Conference PaperPDF Available

Modulation systems for digital audio discs with optical readout

Authors:

Abstract

This paper is the first public disclosure of Eight to Fourteen Modulation (EFM) used in the Compact Disc.
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
anologue-digital
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
dk-limited
sequence
satisfies
simultaneously
the
following
conditions:
a.
d-constraint
- two
logical
ones
are
separated
b
a
run
of
consecutive
zeros
of
length
at
least
d
b.
k-constraint
- 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
d-constraint
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(n-l
J+N(n-d-l)
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.er-symbo.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 NRZ-code;
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
a-sequences
for
recording
we
are
sure,
that
the
transients
are
CJ.l1li10-'i/R1/nnnn.o5R71OO_7'i ©
19R1
IREF
dR(d+1) .R r2SER
.10"
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
"eye-opening"
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
d-limited
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
8-bitssymbol
is
encoded
intc
an n
bits
channelsymbol.
At
the
decoder
we map
the
n
bits
channelsymbol
again
into
an
8-bitssymbol
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
14-bits
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
er-ror-
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;.
Ccrr-espondfng
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
channel-bit
error
r~~~.
We
nOLi~~.
th~1
7
maximum
in
information
der-siLy
can
b~
sepa~ated
at
least
d,
g~v~ng
a
physical
distance
of
Id+11-time
units
of
the
recorder
clock.
However
the
~oss
of
rate,
due
to
the
redundancy
of
the
d-seQuence
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.
IT-ii,
p , 285
(1965).
D.T. Tang and L.R.
Bahl,
Inform.
Contr.
vol.
17,
p.
436,
1970.
P.D.
Shaft,
IEEE
Trans.
Comm.,
vol.
COM-16,
p,
687,
(1973).
G.V.
Jacoby,
IEEE
Trans.
Magn.,
vol.
MAG-13,
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.
COM-23,
no. 9, p. 878, 1975.
M.R. Aaron and D.W.
Tafts,
IEEE
Trans.
Inform.
Theory,
IT-12,
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.
MAG-14
, 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
d-constraint
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
d-c
ons
tr-aint.)
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
8-bitssymbol
ahead,
100,,5
u;:
its
14-bits
channelrepresentation
and
dec~des
whether
a
transient
is
needed
in
the
dummy
01:
stc
preserve
the
k-constraint.
.
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
DC-control
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
DC-control
costs
however
1/17
or
6%
or-the
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
conpar-i.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
r-ange-cl 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
8-data
bits
basis
makes
EFM
very
well
suited
for
the
adopted
Reed-Solomon
error
correction
system.
589
... Modern storage devices employ sequence estimation [7] rather than peak detection, but constrained codes are still used to improve performance [6], [8]. RLL codes also find application in optical recording [9]. When first introduced in [4], lexicographic indexing was used to encode and decode RLL codes, but this was replaced by methods based on finitestate machines (FSMs) in later work [10]. ...
... where the second equality in (9) is reached aided by (7) to compute N q,1 (m − x − 1, x). Now, the cardinality of QC q m,x is computed as follows using (7), (8), and (9): ...
... which is consistent with what we know. Furthermore, the corner case for Group 3 in QC q m,x is the case of 2 ≤ m ≤ x + 2. We know that the cardinality of Group 3 in this case is (9) in the proof of Theorem 1 and also (6): (11) which is consistent with what we know. Note that there is no corner case for Group 1. ...
Article
Full-text available
Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal processing that reduce the effect of physical instabilities. Constrained codes are used in storage to avoid problematic patterns, and thus prevent errors from happening. Recently, we introduced binary symmetric lexicographically-ordered constrained codes (LOCO codes) for data storage and data transmission. LOCO codes are capacity-achieving, simple, and can be easily reconfigured. This paper introduces simple constrained codes that support non-binary physical gates in multi, triple, quad, and the currently-in-development penta-level cell (M/T/Q/P-LC) Flash memories. The new codes can be easily modified if problematic patterns change with time. These codes are designed to mitigate inter-cell interference, which is a critical source of error in Flash devices. The occurrence of errors is a consequence of parasitic capacitances in and across floating-gate transistors, resulting in charge propagation from cells being programmed to the highest charge level to neighboring cells being programmed to lower levels or unprogrammed/erased. This asymmetric nature of error-prone patterns distinguishes Flash memories. The new codes are called q-ary asymmetric LOCO codes (QA-LOCO codes), and the construction subsumes codes previously designed for single-level cell (SLC) Flash devices (A-LOCO codes). QA-LOCO codes work for a Flash device with any number, q, of levels per cell. For q ≥ 4, we show that QA-LOCO codes can achieve rates greater than 0.95 log2 q input bits per coded symbol. The complexity of encoding and decoding is modest, and reconfiguring a code is as easy as reprogramming an adder. Capacity-achieving rates, affordable encoding-decoding complexity, and ease of reconfigurability support the growing improvement of M/T/Q/P-LC Flash memory devices, as well as lifecycle management as the characteristics of these devices change with time, which increases their lifetime.
