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MODULATION
SYSTEMS
FOR
DIGITAL
AUDIO
DISCS
WITH OPTICAL
READOUT
by
Kees
A.
Immink,
Member
IEEE
Philips
Research
Laboratories
The
Netherlands
Abstract
This
paper
describes
a new
recording
code
format,
Eight
to
Fourteen
Modulation
(EFM)
,
designed
for
digital
audio
discs
with
optical
readout.
Atten
tion
is
focused
primarily
on
trade
offs
between
conflicting
parameters
such
as
information
density
and
d.c.
content
that
led
to
the
choice
of
the
adopted
format
EFM.
Introduction
This
paper
describes
the
design
of
a
modula~ion
system
of
a
digital
audio
disc
with
optical
read
out.
The
digital
audio
disc
contains
a
spiral
shaped
track
of
successive
shallow
depressions,
also
called
pits,
in
a
reflective
layer.
The
en
coded
audio
information
is
stored
in
the
lengths
of
these
pits
and
in
the
distances
between them.
The
read
out
is
contactless;
two
servosystems
follow
the
track
in
focus
and
radial
direction
within
the
desired
accuracy.
For
details
of
optical
recording
the
reader
is
referred
to
(9) and
the
special
issue
of
applied
optics
July
1978.
The main
specifications
of
the
audio
disc
are:
2
audiochannels
with
a
playing
time
larger
than
1
hour,
sample
frequency
44.1
kc/s,
16
bits
linear
quantization.
Disc
diameter:
120
mm.
The
data
rate
after
the
anologuedigital
converters
is
32x44.1 kHz =
1.41
Mb/s.
After
the
error
control
encoder
(10) we
yield
a
data
rate
of
4/3xl.41
=
1.88
Mb/s.
For
the
specified
playing
time
we
may
calculate
that
this
audiodisc
is
a
storage
medium
with
the
phenomenalrcapacity
of
more
than
6.5
109
bits
or
108
bits
per
cm2•
A
modulation
system
for
an
optical
audio
disc
has
to
fulfil
the
following
requirements:

self
clocking
ability
high
information
density

small
error
propagation
 low power
at
low
frequencies
immunity
against
tolerances
in
the
lightpath
This
last
requirement
is
not
imposed
because
or
limitations
of
optical
recording
to
reproduce
low
frequencies
as
is
mostly
the
case
in
magnetic
recording.
D.c.
content
causes
interferen~e
with
the
servosystems
and
should
be
avoided.
In
this
paper
we
will
discuss
a
code,
called
Eight
to
Fourteen
Modulation
(EFM),
which
meets
asound compromise between
the
aforementioned
conflicting
criteria.
587
Maximum
data
density,
bandwidth
restrictions
The
present
optical
recording
technology
of
Video Long
Play
and Compact Audio
Disc
restricts
the
input
signal
levels
to
only
two:
pit
or
land.
So
the
information
is
just
contained
in
the
length
of
the
pits
and
the
distan~e
between them. In a
digital
system
these
lengths
and
distances
only
take
discrete
values.
Considerations
such
as low power
at
low
frequencies,
selfclocking
ability
and
limitations
on
intersymbol
interference
make
it
necessary
that
the
input
data
be mapped (modulated
or
coded)
into
a
sequence
of
binary
data
with
some
special
proper
ties.
The
self
timing
property
e.g.
sets
an upper
limit
on
the
maximum
length
of
the
pits
and
lands.
On
the
other
hand
intersymbolinterference
imposes
a
lower
limit
upon
the
minimum
length.
The
theory
of
binary
sequences
with
restrictions
on
minimum
and
maximum
feature
size
goes back
to
KautZ (1)
and Tang
et
al.
(2).
We
adopt
Tangs
definitions:
A
dklimited
sequence
satisfies
simultaneously
the
following
conditions:
a.
dconstraint
 two
logical
ones
are
separated
b
a
run
of
consecutive
zeros
of
length
at
least
d
b.
kconstraint
 any
run
of
consecutive
zeros
is
of
length
at
most
k.
When
we
integrate
modulo 2 a dk
sequence
then
the
iength
of
any
run
is
at
most k+l and
at
least
d+l.
The number N
of
distinct
dk
sequences
of
a
block
of
n
bits
can
be
calculated
by a
recursive
rela
tion.
If
we
restrict
here
for
convenience
to
the
dconstraint
then
the
number
of
distinct
binary
sequences
of
length
n
is
given
by
(2):
on< 0
N(n) =n+1
0<;;
n<; d+1 (1)
N(nl
J+N(ndl)
ns d+1
The
asymtotic
information
rate
R
of
these
sequence
is
determined
by
the
specified
constraints
and
is
given
by:
R==lim 2
log
(N
(n)
)In
(2)
n
....
