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A Reprint (rom the

Volume 396

Advances in Laser Scanning and Recording

April 19-20, 1983

Geneva, Switzerland

Maximization of recording density obtainable in Te-alloys

Kees A. Schouhamer Immink, Ronaid M. Aarts

Philips Research Laboratories

5600 JA, Eindhoven. The Netherlands

IC> 1983 by the Society of Photo-Opticallnstrumentation Engineers

Box 10, Bellingham, Washington 98227-0010 USA Telephone 206/676-3290

Maximization of recording density obtainable in Te-alloys

Kees A. Schouhamer Immink and Ronald M. Aarts

Philips Research Laboratories

5600 JA, Eindhoven, The Netherlands

Abstract

We report on high density recording experiments of digital information in Te alloys on

pregrooved discs. The recording and reading of information is done on a recorder fitted

with an AlGaAs laser. We describe experiments with modulation systems using pit-length

modulation based on runlength-limited codes. Runlength-limited sequences were adopted as

a modulator output because of the fact that this class of restricted sequences bas a great

impact in magnetic and optical recording.

State-of-the-art high power solid-state lasers can emit a light pulse of sufficient

energy for only a limited time and can therefore only be used in a pulsed mode. Pit-length

modulation is achieved by adjusting the rotational velocity of the di sc and laser pul se

write frequency in such a war that oblong pits of overlapping monoholes res~lt.

We demonstrate the feasibility of recording densities of up to 1 Mbit/mm with the

application of pit-length modulation schemes.

Introduction

In this paper we consider the feasibility of high density optical recording in Te alloys.

The recording and reading of information is Qone on a recorder equipped with an AlGaAslaser.

All Dur experiments are d6ne on pregrooved discs with a track pitch of 1.7?m.

We describe experiments with pit-length modulation. All the modulation systems we con-

sidered are based on runlength-limited sequences. Runlength-limited sequences were adopted

as a modulator outP4t because of the fact that this class of restricted sequences bas a

great impact tn2mjgijetic and optical (read-only) recording as the Compact Disc Digital

Audio System. ' , ,

In Section 2 we give a brief definition and theory of runlength-limited sequences.

Section 3 gives theoretical results of the maximum achievable information density and the

sensitivity to parameter tolerances. A description of the experiments is given in Section 4.

2. Definition of runlen~th-limited binary sequences

The theorYsOf binary sequences with restrictions on minimum and maximum runlength goes

back to Kautz , Tang and Bah16. For an exhaustive treatment of th is subject the reader is

referred to ref. 6. Their most important results are summarized here.We

adopt Tang's definitions:

A dk-limited sequence simultaneously satisfies the following conditions:

a. d-constraint -two logical ones are separated by a run of consecutive logical zeros

of at least d.

b. k-constraint -the length of any run of consecutive logical zeros is at most k.

A sequence satisfying the d- and k-constraint is called a dk-sequence. Sequences only

satisfying the d-constraint are called d-sequences. We derive a runlength-limited binary

sequence with at least (d+1) consecutive zeros or ones and at most (k+1) consecutive

zeros or ones by integrating modulo 2 a dk-limited sequence. In this way the "ones" of

a dk-sequence indicate the P9sition of a transit ion zero to one or one to zero of a run-

length-limited sequence. In ref. 6 recursion equations are derived for the number of

distinct dk-limited sequences of block length n as a function of d and k. If for con-venience

we restrict ourselves to d-limited sequences, the number of distinct binary

sequences N of block length n ~s given by the following equation.

.n+1 1:5, n:5, d+1

N(n) = (2.1)

N(n-1) + N(n-d-1) n > d+1

The asymptotic "information rate R of a dk-sequence is determined by the specified con-

straints and is given by

(2.2

lim n--For

large n the number of distinct d-sequences N(n) behaves as

largest real root of aÀn, with À given by the

181

d+1 = 0zd

-z - (2.3)

The maximum information rate (in short

R = 21og).

rate) R is then simply given by

(2.4

Similar relations can be derived for sequences with a d and/or k constraint. The process

of modulation maps the input data stream onto the runlength-limited output stream. In

general m consecutive databits are mapped onto n consecutive channelbits. The existence

of a maximum asymptotic information rate R merely states that mln < R = R (d,k) for any

fin~te mand n. If one wishes to transmit a certain fixed amount of information per time

unit over a dk-limited noiseless channel, then the channel clock should run at least 1/R

times raster than the data clock to compensate for d- and k~constraint. In other words,

a channel bit takes a time which is shorter by a factor of at least R than that needèd

for a data bit. The minimum physical distance per data bit of the runlength-limited

sequence generated by modulo 2 integrating a dk-sequence is ncw given by

Tmin = (d+1)R(d,k) (2.5)

In table I we have listed for some values of d the minimum di stance Tr

transitions and the rate R. Note that d=O is the uncoded (N~Z) case.

