A Reprint (rom the
Advances in Laser Scanning and Recording
April 19-20, 1983
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
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.
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
large n the number of distinct d-sequences N(n) behaves as
largest real root of aÀn, with À given by the
d+1 = 0zd
-z - (2.3)
The maximum information rate (in short
R = 21og).
rate) R is then simply given by
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.
d R T J..= (d+1).R
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
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
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)
v : linear velocity of the disc
NA: numerical aperture of the objective lens
We now find, using eq
erf(x) = vn~
and u = normalized information density given by u=
T = data bit length.
exp(-z2)dz; erf(- = 1
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.
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
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.
'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-
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
Vnom -~+lJ (4.2)
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.
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).
The authors are indebted to Wil Gset-up.
Ophey, who designed the optics in the experimental
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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 .
SNR = 26
Figure 3. Worst-case eye-opening versus
normalised information density withT.
as a parameter, Gaussian roll-off.
A cross-section of the disco
Figure 6. Schematic drawing of the op-tica!
or a BI
E-3 versus minimumsitions
, 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.
a) A runlength limited sequence.
b) A dk-sequence.
c) A pul se derived fr om an RLL se-
quence used for writing overlapping
d) Write pulses for overlapping mono-
holes red to the laser (2 pulses
e) Schematic pits on the di sc when
monoholes are used.
f) Schematic pits on the disc when
pitlength modulation (overlapping
monoholes) is used.
Figure 9. The BER versus velocity devia-
tions (experimental). IC-I.
Figure 10. The BER versus energy de-