IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 3, MARCH 2014 3000307

A Communication-Theoretic Framework for 2-DMR ChannelModeling: Performance Evaluation of Coding and Signal

Processing MethodsShayan Garani Srinivasa1, Yiming Chen2, and Shafa Dahandeh2

1Department of Electronic Systems Engineering, Indian Institute of Science, Bangalore 560012, India2Advanced R/W Technologies, Western Digital Corporation, Irvine, CA 92612 USA

We develop a communication theoretic framework for modeling 2-D magnetic recording channels. Using the model, we definethe signal-to-noise ratio (SNR) for the channel considering several physical parameters, such as the channel bit density, code rate,bit aspect ratio, and noise parameters. We analyze the problem of optimizing the bit aspect ratio for maximizing SNR. The readchannel architecture comprises a novel 2-D joint self-iterating equalizer and detection system with noise prediction capability. Weevaluate the system performance based on our channel model through simulations. The coded performance with the 2-D equalizerdetector indicates ∼5.5 dB of SNR gain over uncoded data.

Index Terms— 2-D magnetic recording (2-DMR) channel modeling, 2-D noise prediction, joint self-iterating 2-D equalization anddetection.

I. INTRODUCTION

THE DEMAND for reliable hard disk drives with increasedareal densities, i.e., beyond today’s commercially existing

1 Tb/in2 magnetic storage media, has created the need for newrecording technologies, such as heat/energy assisted magneticrecording [1], bit patterned media (BPM) [2], and 2-D mag-netic recording (2-DMR) [3]. BPM technology is driven bymedia lithographic considerations. In BPM, magnetic domainsare patterned so that individual magnetic islands are isolated.This results in better thermal stability and reduced jitter.However, fabricating such high end media has many practicalchallenges. HAMR technology uses guided high energy laserbeams for heating the medium to write data. Stabilizingthe write heads without melting them is one of the majorpractical challenges in HAMR. 2-DMR technology is drivenby powerful 2-D signal processing and coding techniques torealize higher areal densities, extending beyond the existingperpendicular recording scheme. Squeezing the track dimen-sions, and writing data in both the track directions, leads tohigher crosstalk. Using wide readers, we can overcome 2-DISI and noise using efficient 2-D signal processing algorithms.Thus, 2-DMR technology can have additive areal density gainswhen coupled with BPM and HAMR technologies.

It is theoretically important to estimate the maximumachievable data density based on the physical characteris-tics of the recording medium. As magnetic grain sizes arereduced, the system is prone to thermal instabilities leadingto changes in the original magnetic state. Further, smallergrain sizes can lead to errors in the writing process dueto insufficient field strengths for aligning the grains in thecorrect direction. To cater to higher areal densities, all therequirements of: 1) smaller grains (media SNR); 2) increase of

Manuscript received July 29, 2013; revised September 22, 2013; acceptedOctober 23, 2013. Date of current version March 14, 2014. Correspondingauthor: S. Garani (e-mail: shayan.garani@wdc.com).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2013.2290007

magnetic anisotropy (media writability); 3) thermal stability;and 4) thermal writability has to be met within the physicalconstraints [4]. The peak limit for areal densities in magneticstorage considering thermal writability is predicted to bebetween 15 and 20 Tb/in2 in [4]. However, these studiesdo not address the practical considerations of getting highreliability rates from information bits written and read fromthe medium. The physical parameters related to the recordingphysics and media can be translated into the underlying signalpower, noise power, and interference effects. The fundamentallimits to storage density driven by high reliability rates aredictated by the SNR of the medium. Developing an amenablecommunication model can facilitate the realization and evalua-tion of practical coding and signal processing methods for the2-DMR channel.

The Voronoi grain model is popularly used in 2-DMRchannel modeling [5], [7]. According to the Voronoi model,the recording medium is modeled as a Voronoi tiling ofshifted grain centers with a certain probability distribution.The degree of variation in the position, size, and location ofgrain boundaries is determined by the choice of the underlyingprobability distribution, normally modeled as Tikhonov distri-bution. The Voronoi approach is clearly more sophisticatedthan the naive discrete grain and the binary error/erasuremodels [8], and a step closer to the micromagnetic modelcommonly used in media simulations. However, prior workon this modeling approach does not incorporate grain den-sity considerations and lacks an amenable description of aread/write channel model toward an SNR definition. It appearsthat the analysis of the noise resulting from irregular grainboundaries of the Voronoi model is difficult since it requiresa priori knowledge of various noise probability distributionscorresponding to different 2-D neighborhood configurations.Given the sophistications in the Voronoi modeling approachthat need experimental characterization with real media data,it is debatable for practical applicability. In a recent prior work,Cai et al. [6] have considered modeling and signal processingfor BPMR channels.