Both Rand T. are specified per data bit length.

[lJJ.n

d R T J..= (d+1).R

m n

between

min

0

1

2

3

4

5

1.0

0.69

0.55

0.46

0.41

0.36

1.00

1.38

1.65

1.84

2.05

2.16

Table

I. Rate Rand Tmin versus d for fixed data rate.

The values of Rand T i in table I are theoretical maxima. In this paper we will not

digc~s~ an actual imp~ëMentation of encoders and decoders. Good algorithms can be found

in ' , and it suffices to state tha7 practical modulators with finite dimensions reach

the maxima of table I towithin 90%.

We note fr om the table that application of dk-sequences enables us to increase the

minimum tim~ between t:ans~tions Tmin' The rate R (or c~annel bit time per,data bit time)

decreases w1th d. Qual1tat1vely we may state that T, lS related to the h1ghest fre-

quency of the modulator and hence to the maximum a~tRinable information density.

Table I shows clearly the possible trade-off between Tmi (related to the highest

frequency in the runlength-limited sequence) and the tim1Hg accuracy (timing window) RT.

To get some idea of the trade-off, Fig. 1 depicts the eye-patterns for RLL codes with

d=O, 1, 2 and 3. In this figure the minimum time between transitions of the modulation

stream Tm is ncw fixed. Consequently the data rate i.e. the number of data bits transmitted

per unit time is different. From eq. 2.5 and table I we derive that, if the d=O code

transmits 1 data bit/s, then the codes with d=1, 2 and 3 transmit 1.38, 1.65 and 1.84data

bit/s, respectively. In the figure we no te clearly the decreasing ere-opening in

both time and amplitude with increasing d. In the next chapter we shall study quantita-

tively the spectral and bandwidth proper ties of the runlength-limited sequences.

3. Maximization of information density

3.1. Bandwidth properties of runlength-limited sequences

We assume that the runlength-lim1ted sequenc~ ist~~~smitted over a linear, bandwidth-

limited channel with impulse response h(t). Furthermore we assume that the channel

output is corrupted with additive Gaussian, zero mean, noise n(t). Hence the output is

the sum of the convolution of the channel impulse response with the runlength-limited

sequence and the noise-

rtt) = Jfh(t')S(t-tl)dtl + n(t) (3.1)

--

where rtt) is the detected output signal

n(t) is noise

s(t) is the RLL-code input signal

h(t) is the impulse response of the channel

182

In this paper we restrict ourselvesto simple, non-equalized amplitude detectors, so

that it is only the total noise power thát is important and not the exact shape of the

spectrum.

With this linear channel model we can calculate the channel bit error (BER). A con-

ceptually simple algorithm was presented by Tufts and Aaron9. They assumed the inter-

symbol interference to be confined to m data bits or equivalently n = m/R channel bits.

In other words, we truncate the impulse response and ignore the contributkon of the data

m/(2R) bits away from the centre of the impulse. Corresponding to the N(m/R) legal

dk-sequences of length m/R, there are at most N(m/R) distinct "eye-openings" at the

sampling moments. The conditional error probabilities are computed for each of the run-

length-limited sequences and then averaged with respect to the probability of occurrence of

these sequences. This procedure bas a wide field of application: any shape of the impulse

response, negative or positive sidelobs can be treated thus. One major disadvantage of this

procedure is the exponential growth of the computational effort with N(m/R). A computa-

tionally more stràightforward method is derived on the basis of the observation that the

bit error rate is dominated by the smallest, worst-case ere opening. A good approximation

of the bit error rate is possible by calculating the worst-case ere opening and then cal-

culating the error probability based on this ere opening only. If we ignore baseline

wandering due to AC-coupling of the modulation stream, then the worst-case ere opening

is the repetition of the minimum and maximum runlengths T. and T respectively (SeeFig.

2). This approximation is only valid if h(t) is str~~~ly pos~~!ve. The channel output

with the worst-case input pattern can now be easily calculated with eq. (3.1), assuming

the amplitude of the RLL sequence to be unity. Note that the ere-opening is the output

signal rtt) sampled at the centre of the channel bit of length RT.