GO
We
now come
to
the
point
to
discuss
the
in
fluence
on Lnt.ersymbo.l
interference
and
consequent
ly
information
density.
Suppose
we
have an
infor
mation
source
that
transmits
1
bit
per
second
in
the
format
of
an NRZcode;
i.
e.
a
logical
one
is
e.g.
pit
and a
logical
zero
is
land.
In
this
case
the
minimum
distance
between
transients
is
1
second.
Using
integrated
modulo 2
asequences
for
recording
we
are
sure,
that
the
transients
are
CJ.l1li10'i/R1/nnnn.o5R71OO_7'i ©
19R1
IREF
dR(d+1) .R r2SER
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oSNR e 20dB
O~
•
5NR.
25dB
1
0.69
,1.39
2NA
oSNA.
JOdB
2
0.55
1.65
J
0.46
1.86
...
0.41
2.03
5
0.36
2.17
Table
1.
Rate
and Tmin
versus
d.
_d
TlTl,o
1 2 J
138 155 184
Maximum
achievable
information
density
versus
minimum
pitsize
(Tmin>
for
a
Gaussian
channel.
Substituting
some
practical
values:
SNR
~
26 dB,
NA
=
C.4,
A=
780
nm
yields
a
maximum
density
of
2.25
bits
per
micron.
a
10
figure
1.
attained
if
we
choose
a
modulation
system
with
d=2
or
d=3. The
difference
with
other
choices
is
only
slight.
According
to
figure
1
the
maximum
info
density
equals
for
the
specific
conditions:
0/f
c
~
2.2
at
SNR =26 dB
with
D
is
information
density
(bits
per
meter).
In
the
calculations
cere
presented
we on_y
took
into
account
the
"eyeopening"
at
the
sampling
moments.
Another
parameter,
not
yet
discusseG,
is
the
self
clocking
ability
of
the
modulation
system.
The
desired
accuracy
of
Lhe
timing
(for
a
constant
data
rate)
is
proportional
to
R. However
tne
clOCK
content
or
average
number
of
transients
is
relatec
to
the
reciprocal
of
Tm1n. So from
the
point
of
view
of
timing
we
prefer
a
system
with
d=2
over
"d=3.
Anothpr
point
in
the
favor
of
a d=2
system
~s
that
for
practical
implemented
codes
the
rate
1S
smaller
(say
90%)
than
~he
theoretical
max~ma
de
picted
In
table
1.
All
these
factors
togetnpr
lead
to
tne
choice
of
a
modulation
system
with
d:2.
Experiments
with
practical
codes
(in
coope
ration
with
engineers
of
SONY
Corporation)
led
to
the
same
:onclusicn.
EFM
code
In
the
preceding
chapter
we
studiec
the
performance
of
some
theoretical
dlimited
codes
and
n0ticec
tha
t a d=2
code
is
a
qui
te
optimal
cboice
.,1.
ttl
respect
to
information
de~sity.
A
pracLical
im
plementation
of
qn
encoder
is
most
often
b~~~c
on
a
block
code,
that
maps III
consecutive
dQ.t~
l~iJ'lt
bat.s
into
n
channelbits.
From
the
point
of
Vlew
cf
the
error
control
system
it
is
favourable
to
choose
m=8,
so
that
an
8bitssymbol
is
encoded
intc
an n
bits
channelsymbol.
At
the
decoder
we map
the
n
bits
channelsymbol
again
into
an
8bitssymbol
•
In
this
way we
restrict
errorpropagation
to
only
one
symbol.
We
assume
that
the
receiver
knows
via
some
technical
provision,
the
synchronization
unit,
where
the
beginning
of
each
word
is
situated.
From
eq.
(1) we
derive
that,
for
n=14, we have
N=277
d~stinct
14bits
sequences
satisfying
the
d=2
588
constraint.
Delet~ng
21
patterns
with
the
longest
rllnleng~n
yields
an
alphabet
of
256
sequences,
so
that
a un1Qua
on~
to
ene mapping by
e.g.
8leoK up
(4
)
(J)
B=
1/
(2
T . )
mi
n
For
1nstance,
with
d=4 we
are
able
to
guaran
~ee
a
m~nimum
distance
between
transients
of
about
~w'
daLa
clock
per10ds.
The
relation
between Tmin and
bandwidth
pro
carLies
of
the
code
is
not
so
clear.