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3000307 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 3, MARCH 2014

Our channel modeling approach is based on an extensionof existing approaches used in longitudinal/perpendicular mag-netic recording [18] applicable to a 2-D setting. By appropri-ately defining and incorporating various physical parameters,such as the channel bit density (CBD), code rate, bit aspectratio, and noise parameters, we develop a tractable SNR modelfor 2-DMR channel modeling, and use this for performanceevaluation of coding and signal processing methods.

Signal processing and coding are an integral part of theread channel architecture. Vasic et al. [5] have proposed a 2-Dzero forcing equalizer and error correcting schemes based onsoft decoding of low density parity check (LDPC) codes. Ina recent prior work, Hwang et al. [9], [10] have proposed a2-D LMMSE-based equalization, followed by LDPC decod-ing, as a part of the 2-DMR signal processing architecture.Recently, Chen and Srinivasa [11], [12] developed a novel2-D MAP-based detector and combined this engine with aself-iterating soft equalizer [13] within a turbo-equalizationframework [14]. We use this framework and modify the 2-Ddetection algorithm to incorporate noise whitening filters fordecoloring media noise due to jitter.

Our work is novel on two fronts: 1) we develop an amenablecommunication theoretic model for 2-DMR channels consid-ering physical parameters and 2) we modify the joint 2-Dself-iterating equalizer and detection (JTED) algorithm toincorporate media noise whitening capability. This paper isorganized as follows. In Section II, we develop a communica-tion theoretic framework for 2-DMR channels and define anSNR metric. We then investigate the optimal selection of bitaspect ratio parameter for maximizing SNR. In Section III, wediscuss the read channel architecture for 2-DMR incorporatingnoise whitening feature within the JTED engine. We presentsimulation results over the LDPC coded system in Section IV.Finally, conclusions are drawn in Section V.

II. 2-DMR CHANNEL MODELING

The 2-DMR channel modeling fundamentally differs fromconventional 1-D approaches in each of the following aspects:1) media grain modeling; 2) recording the grains on themedium (write model); and 3) read back mechanism (readmodel). The choice of ordered grains versus random grainsaffects media modeling since the concept behind 2-DMR isapplicable over both these choices. The write model accountsfor any erroneous unwritten/rewritten regions. These artifactsare captured within the read back signals and have to beovercomed via error correction coding schemes. The readmodel can be succintly captured using a 2-D read headsensitivity function that accounts for 2-D spatial ISI along withjitter.

Fig. 1(a) shows a conventional PMR disk drive where dataare recorded along a track. The read head captures the desiredsignal with noise and interferences along a track. Fig. 1(b)shows a 2-DMR disk drive with increased track densities.A wide read head captures the desired signal with 2-Dcrosstalk and noise. Even though the 2-DMR system admitsmore crosstalk, it has many advantages over the conventionalPMR system. Due to wide read heads, 2-D recording is less

Fig. 1. (a) Conventional PMR disk with magnetic state orientations.(b) 2-DMR-based disk drive comprising squeezed tracks. The system isenvisoned to have a wide reader capable of reading data over multiple tracks,thereby capturing signal, interference, and noise in the down-track and cross-track directions.

sensitive to timing drifts and instabilities. With powerful 2-Dsignal detection methods, guard bands between 2-D codedblocks can be eliminated, thereby, improving format efficiency.In short, 2-D crosstalk can be gainfully exploited for realizinghigher areal densities by clever signal processing.

In Section II-A, we focus on the read channel model for the2-DMR system with an eye toward SNR definition.