... Modern storage devices employ sequence estimation [7] rather than peak detection, but constrained codes are still used to improve performance [6], [8]. RLL codes also find application in optical recording [9]. When first introduced in [4], lexicographic indexing was used to encode and decode RLL codes, but this was replaced by methods based on finitestate machines (FSMs) in later work [10]. ...
... where the second equality in (9) is reached aided by (7) to compute N q,1 (m − x − 1, x). Now, the cardinality of QC q m,x is computed as follows using (7), (8), and (9): ...
... which is consistent with what we know. Furthermore, the corner case for Group 3 in QC q m,x is the case of 2 ≤ m ≤ x + 2. We know that the cardinality of Group 3 in this case is (9) in the proof of Theorem 1 and also (6): (11) which is consistent with what we know. Note that there is no corner case for Group 1. ...
Preprint
Full-text available
Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal processing that reduce the effect of physical instabilities. Constrained codes are used in storage to avoid problematic patterns. Recently, we introduced binary symmetric lexicographically-ordered constrained codes (LOCO codes) for data storage and data transmission. This paper introduces simple constrained codes that support non-binary physical substrates; multi, triple, quad, and the currently-in-development penta-level cell (M/T/Q/P-LC) Flash memories. The new codes can be easily modified if problematic patterns change with time. These codes are designed to mitigate inter-cell interference, which is a critical source of error in Flash devices. The occurrence of errors is a consequence of parasitic capacitances in and across floating gate transistors, resulting in charge propagation from cells being programmed to the highest charge level to neighboring cells being programmed to lower levels. The new codes are called $q$-ary asymmetric LOCO codes (QA-LOCO codes), and the construction subsumes codes previously designed for single-level cell (SLC) Flash devices (A-LOCO codes). QA-LOCO codes work for a Flash device with any number, $q$, of levels per cell. For $q \geq 4$, we show that QA-LOCO codes can achieve rates greater than $0.95 \log_2 q$ information bits per coded symbol. The complexity of encoding and decoding is modest, and reconfiguring a code is as easy as reprogramming an adder. Capacity-achieving rates, affordable encoding-decoding complexity, and ease of reconfigurability support the growing development of M/T/Q/P-LC Flash memory devices, as well as lifecycle management as the characteristics of these devices change with time.
... Moreover, constrained codes improve the performance on low resolution media [7] by preventing short pulses. The requirement that the power spectrum of a line code vanishes at frequency zero, i.e., the code is direct-current-free (DC-free), is important in optical recording [8]. This requirement is typically accomplished by balancing signal signs in the stream of transmitted (written) codewords (for a frequency domain approach, see [9]). ...
... Observe that (8) in Remark 3 shows that LOCO codes are more efficient compared with LO-RLL codes in the finite-length regime. The reason is that from (8) and (3), the difference between the cardinalities of a LOCO code C m,x and a (d, ∞) LO-RLL code with d = x and length m is: ...
... There are also other applications for constrained codes in data storage and data transmission. In data storage, constrained codes find application in optical recording systems [29]. In data transmission, constrained codes are used to mitigate crosstalk between wires or through-silicon vias (TSVs) in integrated circuits [30]. ...
Article
Full-text available
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of solid-state storage devices, and in increasing the reliability of data transmission over wires. Over the years, designing practical (complexity-wise) capacity-achieving constrained codes has been an area of research gaining significant interest. We recently designed various constrained codes based on lexicographic indexing. We introduced binary symmetric lexicographically-ordered constrained (S-LOCO) codes, q-ary asymmetric LOCO (QA-LOCO) codes, and a class of two-dimensional LOCO (TD-LOCO) codes. These families of codes achieve capacity with simple encoding and decoding, and they are easy to reconfigure. We demonstrated that these codes can contribute to notable density and lifetime gains in magnetic recording (MR) and Flash systems, and they find application in other systems too. In this paper, we generalize our work on LOCO codes by presenting a systematic method that guides the code designer to build any constrained code based on lexicographic indexing once the finite set of data patterns to forbid is known. In particular, we connect the set of forbidden patterns directly to the cardinality of the LOCO code and most importantly to the rule that uncovers the index associated with a LOCO codeword. By doing that, we reveal the secret arithmetic of patterns, and make the design of such constrained codes significantly easier. We give examples illustrating the method via codes based on lexicographic indexing from the literature. We then design optimal (rate-wise) constrained codes for the new two-dimensional magnetic recording (TDMR) technology. Over a practical TDMR model, we show notable performance gains as a result of solely applying the new codes. Moreover, we show how near-optimal constrained codes for TDMR can be designed and used to further reduce complexity and error propagation. All the newly introduced LOCO codes are designed using the proposed general method, and they inherit all the desirable properties in our previously designed LOCO codes.