Some
authors
(3)
claim,
that
the
minimum
bandwidth
required
to
transmit
the
bitstream
is
s~mply
related
to
Tmin:
Nciss :.;
the
optical
reac
out
system
has
been
~eS('~::'Dec
c;' :Jeemskerk
(6),
who
investigated
seve
r
a;
r.oi
se
5:;';.'ces
in
a vi.deocn
sk
system.
Most
of
h~J
·~sL.l~=
~~ply
to
the
case
of
a Compact Audi0
D.:.::,'.
:'1:1:
t;':
model
of
the
read
out
mechanism arl04
tne
''y,
oss<.lur~~s
we
are
now
able
to
calculate
the
_I~",nr'el
bit
error
rate
(BER)
of
the
theoretical
cnannc,vc , I nf'cdensit.y
with
Tmin
as
parameter.
We
~r,
_eG'::
ir: a "lay
as
presentee
by
Tufts
and
A3.:'':)n
\~;
we
a~sume,
that
the
contribution
to
the
LntG
':~rence
is
confined
to
m
databits
or
equi
valGn~lJ
to
n
~
m/R
channelbits
(with
R=R(d)
or
R{~m:L.JI;.
Ccrrespondfng
to
the
N(m/R)
possible
3·1:~'~tec
chei
ces
of
the
truncated
message
secuen
~8
~~re
are
N(m/R)
distinct
"eye
openings"
at
th~
s~m;~~~~
moments. The
conditional
errorprobabili
•
~,~
~ssuming
a
Gaussian
probabiJity
function
of
:.1"
::(.~se,
are
computed
for
each
of
the
run
length
l_m~ced
pulse
sequences
and
then
averaged
with
r,,"'p~ct
to
the
probability
of
occurence
of
these
se ;..
:r.ces.
In
fi~.
!we
plotted
the
locus
of
information
dp.nSlty
vs.
T~Ln
that
can
be
atLa~ned
at
an
arbi
trarily
high
channelbit
error
r~~~.
We
nOLi~~.
th~1
7
maximum
in
information
dersiLy
can
b~
sepa~ated
at
least
d,
g~v~ng
a
physical
distance
of
Id+11time
units
of
the
recorder
clock.
However
the
~oss
of
rate,
due
to
the
redundancy
of
the
dseQuence
is
R. So
the
actual
minimum
distance
be~ween
transients
in
source
time
units
is:
~
=(d+1)R(d)
(seconds)
Lmi n
In
table
I we
tabulated
for
some
values
of
d
the
minimum
distance
between
level
crossings
that
can
be
obLained.
r~~cna~
et
al.
(7) have shown
that
Tmin
is
not
a
_iable
indication
of
the
bandwidth
requirements.
_
0,'
a
realistic
channel
(magnetic
recording)
band
'Its
restrictions
are
derived
by
Jacoby
(4).
For
JpLical
recording
the
following
results
can
be
der1ved.
The most
important
parL
of
the
optical
system
~s
Lhe
)bject~ve
lens.
Its
modulation
transfer
funct~on
MTF
sets
a
limit
to
the
maximum
spatial
~requency,
Lhat
can be
resolved.
The
MTF
is
deLer
Inned
oy
the
numerical
aperture
(NA),
the
wave
len~th
(AJ
and
the
state
of
correction
of
the
ob
lcct1ve
:5/.
The
MTF
is
zero
above
the
spatial
cut
~r'f
f'r"::'L.~ney
(fcl
given
by:

References
figure
2bLower
part
of
the
power
density
functions.
os
,
.....
EFM
3PM
M2
/'',
./ "\"\,
".
JPM
 EFM one pomt DC
contrOl
_.
EFM
"""
""lnt DC
C<lnlrol
······1012
025

~~.
W.H.
Kautz,
IEEE
Trans.
Inform.
Theory,
vol.
ITii,
p , 285
(1965).
D.T. Tang and L.R.
Bahl,
Inform.
Contr.
vol.
17,
p.
436,
1970.
P.D.
Shaft,
IEEE
Trans.
Comm.,
vol.
COM16,
p,
687,
(1973).
G.V.
Jacoby,
IEEE
Trans.
Magn.,
vol.
MAG13,
no.
5,
p , 1202
(1977).
G. Bouwhuis and
J.
Braat,
Applied
Optics
vol.
17, p , 1993, 1978.
J.
Heemskerk, Appl.
Optics
vol.
17, p. 2007,
1978).
M.G.
Pelchat
and J.M.
Geist,
IEEE
Trans.
on
Comm.,
vol.
COM23,
no. 9, p. 878, 1975.
M.R. Aaron and D.W.
Tafts,
IEEE
Trans.
Inform.
Theory,
IT12,
pp. 26
(1966).