-RT/2 (Tmin-R/2JT -

ere = fh(tJdt -f h(tJdt + fh(tJdt

---RT/2 (Tmin-R/2JT (3.2)

Assuming a symmetric impulse response or h(t) = h(-t), eq. (3.2) simplifies to eq. (3.3)

For optical recording many approximations a,Ö possible to obtain a useful moOel of

the impulse response of the read-out mechanism. We base our discussions on a Gaussian

roll-off frequ~ncy characteristic. Such a model is also of ten adopted in magnetic

recording.11,1 We ignore any radial contribution, so we adopt a completely linear

one-dimensional read-out model.

We first assume that the impulse response is given by

h(t) = in BexP(-B2t2) (3.4) 0'

The cut-off frequency B is given by c;L'iè

., -.~,

B :' 2.8 NA ~ v/À (3.5)

where

v : linear velocity of the disc

NA: numerical aperture of the objective lens

À: wavelength

We now find, using eq

3.1

-1 (3.6)

where 2

erf(x) = vn~

and u = normalized information density given by u=

T = data bit length.

exp(-z2)dz; erf(- = 1

IBT

183

In Fig. 3 we give the minimum worst-case eye-opening as a function of the normalized

information density for d and consequently for T, as a parameter. All these calculations

are based on the theoretical maximum rate R and ~1~ of the theoretical runlength-limited

codes (see table I). We notice from this figure tWà-e the ere-opening for a certain d de-

creases with the information denisty U .For a value d' > d we notice that the ere-opening

is initially smaller at low densities, but then decreases more slowly. The result is that

at a certain density both eye-openings are equal and for still larger densities the

ere-opening is larger for d' > d. It is quite clear from this figure that if we wish to

design a high~density modulation system, then the choice of a certain d and hence Tmin

depends on both the minimum tolerable ere-opening and the information density. We note that

it is only worthwhile to consider a d=2 over a d=1 system if we may tolerate a minimum

relative ere height smaller than 28 percent (-11 dB).

For the Gaussian noise model the channel bit error rate (BER) can be approximated by

BER =-! 11 -erf(~~) I (3.7)

wh~re2A = amplitude of the runlength-constrained signal

and N = variance or power of the additive noise.

The signal-to-noise ratio is simply given by: A2/N2 (the runlength-limited sequence is

binary-valued with amplitude A). The actual data bit rate (due to error propagation) is a

function of the channel bit error rate. This function depends on the typical implementation

of the mapping of data onto channel bits and vice versa.

With eq. 3.7 and a given channel bit error rate, we can calculate the minimum tolerable

ere-opening as a function of the signal-to-noise ratio. Most certainly other factors than

noise are operative, such as ~olerances in the transmission path, governing the minimum

tolerable ere-opening. For a given minimum tolerable ere-opening we nou proceed to calculatl

the maximum information density as a function ofd and Tmin. In Fig, 3 we draw horizontal

lines at the specified tolerable ere-opening anddetermine the intersectións with the otter

curves. T~i~ res~lts iJ? the.maximut;i achieva~le inform,at,ion ?e,:!sitY,versus d (or ~ i ) for

some speclfled slgnal-t'o-noJ.se-ratlo (See Flp;. 4). The specJ.fJ.ed blt error F rate lW ~0-3..

In Figure 4 we notice maxima in information density for some value of d. or small d

values a high intersymbol interference occurs which limits the information density.

At large d values, the high accuracy of the transition positioning also sets a limit to the

maximum density. We note that for an SNR = 26 dB a flat maximum in information density

occurs for d = 2 and 3. Note that the difference in maximum attainable information

density for a given tolerable ere height is small. In principle we can infinitely increase

the information density for the given Gaussian impulse response, if the signal-to-noise

ratio is correspondingly improved. If for practical reasons a minimum ere-opening of sar

-20 dB is a limit (tolerances, etc.), th en systems with d > 5 should not be considered.

4. Description of the experiments

4.1. The di sc

The rècording of information is done by locally heating the Te-alloy layer. Figure 5

shows a cross-section of the actual disco A 2P (photo-polymer) layer with a groove struc-

ture <1.7pm track pitch) in its top surface bas been deposited on a glass substrate. The

Te-alloy 1ayer bas been flash evaporated on the 2P layer. The entire di sc can be sandwiched

w,ith a si§O9~ glass or plastic substrate for protection of the sensitive layer (see forexample.