... They find application in the emerging two-dimensional (2D) magnetic recording devices as well [10], [11]. Moreover, constrained codes are used to achieve DC balance and self-calibration in optical recording devices [12] in addition to many computer standards for data transmission [13]. ...
Preprint
Full-text available
The pivotal storage density win achieved by solid-state devices over magnetic devices in 2015 is a result of multiple innovations in physics, architecture, and signal processing. One of the most important innovations in that regard is enabling the storage of more than one bit per cell in the Flash device, i.e., having more than two charge levels per cell. Constrained coding is used in Flash devices to increase reliability via mitigating inter-cell interference that stems from charge propagation among cells. Recently, capacity-achieving constrained codes were introduced to serve that purpose in modern Flash devices, which have more than two levels per cell. While these codes result in minimal redundancy via exploiting the underlying physics, they result in non-negligible complexity increase and access speed limitation since pages cannot be read separately. In this paper, we suggest new constrained coding schemes that have low-complexity and preserve the desirable high access speed in modern Flash devices. The idea is to eliminate error-prone patterns by coding data only on the left-most page while leaving data on all the remaining pages uncoded. Our coding schemes work for any number of levels per cell, offer systematic encoding and decoding, and are capacity-approaching. Since the proposed schemes enable the separation of pages, we refer to them as read-and-run (RR) constrained coding schemes as opposed to schemes adopting read-and-wait for other pages. We analyze the new RR coding schemes and discuss their impact on the probability of occurrence of different charge levels. We also demonstrate the performance improvement achieved via RR coding on a practical triple-level cell Flash device.
... Constrained codes preventing certain, error-prone TD patterns increase the reliability of TDMR devices [18]. Constrained codes find application in optical recording devices [19]. Constrained codes are also used in various data transmission systems, as they can mitigate cross-talk between wires over which the data is transmitted [20], and they can achieve DC-balance, i.e., zero average power at frequency zero [21]. ...
Article
Full-text available
In various practical systems, certain data patterns are prone to errors if written or transmitted. In magnetic recording and communication over transmission lines, data patterns causing consecutive transitions that are not sufficiently separated are prone to errors. In Flash memory with two levels per cell, data patterns causing high–low–high charge levels on adjacent cells are prone to errors. Constrained codes are used to eliminate error-prone patterns, and they can also achieve other goals. Recently, we introduced efficient binary symmetric lexicographically-ordered constrained (LOCO) codes and asymmetric LOCO (A-LOCO) codes to increase density in magnetic recording systems and lifetime in Flash systems by eliminating the relevant detrimental patterns. Due to their application, LOCO and A-LOCO codes are associated with level-based signaling. Studying the power spectrum of a random signal with certain properties is principal for any storage or transmission system. It reveals important properties such as the average signal power at DC, the bandwidth of the signal, and whether there are discrete power components at certain frequencies. In this paper, we first modify a framework from the literature in order to introduce a method to derive the power spectrum of a sequence of constrained data associated with level-based signaling. We apply our method to infinitely long sequences satisfying symmetric and asymmetric constraints. Next, we show how to generalize the method such that it works for a stream of finite-length codewords as well, thus demonstrating how to overcome the associated finite-length challenges. We use the generalized method to devise closed forms for the spectra of finite-length LOCO and A-LOCO codes from their transition diagrams. Our LOCO and A-LOCO spectral derivations can be performed for any code length and can be extended to other constrained codes. We plot these power spectra, and discuss various important spectral properties for both LOCO and A-LOCO codes. We also briefly discuss an alternative method for deriving the power spectrum and introduce an idea towards reaching the spectra of self-clocked codes.
... There are also other applications for constrained codes in data storage and data transmission. In data storage, constrained codes find application in optical recording systems [29]. In data transmission, constrained codes are used to mitigate crosstalk between wires or through-silicon vias (TSVs) in integrated circuits [30]. ...
