IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 6, JUNE 2013 2555

Two-Dimensional Soft Output Viterbi Algorithm With Dual Equalizers forBit-Patterned Media

Keunhwi Koo , Soo-Yong Kim , Jae Jin Jeong , and Sang Woo Kim

Department of Electrical Engineering, Pohang University of Science and Technology, Pohang, Gyeongbuk 790-784, KoreaEmerging SOC Group, Semiconductor Division, Samsung Electronics Co., Ltd., Yongin, Gyeonggi 446-711, Korea

Department of Creative IT Excellence Engineering and Future IT Innovation Laboratory, Pohang University of Science andTechnology, Pohang, Gyeongbuk 790-784, Korea

This study proposes a two-dimensional (2D) detection method using partial response maximum likelihood (PRML) for bit-patternedmedia (BPM) storage. Because the readback signals are deteriorated by 2D channel effect, that is, intersymbol interference along thetrack direction and intertrack interference across the track direction, it is necessary to use “2D” PRML in order to improve the bit errorrate (BER) performance. The 2D PRML in the proposed method is based on the 2D soft output Viterbi algorithm (SOVA), which iscomposed of two one-dimensional SOVAs. In addition, we propose a 2D SOVA for a 2D partial response (PR) target using dual equal-izers: one estimates the correlated signal (output data of the PR target), used as the main information with encoding rule, and the otherestimates the binary signal (binary data recorded on BPM), used as extrinsic information on the other direction’s neighboring bits. Thesimulation results show that the proposed method improves the BER performance at a low computational complexity.

Index Terms—Bit-patternedmedia, equalizer, intersymbol interference, intertrack interference, partial responsemaximum likelihood,readback signal, soft output Viterbi algorithm.

I. INTRODUCTION

B IT-PATTERNED MEDIA (BPM) can achieve ultrahighareal density that reaches over 1 Tbit/in because each

data bit is recorded on a single-grain magnetic island [1]. Thus,many people expect the BPM storage to be one of the next-gen-eration storage. Unfortunately, in contrast to conventional mag-netic storage, the readback signals suffer from intertrack inter-ference (ITI) across the track as well as intersymbol interference(ISI) along the track [2]. Because the BPM generates two-di-mensional (2D) interference (ISI and ITI) among neighboringbits, it is necessary to use a “2D” detection method, instead of aone-dimensional (1D) method, to reduce the bit errors in recon-struction process of the readback signals.To detect the readback signals degraded by 2D interference,

recent papers proposed various methods based on a 2D equal-izer [3], modified Viterbi algorithm [4], and 2D soft outputViterbi algorithm (SOVA) [5]–[7]. Especially, the 2D SOVA,introduced by Kim and Lee [6], [7], exhibits a superior bit errorrate (BER) performance than the other methods. In addition,the 2D SOVA consists of two 1D SOVAs, not a pure 2D Viterbialgorithm, to reduce computational costs.We focus on only the 2D partial response maximum like-

lihood (PRML) method using the 2D SOVA. Because the2D PRML in [6] iteratively processes two 1D SOVAs withextrinsic information in the 2D SOVA, the BER performanceis improved; however, the computational cost is rather high. Inthis study, we propose a 2D PRML method using dual equal-izers that can improve the BER performance without iteration.The dual equalizers provide the 2D SOVA with two differenttypes of data, namely, the main and extrinsic information,

Manuscript received December 01, 2012; revised February 10, 2013;accepted February 25, 2013. Date of current version May 30, 2013. Corre-sponding author: S. W. Kim (e-mail: swkim@postech.ac.kr).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMAG.2013.2251614

Fig. 1. Along-track profile of isolated island response for BPM with SUL.

used in the trellis diagram of the 1D SOVAs at one time. Thesimulation results show that the proposed method has a betterBER performance, without iteration.