,

4.2. Theoptic~l_~_e_cord~x:

The optical recorder'~ bas to perform two functions:

a) local heating of the bit locations

b) detection of the pits created

In Figure 6 a schematic drawing of the optics is shown. The light source is a high-power

AlGaAs laser with a wavelength of 840 nm. Approximately 40% of the light output is use-

fully captured by an objective with a numeri cal aperture of 0.3. The parallel team

traverses a polarizing beamsplitter and a À/4 plate and is focussed onto the disc

by an objective with N.A.: 0.6. The half-width of the lightspot is slightly smaller than

one micron. When recording information, the laser is driven by a pulse of 50 nsec duration

at intervals of at minimum 250 nsec. The peak power is 60 mW; Dwing to losses in the light

path, 10 mW is available in the focussed light spot.

A pit generated by a single light pulse bas a circular shape with a diameter of typically

1 micron. Oblong pits are generated by applying several light pulses at 250 nsec. inter-

vals.Figure 7 shows an SEM microscope photograph of written pits in the pregrooved spiral

on a disco The sequence represents a typical digital signal with oblong pits of discrete

lengths. The minimum pit length (not the bit length) is 1 micron and the spacing between

tracks is 1.7 microns.

When detecting written pits, the laser is pulsed at a high frequency (15 MHz) with a duty

cycle of 0.15 and a peak power of 8 mW. A quasi-continuous power of 0.3 mW is available

on the disc and this is sufficiently low for the recorded pits not to be perturbed. Through

184

the polarizing beamsplitter and a semi tr~nsparent mirror the light is thrown onto a photo

diode detector, see Fig. 6. Af ter that the photo current is electronically processed.

During recording and reading a small part of the light (10%) is coupled out to the

tracking (push-pull) and focussing optics (Foucault double-wedge method). An automatic gain

control is incorporated in order to compensate for the large difference in light power

during recording and reading.

4.3. ?it length modulation

The--àeSign-ana-5Uilding of real-time modulators and demodulators is a time-consuming

activity. In earlier experiments we noticed that a maximal density study can be done quite

welIon the so-called "channel level" i.e. we do not have (de)modulator rules, but compare

in BER measurements the channel bits. We used as a data source the "produlator", aPROM,

filled with the desired bit stream, which is periodically re ad out. We filled 6 PROMs each

with a frame sync pattern (27 bits) and a dk-sequence (561 bits) increasing fr om d=1 to

d=6, k=10 fixed. The channel bit rate was 4 Mbit/sec. during all experiments.

4.4. Experime:nts

'Pulse length modulation differs physically from monohole modulation mainly in twoaspects:

-the present state-of-the-art solid-state laser is not capable of emitting light of the

required (hight constant intensity level during the ap'propriate time;

-the behaviour of the sensitive layer during a relatively long exposure to high intensity.

To eliminate possible effects due to the above mentioned problems we have written oblong

pits by writing overlapping monoholes. Figure 8a depicts the desired pit-farm and Fig. 8d

shows the pulses red to the laser.

The length of the pit is

'.

( .

11 = 1-

(4.1v.Tc+,swhere

Pi = pit length

i = number of overlapping monoholes

v = tangential di sc velocity

T = time between 2 successive laser pulses

Ac = monohole diameter.

To reach the maximal density, the minimal pit size must be chosen equal to S.

According to Fig. 8 a minimum pit is equivalent to ( d+1) pulses and hence d pulses of

the sequence must be deleted. For the d = 2 sequence of Fig. 8c this leads to a pulse

stream in Fig. 8di the latter shows the pulses of the nominal duration, 50 nsec duringwriting,

being fed to the laser. With a fixed Tand deleting d pulses the veloéity is

fixed and is c

-c5

Vnom -~+lJ (4.2)

cDeviations

from the nominal velocity lead to unwanted deviations in Pi. The effect of a

deviation from the nominal velocity is measured and plotted in Fig. 9.

Figure 9 is not symmetrical around v/v = 1 because of the decreasing density and

consequently increasing eye opening at v/uom > 1. The energy used for creating a hole in

the Te alloy film determines its size and E81'lsequently thepit length is a function of the

energy in the write pulse. The sensitivity of energy deviations in the write pulse to the

BER is measured and Fig. 10 depicts the result. The figure shows a BER optimum when an

energy of approximately 1 nJ during the write pulses is used. At the nominal speed and a

BER of 5E-4 the maximum obtainable density was about 2 data bit/flm.

