detection schemes developed using the foregoing model would estimate the coded bit vector sequence b[k], from which the estimate for the actual input sequence a[k] can be obtained by decoding (i.e., every

used. In this work, we do not consider RLL codes, and hence do not include the simple threshold detection in the evaluations.

111. NUMERICAL RESULTS AND DISCUSSION

An isolated set of 4 tracks with no guard space between tracks was assumed to be read together with 4 photo- detectors. The multi-channel zero-forcing equalizer (ZFE) and the decision feedback equalizer (DFE), which combine the multi-track readback signals, were determined using the foregoing PWM channel model, after approximating V[k] by a finite sequence. The multi-channel ZFE removes all the two-dimensional interference and is defined by the matrix sequence W[k] so that [k] 63 V[k] = I, where I is the identity matrix. The structure of the multi-channel DFE is

(a) Track density = 32564 tracksfinch

DECISION

OF SAMPLER FEEDBACK

Fig 3. Structure of the multi-channel DFE

shown in Fig. 3. The multi-channel DFE consists of a forward equalizer that removes all anti-causal interference in both spatial and temporal sense, and the causal interference in removed by a strictly causal feedback equalizer and feedback elements within the decision block. The input to the decision block has only spatial causal interference, i.e. the signal on any track is affected by interference from the data in only the tracks below. Within the decision block, decision is first made on the lowest track, and the estimates are fedback to make the decisions sequentially on the higher tracks. The details of the development of the multi-channel ZFE and DFE are given in 131.

The performance of the multi-channel equalizers was compared with their single-channel counterparts (single- channel equalizers act on the readback signal from each track independently thus ignoring the ITI). The numerical evaluation of the model showed that only a small set of neighboring bits interfere significantly. Therefore the probability of error (P,) was determined by averaging it over all possible patterns of these neighboring bits, at an input SNR of 20.68db. The input noise is assumed to be white, and uncorrelated across tracks, and the input SNR is defined in the system bandwidth (the noise after the multiple matched filter is correlated). Since bit-by-bit simulation was not used, the following results for the DFE do not include feedback errors. Fig. 4 shows the numerically evaluated effective output signal-to-noise ratio (Smff) versus linear density at the two values of the track density: 32564 trackslinch and 43419 trackshnch. The SNReff is related to P, by Pe = a(,/--). where Q(.) is the complementary

Gaussian error function defined by

Q(x) = J G F e e x p , At the lower track density, X

the performance of single-channel and multi-channel schemes are almost the same, especially at higher linear densities, where the IS1 dominates. However, it is clear that at the higher track density (when inter-track interference is more severe), the multi-channel equalizers offer a significant improvement over the single-channel equalizers. The performance of the single-channel equalizers has dropped considerably at the higher density, while that of the multi- channel equalizers has not dropped noticeably. The multi- channel DFE offers an additional 2-3 db improvement in performance over the multi-channel ZFE. While the multi- channel equalizers are definitely more complicated to implement, the performance improvement indicates that they could still be very cost effective.

12‘ 3 3.5 4 4.5 5 5.5 6 6.5

Linear density (IO Kbitslinch)

(b) Track density = 43419 trackslnch : 10 l2 t

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0

3 3.5 4 4.5 5 5.5 6 6.5 7 Linear density (10 Kbits/inch)

Fig. 4. Effective SNR of multi-channel vs single-channel schemes for two different track densities

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[7] J. W. Goodman, Introduction fo Fourier Optics, McGraw-Hill Book Company, New York, 1968. [SI L. Cheng, M. Mansuripur, and D. G. Howe, “Parthl-response equalization in magneto-optical disk readout: a theoretical investigation,” Applied Optics, Vol. 34, pp. 5153-5166, Aug. 1995. [9] W. Van Etten, “Maximum likelihood receiver for multiple channel transmission systems,” IEEE Trans. Commrtn., Vol. 24, pp. 276-283, 1976.

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