II. BPM CHANNEL MODEL

We consider only the BPM with a soft underlayer (SUL) cor-responding to an areal density of 1 Tbit/in [6] to evaluate 2Ddetection methods. The BPM has square islands with a lengthof 12.5 nm and a period of 25 nm. Like [6], the pulse responseof the square island is simply expressed as

(1)

where and are the along- and across-track profilesof the island response, respectively. We design the along-trackprofile using the sum of two Gaussian pulses [3], as shown inFig. 1, and the pulse width at half maximum is 21.2 nm.The across-track profile is modeled as a Lorentzian pulse [2], [6]and has of 31.2 nm. From the continuous-time 2D pulseresponse, we obtain the discrete-time 2D channel model thatconsiders the effect of the read-head offset. The discrete-timechannel model, composed of a 3 3 array, is expressed as

(2)

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2556 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 6, JUNE 2013

Fig. 2. Proposed method: 2D SOVA for 2D PR target with dual equalizers: below equalizer estimating correlated signal (output data of PR target) and aboveequalizer estimating binary signal (binary data recorded on BPM).

TABLE IDISCRETE-TIME 2D CHANNEL MODELS WITH TMR FOR BPM WITH SUL

where , and are the indexes and island periods alongand across the track directions, respectively; Jitter and TMRdenote the degree of the read-head offset along and across thetrack directions, respectively, expressed as a percentage (%) [4].In other words, the island position jitter and track misregistra-tion (TMR) are defined as, respectively

% (3)

and

% (4)

Table I lists the discrete-time 2D channel models when the TMRis 0% (on track), 5%, and 10% without the jitter. Through thechannel models and random jitter, the readback signal of theBPM is given by

(5)

where is a random 2D binary data is a 2Dconvolution operation, and is an additive white Gaussiannoise (AWGN). The signal-to-noise ratio (SNR) in the AWGNis defined as , where is the AWGN power.

III. PREVIOUS WORKS USING 2D SOVA

The holographic data storage (HDS) system first applied the2D SOVA to the maximum likelihood (ML) part of PRML [8].

The 2D SOVA consists of two 1D SOVAs in the horizontal andvertical directions because pure 2D Viterbi algorithm requiresa high computational cost. In [8], the partial response (PR) partof PRML uses the 2D PR target as an encoding rule for the 1DSOVA. However, there exists a problem that the 1D SOVA forthe 2D PR target employs an approximate trellis diagram. Tosolve this problem, the PR part in [9] uses two 1D PR targetsinstead of the 2D PR target. Further, Kim and Lee [9] proposedthe modified 2D SOVA reflecting the effect of the 2D channel.Because the 1D PR targets cannot include the 2D information,improving the performance is constrained in the modified 2DSOVA. Koo et al. [10] also proposed another method applyingthe 2D PR target and solved the problem employing a trellis dia-gram in structural accordance with the 2D PR target. The trellisdiagram requires two kinds of data such as the main informa-tion with encoding rule and extrinsic information on the otherdirection’s neighboring bits. To improve the BER performancein [10], it was necessary to use exact extrinsic information. Be-cause the BPM suffers from the effect of 2D interference similarto the HDS, various methods using the 2D SOVA can also be ap-plied to the BPM to improve the BER performance. In [6], theiterative 2D SOVA, based on [9], for the BPM was first intro-duced, which shows a superior BER performance. However, themethod requires rather high computational cost because of theiterative process. In this study, we propose a detection methodusing the 2D PR target and dual equalizers, based on [10].

IV. PROPOSED METHOD

We propose the 2D SOVA (as the ML part) for the 2D PRtarget with the dual equalizers (as the PR part). Fig. 2 shows theblock diagram of the proposed method. In this study, the 2D PRtarget uses PR({0,0.2,0}, {0.1,1,0.1}, {0,0.2,0}), similar to thediscrete-time BPM channel model.