Conclusions

We have described experiments with modulation systems based on pit length modulation in

Te-alloy based discs. Computer simulations show a superiority modulation system based on a

d = 2 runlength-limited sequence2 Experiments confirmed these results. We achieved an

information density of 1 Mbit/mm (1.7?m track pitch and O.6?m tangential density).

Acknowle_d~~m~nt

The authors are indebted to Wil Gset-up.

Ophey, who designed the optics in the experimental

185

References

I. J.C. Mallinson and J.W. MilIer, "Optimal Codes for digital magnetic recording",

Radio and Elec. Eng., 47, p. 172-176 (1977).

2. G.V. Jacoby, "A new loöK-ahead code for increased density", IEEE Trans. Magn.,

vol. MAG-13, no. 5, pp. 1202-1204 (1977).

3. K.A. Immink, "Modulation Systems for Digital Audio Discs with Optical Read Out",

Int.. Conf. ASSP, Atlanta, pp. 578-590 (1981).

4. J.P.J. Heemskerk and K.A. Schouhamer Immink, "Compact Disc; system aspects and

modulation", Philips Techn. Rev. 40, pp. 157-164 (1982).

5. W.H. Kautz, "Fibonacci codes for synchronization control", IEEE Trans. Inform. Theory

vol. IT-11, pp. 284-292 (1965).

6. D.T. Tang and L.R. Bahl, "Block codes for a class of constrained noiseless channels",

Inform. Control. vol. 17, pp. 436-461 (1970).

7.~lP.A. Franaszek,"Sequence-state methods for runlength limited coding", IBM J. Res.

Develop., pp. 376-383 (1970).

8. G.F.M. Beenker and K.A. Schouhamer Immink, "A simple method for coding and decoding

of runlength-limited sequences", IEEE Conf. on Information Theory, les Arcs (1982).

9. M.R. Aaron and T.W. Tufts, ttIntersymbol Interference and Error Probability", IEEE

Trans. Inform. Theory, IT-12, pp. 26-34 (1966).

10. G. Bouwhuis and J. Braat, "Video disk player optics", Applied Optics, Vol. 11,

pp. 1993-2000 (1978).11.

A.S. Hoagland, "Digital Recording", Wiley (1963).12.

N.D. Mackintosh, "A superposition-based analysis of pulse-slimming techniques for

digital recordingt', Int. Conf. on Video and Data Recording, Southampton (1979).13.

K. Bulthuis et al., "Ten billion bits on a disc", IEEE Spectrum (August 1979).

14. P. Kivits et al., "The hole format ion process in Tellurium layers for optical data

storage". Thin solid films, 87, pp. 215, (1982).

186

.!!!!-..,

read-aut spat

Figure 2. Worst-case input pattern and

impulse response of the read-out system.

Figure 1. Eye-pattern of some run1ength-

1imited codes for a fixed minimum time

between transitions T .

m

Figure 4

density

di stance

certain

Substitu

SNR = 26

yields a

data bit

Figure 3. Worst-case eye-opening versus

normalised information density withT.

as a parameter, Gaussian roll-off.

mln

A cross-section of the disco

Figure 5

Figure 6. Schematic drawing of the op-tica!

set-up.

187

Maxir

or a BI

betweENRs,

(ing

SI

dB, NImaximl

per r

urn ac

R of

n traaussi

me pr

= o.

m den

icron

ievable

information

E-3 versus minimumsitions

T. for

mln

n roll-ofr.ctical

values :

, À =. 840 nm

ity of about 2

Figure 7. A scanning electron microscope

photograph of a 10000 times enlarged

disc sample with a Te compound layer.

The upper track contains monohole in-

formation, the other tracks runlength

seauences. The observation angle is

45 , with one white bar corresponding

to 1 jum.

Figure B.

a) A runlength limited sequence.

b) A dk-sequence.

c) A pul se derived fr om an RLL se-

quence used for writing overlapping

monoholes.

d) Write pulses for overlapping mono-

holes red to the laser (2 pulses

deleted).

e) Schematic pits on the di sc when

monoholes are used.

f) Schematic pits on the disc when

pitlength modulation (overlapping

monoholes) is used.

1BER (iogl

10-2

510-3

10-3

510-4

Figure 9. The BER versus velocity devia-

tions (experimental). IC-I.

Figure 10. The BER versus energy de-

viations (experimental).

188