A. Read Channel Model

The read back process can be modeled as a convolution ofthe ideal binary magnetization over the cells with the 2-D readhead sensitivity function [10], [15] given by

h(x, y) = exp

(−c

((x

PW50,d

)2

+(

y

PW50,c

)2))

(1)

where c is a constant, x and y are the down-track and cross-track positions on the disk, PW50,d and PW50,c are thepulsewidths at half maximum in the down-track and cross-track directions. Let (lc,δc,W ) and (ld ,δc,B) denote the bitindexes, jitter and bit duration in the cross-track and down-track directions, respectively. We have

x = ld B + δd

y = lcW + δc. (2)

Let BAR denotes the bit aspect ratio and a denotes the ratioof PW50,c to PW50,d . We have

BAR = W

B

a = PW50,c

PW50,d. (3)

The 2-D CBD (D2D) is defined as

SRINIVASA et al.: COMMUNICATION-THEORETIC FRAMEWORK FOR 2-DMR CHANNEL MODELING 3000307

D2D = PW50,c × PW50,d

BW. (4)

The parameter D2D in (4) is related to the user bit density(U2D) via the code rate parameter R as

D2D = U2D

R. (5)

Using (3), we can rewrite (4) as

PW50,d

B=

√D2D × BAR

a. (6)

Using (6) in (2), we have

x

PW50,d= ld

√a

D2D × BAR+ δd

PW50,d

y

PW50,c= lc

√BAR

a D2D+ δc

PW50,c. (7)

Expanding the 2-D read sensitivity function in (1) with afirst-order Taylor series expansion, we have

h(x + δd , y + δc) = h(x, y) + δd∂h(x, y)

∂x+ δc

∂h(x, y)

∂y. (8)

Using (8) in (1), the desired signal power can be expressedas

Sp = π D2D

2c. (9)

Assuming that the jitter along down-track and cross-trackdirections is Gaussian distributed random variables, i.e., δd ∼N (0, σ 2

d ), δc ∼ N (0, σ 2c ), and statistically independent,

using (8), the jitter power can computed as

Jp = 1

W B

[σ 2

d

∥∥∥∥∂h(x, y)

∂x

∥∥∥∥2

+ σ 2c

∥∥∥∥∂h(x, y)

∂y

∥∥∥∥2]

(10)

where the ‖.‖ denotes the usual L2 integral norm for contin-uous functions.

Equation (10) can be simplified using (7) as

Jp = 2π

W B

[σ 2

dBAR

a+ σ 2

ca

BAR

]. (11)

Let σ 2w denotes the variance of electronic noise which

is assumed to be Gaussian N (0, σ 2w). Assuming that the

electronic noise is statistically independent of the jitter noisecomponents in two-dimensions, we can combine the signalpower, jitter power, and noise power into an effective SNRmetric as

SN R = 10 log10

(Sp

Jp + σ 2w

)d B. (12)

It must be noted that we have assumed a head sensitivityfunction based on prior work [9], [15] within this paper. Inpractice, the read sensitivity function may be specific to aread head design. However, the framework we have outlinedin computing the SNR metric holds good for any arbitrary 2-Dimpulse response h(x, y).

Fig. 2. Schematic of a simulation setup for generating read back signals. Datax are filtered through a discrete version of the 2-D impulse response h(x, y).By filtering through the first-order 2-D derivative filters, we can generate thejitter signal corresponding to δc ∼ N (0, σ 2

c ), δd ∼ N (0, σ 2d ). Electronic

noise ne ∼ N (0, σ 2w) is added to the signal path corresponding to the SNR.

Fig. 2 shows the schematic for simulation of the read backsignal. Data are filtered through a 2-D ISI channel along with2-D jitter filters. Depending on the SNR, electronic noise isadded to the resulting signal to get the overall read back signalfor further signal processing.

B. Optimized Bit Aspect Ratio

The requirement for higher areal densities envisages theneed to push channel bit densities higher. However, thisresults in greater 2-D ISI and lower desired signal power.The variances σ 2

d , σ 2c , and σ 2

w depend on the media and readhead fly height and can be set depending on the ability of theunderlying signal processing algorithms to overcome the signalartifacts. The parameter a depends on the read head response.However, the BAR parameter can be optimized during customfabrication if the remaining parameters are fixed. We wouldlike to investigate on the choice of bit aspect ratio (BAR∗)that maximizes the SNR

BAR∗ = maxBAR

[10 log10

(Sp

Jp + σ 2w

)]. (13)

We set d(SN R)/d(BAR) = 0 in (12), and verifyd2(SN R)/d(BAR)2 < 0 to solve for optimal BAR. Withalgebraic simplifications, the optimal value of BAR∗ can besolved using the equation

[σ 2

w+2π

(σ 2

dBAR

a+σ 2

ca

BAR

)][1

2

(√1

a×BAR−

√a

BAR3

)]

= π D2D

c

[2πaσ 2

c

BAR2 − 2πσ 2d

a

]. (14)

A careful inspection of (14) indicates that if σ 2d = σ 2

c ,BAR∗ = a. This corroborates some of the numerical figuresthat correspond to 4 Tb/in2 customer densities [16], whereB = 5.18 nm, W = 15.6 nm, PW50,c = 27.2 nm, andPW50,d = 9.07 nm.