A. PR Part: 2D PR Target With Dual Equalizers

To design the trellis diagram of the 1D SOVA in structuralaccordance with the 2D PR target [10], the dual equalizers inthe PR part produce simultaneously two kinds of data requiredin the ML part, which are the main information with encodingrule and the extrinsic information on the other direction’s neigh-boring bits. The main and extrinsic information are determinedby equalizers and estimating the output data of

KOO et al.: TWO-DIMENSIONAL SOFT OUTPUT VITERBI ALGORITHM 2557

Fig. 3. Comparison of BER performance using threshold method between dualequalizers.

the PR target and the binary data recorded on the BPM, respec-tively. In contrast with [6], [9], and [10], to reduce the compu-tational cost, the extrinsic information in the proposed methodis obtained by the additional equalizer using the least meansquare (LMS) algorithm instead of the iterative process of two1D SOVAs that require expensive cost. In addition, because theequalizer estimates a binary signal, not a correlated signal, it canimprove the accuracy of the extrinsic information (Fig. 3) [11].Coefficients and are composed of a 5 5 arrayand are updated by the LMS algorithm [6], [11]. Usingand , we define the outputs of the dual equalizers as, re-spectively

(6)

(7)

B. ML Part: 2D SOVA Using Dual Equalizers

The 2D SOVA consists of the horizontal and vertical 1DSOVAs for the 2D PR target. Based on [10], a trellis diagramin the 1D SOVAs is organized in structural accordance with the2D PR target using two elements: the general trellis diagramfor the 1D PR target and the modified cost function to calculatethe branch metric in the trellis diagram.In the case of the horizontal 1D SOVA, the trellis diagram

is organized by encoding rule according to 1D PR{0.1,1,0.1}target. The branch metric for the transition from the current stateto the next state is calculated using (8) with two kinds of

data received from the dual equalizers.

(8)

where , and are decisions inand is the main information with encoding rule for the2D PR target; is the extrinsic information on the verticaldirection’s neighboring bits and determined by

(9)

In (9), Ad is experimentally selected from Fig. 4 (Ad is 1.0).Finally, is obtained by the horizontal 1D SOVA. In the

Fig. 4. BER performance according to various “Ad” (SNR: 13 dB).

Fig. 5. Comparison of BER performance about detection methods using 2DSOVA according to SNR for BPM with SUL.

same manner, the vertical 1D SOVA according to 1D PR{0.2,1,0.2} target is also carried out. From the outputs of the 1DSOVAs, the final binary decision is determined by

(10)

(11)

V. SIMULATION RESULTS

To evaluate the detection methods, we assume that the databits in the BPM are read in the form of 2D page composed ofa 1024 1024 array like [6] and [7]. Under the BPM channelmodel, 1000 pages were simulated. Fig. 5 shows the BERperformance of the 2D PRML methods according to the SNR.From the result, it is found that the proposed method withoutiteration (curve 1) shows a better BER performance than theother methods. Finally, we perform the simulation under the2D channel model reflecting the effect of the read-head offsetsimilar to the practical BPM channel according to the SNR. Theread-head offset consists of random jitter between % and5% and the TMR (on track, 5%, or 10%) along and across thetrack directions, respectively. Fig. 6 shows that the proposedmethod (curve 1) also has a superior BER performance, withlow computational complexity.

2558 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 6, JUNE 2013

Fig. 6. Comparison of BER performance between 2D SOVAwith dual equalizers and iterative 2D SOVA (one iteration) under: (a) 5% TMRwithout jitter; (b) 10%TMR without jitter; (c) random jitter and 0% TMR (on track); and (d) random jitter and 10% TMR according to SNR for BPM with SUL.

VI. CONCLUSION

We proposed the 2D SOVA for the 2D PR target with dualequalizers for BPM storage. Because the dual equalizers simul-taneously provide bothmain informationwith encoding rule andextrinsic information on the other direction’s neighboring bits,the 2D SOVA can be carried out without iteration. In addition,the BER performance can be improved from the accurate ex-trinsic information extracted by the equalizer that estimates thebinary data recorded on the BPM. Finally, the proposed methodexhibits not only a low computational cost but also a superiorBER performance. Thus, the possibility of applying the pro-posed method to a practical system is rather high.

ACKNOWLEDGMENT

This research was supported by the Ministry of KnowledgeEconomy (MKE), Korea, under the IT Consilience CreativeProgram supervised by the National IT Industry PromotionAgency (NIPA) (C1515-1121-0003).

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