K. Compaan,
Philips
Tech.
Rev.,
p, 1978 (1973).
T.
Doi,
Conference
Paper
ASSP,
Atlanta,
1981.
J.e.
Mallinson
and
J.w.
Miller,
Radio and
Elec.
Eng
, ,
47,
p, 172
(1977).
D.A.
Lindholm,
IEEE
Trans.
on Magn.,
vol.
MAG14
, p.
321,
(1978).
jXIWl!f
IhneorJ
1
power
lhneoor
I
(1)
(3)
(2)
(4 )
(5)
(8)
(6)
figure
2aPower
density
function
of
EFM,
one and
four
point
look
ahead
strategy
compared
with
3PM
and
M2,
fb
is
the
bitrate.
(7)
(9)
(10)
(11 )
(12)
ta~le
of
8
to
14
bits
and
vice
versa
is
possible.
The
l~bits
blocks
however
cannot
be
concatenated
.,': cnout,
violating
the
dconstraint
at
the
bounda
ries.
The
insertion
of
two
merging
bits
between
successive
blocks,
where
normally
no
transient
occurs,
1s
sufficient.
The two
merging
bits
do
not
conuai.n
any
information
and
are
skippped
by
the
decoder.
It
appears,
that
the
maximum
runlength
is
k=iO,
if
the
merging
bits
are
used
(with
preser
vi:,;
the
dc
ons
traint.)
to
insert
a
single
tran
sient
between
the
blocks
if
the
runlength
is
lar
~e~
than
10 by
concatenating
the
blocks.
So
the
~odulator
looks
one
8bitssymbol
ahead,
100,,5
u;:
its
14bits
channelrepresentation
and
dec~des
whether
a
transient
is
needed
in
the
dummy
01:
stc
preserve
the
kconstraint.
.
Tnere
are
cases
where
the
merging
bits
are
no,
~niquely
determined
by
the
concatenation
rule~
this
freedom
of
choice
is
used
for
minimizing
the
po~er
a:
low
frequencies
with
e.g.
the
DSV
(digital
sue
variation)
as
criterion.
The
DSV
is
defined
as
the
Lncegr'aL
of
the
modulation
stream
with
a
loci
cal
~ero
counted
as
minus
one.
Our
experiments
sh;wed
:hat
this
DCcontrol
is
not
sufficient,
so
we
increased
the
number
of
merging
bits
to
3,
which means
that
in
65%
of
all
mergings
an
extra
transient
can
be
set
or
omitted
freely.
This
more
effec(:',e
DCcontrol
costs
however
1/17
or
6%
orthe
inforJr.aLion
density.
Depending on
the
exact
stra
tegy
one may
minimize
the
power
at
low
frequencies.
In
fib'
2
alb
we
depicted
the
power
density
spec
t.run.
of
EFi'1
with
two
different
strategies.
Curve a
results
if
a one symbol
look
ahead
strategy
is
im
plemented
e.
i.
the
decision
of
placing
or
omitting
a
transient
(with
preserving
the
d
and k
con
str5.im.!
I
is
only
based
on
Ute
knowledge
of
one
future
symbol.
The
Jecision
is
based
on
the
minimization
of
the
DSV
afLer
(he
concatenation
of
the
new
block.
For
conpari.aon
we
plot
ted the
power
densi
ty
spec
trum
of
two
modulation
schemes known from
the
magnetic
recording
field
M2
and
3PM
(4,11,12).
Curve b
is
the
result
if
a more
sophisticated
DC
cQl1trol
is
applied
based
on
the
knowledge
of
4
futare
symbols.
We
note
that
a
net
10 dB
improve
ment
is
possible
in
the
frequency
rangecl O kHz.
Experiments
showed
that
no
significant
inter
ference
w:th
the
servo
systems
appeared
if
a one
symbDl
look
ahead
strategy
was
applied.
Conclusio:lS
A
ne~
digital
coding
format,
EFM,
has
been
described,
which
should
be
very
useful
in
digital
audio
disk
systems
with
optical
read
out.
Back
ground and
design
parameters
which
led
to
the
actual
choice
of
the
adopted
modulation
system
has
been
ell.:cidated.
The
choice
of
system
with
d=2, k=10 was based
on many
experiments
and
simulations,
that
showed a
superior
performance
over
other
choices.
Small
power
at
low
frequencies
is
an
important
parameter
that
could
be
attained
by
using
the
degree
of
freedom
in
the
merging
bits
that
conca
tenate
successive
blocks.
The
blockstructure
on
an
8data
bits
basis
makes
EFM
very
well
suited
for
the
adopted
ReedSolomon
error
correction
system.
589