Example 1: Suppose D2D = 1.5, σ 2d = 1, σ 2

c = 1.25, σ 2w =

1.5, a = 3, and c = 4.7. Using (14), the optimal value wasevaluated as BAR∗ = 3.4, implying the role of unequal jitter

3000307 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 3, MARCH 2014

Fig. 3. Schematic of a read channel architecture. Modulation coded datagets appended with a block of parity bits and written on to the medium. Theread head receives the analog information from the medium and processedby the analog front end circuitry. The sampled signals are digitally processedthrough timing recovery, equalization, and signal detection blocks before beingdecoded.

Fig. 4. Schematic of a 2-D noise whitener. The ideal read back signal Yideal isgenerated by convolving the 2-D response H2D with the data X . The colorednoise samples {wc} are then filtered using a whitening filter P(z) to yielddecolored samples {wnc}.

variances within the optimization setup. The choice of c is toensure unit energy constraints for h(x, y).

III. SIGNAL PROCESSING METHODS

In this section, we focus on the signal processing aspectsof 2-DMR.

A schematic of the read channel architecture is shownin Fig. 3. In contrast to recent prior work [9], [10], our2-DMR architecture uses the JTED algorithm [13] with noisewhitening feature. In the following section, we outline thebasic approach for generating 2-D noise whitening filters andmodify the JTED algorithm as appropriate.

A. 2-D Noise Whitening

Let {wc} denotes the colored noise samples obtained bysubtracting the read back signal y with the ideal samplesyideal = H2D ∗ x (* is the usual 2-D convolution operation)as shown in Fig. 4. Let P(z) denotes the whitening filter oforder K × K

wc(n1, n2) =K∑

i=1

K∑j=1

pi, j wc(n1 − i, n2 − j). (15)

The cost function for obtaining the filter P(z) can be setupusing the mean squared error criterion as

Fig. 5. Schematic of a 2-D detector with noise whitening. Two multi-row/column MAP-based detectors are connected using a turbo framework.The noise prediction capability is embedded within the branch metric com-putations.

J = minP

E((wc(n1, n2) − wc(n1, n2))

2)

. (16)

Setting ∂ J∂pk,l

in (16), we can solve for the filter coeffi-cients pi, j by solving the set of normal equations in 2-D asfollows:

E [wc(n1, n2)wc(n1 − k, n2 − l)]

=∑i, j

pi, j E [wc(n1− i, n2− j)wc(n1−k, n2−l)] . (17)

The prediction error variance can be computed as

E(

e(n1, n2)2)= E

(w2

c (n1, n2))−∑l1,l2

pl1,l2 Rwc (−l1, l2) (18)

where Rwc (k, l) = E(wc(n1 − i, n2 − j)wc(n1 − k, n2 − l)).The noise whitening filter can be calibrated using known

input samples and the 2-D impulse response.

B. 2-D Detector With Noise Whitening

Fig. 5 shows the description of the 2-D detector with noiseprediction embedded within its framework. Though the 2-Ddetector is described in [11] and [12], we would like todescribe the algorithm here for the sake of completeness.

Before we begin with the details of the 2-D MAP-basednoise whitening algorithm, we would like to define a few termsrelevant to the 2-D channel eventually toward a descriptionof the trellis. Without loss of generality, we assume that the2-D discrete impulse response of the channel is of dimensions(2A + 1) × (2A + 1):

1) Sj := [sk,l ]; i − A ≤ k ≤ i + A, j − 2A ≤ l ≤ j denotesthe current trellis state. The single subscript j denotesthe time step over the rectangular array of elements thatform the state.

2) Z(i)R ; −A ≤ i ≤ A is a row strip of received samples of

width 2A + 1 centered at location i .3) Z(i)

C ; −A ≤ i ≤ A is a column strip of received samplesof width 2A + 1 centered at location i .

4) y(i, j ) := [yk, j−A]; i − A ≤ k ≤ i + A is a column vectorof height 2A+1 centered at location (i, j − A) denotinglocally received samples needed at the j th computationalstep.

SRINIVASA et al.: COMMUNICATION-THEORETIC FRAMEWORK FOR 2-DMR CHANNEL MODELING 3000307

5) u(i, j ) := [uk, j ]; i − A ≤ k ≤ i + A is a column vectorof height 2A + 1 centered at location (i, j) denoting theinput bits.

6) �(i, j )R := [ωk,l ]; [i − A − W ≤ k ≤ i − A − 1]∪[i+A+

1 ≤ k ≤ i + A + W ], j − 2A ≤ l ≤ j , denotes two rowstrips of feedback elements of height W each.

We assume a boundary taking values −1 around x tocompute the received 2-D data y. The detector uses thisboundary condition to initialize the MAP trellis to begin andend in an all -1 state (zero state bipolar mapped to -1).

Let us consider the multi-row detector. We need to capturethe joint statistics of the state information, locally receivedsamples, and the input over the row strip, with an eye towardbit likelihood estimation. The joint probability over the inputvector u(i, j ), state Sj and the row strip Z(i)

R is defined as

λu(i, j)

i, j (s) � P(

u(i, j ), Sj = s, Z(i)R

). (19)

Using (19), the a posteriori probability for the multi-rowdetector is computed as

P(

u(i, j ) | Z(i)R

)=

∑s

λu(i, j)

i, j (s)/P(

Z(i)R

). (20)

As in [17], we define the modified forward, backward, andstate transition (branch metrics) probabilities as follows:

αi, j (s) = P(

Sj = s, {y(i,a)}1≤a≤ j

)βi, j (s) = P

({y(i,a)} j+1≤a≤N |Sj = s

)γi, j (s

′, s) = P(Sj = s, y(i, j )|Sj−1 = s′). (21)

With the above definitions in place, we will sketch thegeneral procedure for the multi-row detector.

Outline of the generalized multi-row MAP detector:

1) Branch metric computations: Compute the state transi-tion probabilities for all the branches given the localreceived samples according to

γi, j (s′, s) = P(Sj = s, y(i, j )|Sj−1 = s′)

= P(y(i, j )|Sj =s, Sj−1 =s′)P(Sj =s|Sj−1 =s′)= P(y(i, j )|Sj = s, Sj−1 = s′)P(u(i, j )). (22)

Compute the first term in (22) as

P(yi, j | Sj = s, Sj−1 = s′) ≈ P(yi, j | Sj = s, Sj−1 = s′)A∏

m=−A,m =0

P(yi+m, j−A | Sj = s, Sj−1 = s′)

= 1√2πσ 2

p

exp

(−

(yi, j−A − E

(yi, j−A

) − wi, j−A)2

2σ 2w

)

A∏m=−A,m =0

∑�

(i+m, j−A)R

P(�

(i+m, j−A)R

) 1√2πσ 2

p

exp

(−

(wi+m, j−A − wi+m, j−A

)2

2σ 2w

)(23)

where wi+m, j−A = yi+m, j−A−E(yi+m, j−A

(�

(i+m, j−A)R

))denotes the colored noise sample, wi, j−A and wi+m, j−A

denote the predicted noise samples as per (15) and σ 2p

denotes the prediction error variance according to (18).In the absence of any noise coloration, σ 2

p = σ 2w. The

decoloring filters are not trained specific to individual2-D data patterns. Using the well known data-dependentnoise prediction (DDNP) scheme [18] for the 1-D case,we can extend the framework to our system as well,albeit, with a high computational complexity.

It must be noted that for all practical purposes, inde-pendence assumption is used for computing the secondterm in (22). The expectation within the exponentialterm of the Gaussian probability density function in (23)can be straightforwardly computed using the feedbackterms �

(i, j )R and state values by a 2-D convolution with

the channel impulse response. It must be noted that thefeedback terms are computed from the LLRs passedfrom the previous iteration by the column detector.

2) Forward probability computation: For each stage, com-pute the forward probabilities recursively as

αi, j (s) =∑

s ′αi, j−1(s

′)γi, j (s′, s). (24)

3) Backward probability computation: For each stage, com-pute the backward probabilities recursively as

βi, j−1(s′) =

∑s

βi, j (s)γi, j (s′, s). (25)

4) Computation of λu(i, j)

i, j (s): Using the results from steps1–3, compute the joint probability term in (19) as

λui, ji, j (s) =

∑s ′

αi, j−1(s′)γi, j (s

′, s)βi, j (s). (26)

5) Marginalization for computing λui, ji, j (s): To estimate the

pixel located at position (i, j), marginalize (26) overother input pixels in the vector u(i, j ) as

λui, ji, j (Sj ) =

∑u(i, j)\ui, j

λu(i, j)

i, j (Sj ). (27)

6) Soft information and hard decisions for each user pixelat location (i, j): The output pixel LLR is finally com-puted from (27) as

L(i, j) = ln

⎛⎝∑

S jλ

ui, j =+1i, j (Sj )∑

S jλ

ui, j =−1i, j (Sj )

⎞⎠ . (28)

If L(i, j) > 0 pixel (i, j) is detected as +1, otherwise,it is detected as −1. The value L(i, j) corresponds tothe soft output of the 2-D multi-row algorithm (i.e., withthe extrinsic and the a priori components).

It must be noted that processing of rows and columns canbe accomplished by mere transposition of the array of receivedsamples. In effect, the same multi-row engine can be easilyconfigured as a multi-column-based detector engine withinthe 2-D iterative multi-row/column feedback detector structuredescribed in Fig. 5.

3000307 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 3, MARCH 2014

Fig. 6. Schematic of a 2-D detector with noise whitening coupled to a 2-Dself-iterating soft equalizer.

Fig. 7. Noise characteristics of colored and decolored samples. (a) 2-Dautocorrelation of colored samples. (b) 2-D autocorrelation of decoloredsamples.

C. Joint Equalizer and Detection

Fig. 6 shows the schematic of the 2-D equalizer/detectorarchitecture. The 2-D detector is coupled to a novel 2-D self-iterating soft equalizer developed in [13]. The self-iteratingsoft equalizer and the 2-D detector exchange soft informationusing a turbo setup. It must be noted that the combinationof the equalizer and detector brings turbo gains for the 2-Dsystem. We omit the mathematical details since it is describedin [13].

IV. SIMULATIONS AND DISCUSSION

In this section, we present simulation results based on theSNR model we developed. The 2-D data had dimensions64 × 64 corresponding to 512 bytes of sector data. The2-D read head response was discretized. We assume a 2-Ddiscrete ISI response h = [0.002 0.043 0.002; 0.043 1 0.043;0.002 0.043 0.002] of dimensions 3 × 3 within our setup.

Fig. 7 shows the autocorrelation of colored and decolorednoise samples using an order 3 × 3 whitening filter.

We used an LDPC array code [19] of length 512 bytes andrate R = 0.5 for evaluating the efficacy of the coded systemperformance. The CBD D2D was set to 1.5. The bit aspectratio BAR was kept at 3, and the parameter a was chosenas 3. The jitter parameters were set to zero. The parameter δwithin the 2-D detector was set to 0.8. The scale factors δ

Fig. 8. Coded performance of the 2-D equalizer/detector system.

within the 2-D joint equalizer/detector architecture were to 0.5.The LDPC decoder employed 16 inner iterations. Two globaliterations were exchanged between the 2-D equalizer and thedetector. Four iterations were exchanged between the multi-row and multi-column detectors. The 2-D equalizer dimensionwas set to 3 × 3 and configured to self-iterate four times. Allthe iteration numbers were programmed based on the gainsaturations observed within the turbo setup. In other words,no further gains were observed beyond the iteration numbersmentioned as above.

Fig. 8 shows the performance of the system. As we see, onecan obtain ∼5.5 dB of SNR gain over the uncoded system.

V. CONCLUSION

We developed an amenable read channel model for the2-DMR system and analyzed the problem of setting thebit aspect ratio for maximizing SNR. We modified the 2-DMAP-based detector to incorporate 2-D noise whitening capa-bility. The 2-D detector with a simple noise prediction capa-bility is integrated within a novel 2-D self-iterating equalizerto operate in a turbo fashion. We evaluated the performanceof the overall system and observed significant SNR gains of5.5 dB over the proposed 2-DMR read channel.

There are plenty of open problems that still need to beaddressed. It would be interesting to simplify and incorporatean appropriate media and write channel model along with theproposed read model toward an eventual 2-DMR simulationplatform. The issues related to 2-D timing recovery and lowcomplexity 2-D DDNP algorithms are yet to be addressed,and their gains are to be assessed. Two-dimensional codingtechniques can be customized depending upon the underlyingerror patterns observed. It would be interesting to build a2-D read head along with appropriate changes in head/mediadesigns for experimentally evaluating the 2-D coding and sig-nal processing techniques to assess the 2-DMR technologicaladvantage.

ACKNOWLEDGMENT

The authors would like to thank Western Digital for encour-agement and support.

SRINIVASA et al.: COMMUNICATION-THEORETIC FRAMEWORK FOR 2-DMR CHANNEL MODELING 3000307

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