Preprint
Full-text available
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage devices, and in increasing the reliability of data transmission over wires. We recently introduced families of lexicographically-ordered constrained (LOCO) codes. These codes achieve capacity with simple encoding and decoding, and they are easy to reconfigure. In this paper, we generalize our work on LOCO codes by presenting a systematic method that guides the code designer to build any constrained code based on lexicographic indexing once the finite set of data patterns to forbid is known. In particular, we connect the set of forbidden patterns directly to the cardinality of the code and to the rule that uncovers the index associated with a codeword. By doing that, we reveal the secret arithmetic of patterns, and make the code design significantly easier. We design optimal (rate-wise) constrained codes for the new two-dimensional magnetic recording (TDMR) technology. We show notable performance gains as a result of solely applying the new codes. Moreover, we show how near-optimal constrained codes be designed and used to further reduce complexity.
... Constrained codes preventing certain, error-prone TD patterns increase the reliability of TDMR devices [18]. Constrained codes find application in optical recording devices [19]. Constrained codes are also used in various data transmission systems, as they can mitigate cross-talk between wires over which the data is transmitted [20], and they can achieve DC-balance, i.e., zero average power at frequency zero [21]. ...
Preprint
Full-text available
Constrained codes are used to eliminate error-prone patterns in various practical systems. Recently, we introduced efficient binary symmetric lexicographically-ordered constrained (LOCO) codes and asymmetric LOCO (A-LOCO) codes to increase density in magnetic recording systems and lifetime in Flash systems by eliminating the relevant detrimental patterns. Due to their application, LOCO and A-LOCO codes are associated with level-based signaling. Studying the power spectrum of a random signal with certain properties is principal for any storage or transmission system. In this paper, we first modify a framework from the literature in order to introduce a method to derive the power spectrum of a sequence of constrained data associated with level-based signaling. We apply our method to infinitely long sequences satisfying symmetric and asymmetric constraints. Next, we show how to generalize the method such that it works for a stream of finite-length codewords. We use the generalized method to devise closed forms for the spectra of finite-length LOCO and A-LOCO codes from their transition diagrams. Our LOCO and A-LOCO spectral derivations can be performed for any code length and can be extended to other constrained codes. We plot these power spectra, and discuss various important spectral properties for both LOCO and A-LOCO codes.
... A channel coding is an essential technique to broadcast or record digital audio that maintains bit accuracy such as an Eight-to-fourteen modulation that used in the audio compact disc (Audio track CD) that has a sampling rate of 44.1 kHz. [6]. ...
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Does anybody know the extent to which conference papers are abstracted when they are published independently of a journal ? What about The Institute's Conference Series, the photovoltaic specialist conferences in the USA, and other series of conferences?
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This paper investigates some of the properties of a class of two-level codes with constrained run length, whose use has been proposed for purposes of bandwidth compression. It is shown that such codes can indeed reduce the bandwidth containing a given percentage of the transmitted power. To communicate information, however, different transmitted codewords must be distinguishable at the receiver, and this requires that the channel bandwidth be sufficiently wide to allow the difference waveform to propagate. It is demonstrated that decreasing the X -percent bandwidth using these codes leads to a rapid increase in the difference waveform bandwidth, and hence in the channel bandwidth necessary to maintain error rate performance. Thus, these codes are bandwidth expansion codes in disguise. Signal-to-noise ratio and channel bandwidth requirements for these codes are discussed and compared with those of M -level codes [pulse-amplitude modulation (PAM)] for two kinds of receivers.
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The familiar error-correction codes allow a reduction in the required signal-to-noise ratio at the expense of an increase in bandwidth. Here we reverse the problem and investigate codes that permit a reduced bandwidth at the expense of an increase in the required signal-to-noise ratio. Theoretical properties of these bandwidth compaction codes have been published previously. This paper emphasizes the tradeoff between bandwidth and signal-to-noise ratio when the codes are used. The inherent error detection and error correction properties of the codes are also explored.
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A special case with binary sequences was presented at the IEEE 1969 International Symposium on Information Theory in a paper titled “Run-Length-Limited Codes.
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In this paper different noise sources are investigated which may be important in an optical readout system for video disks. These noise sources can be divided into three categories: (1) noise due to the light source; (2) noise due to the storage medium; and (3) noise due to the electronics of the detecting system. The relative importance of the three noise terms is discussed for different light levels. Finally an experimental readout scheme is discussed, based upon an AlGaAs diode laser, and it is shown that this laser, like the He-Ne laser, is suitable for video disk reading.
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The optics of a video disk player are described. The bandwidth and the playing time of a disk had been specified at 12 MHz and 30 min, respectively. A readout photodetector signal of high quality can be obtained with a well-corrected objective having a numerical aperture of at least 0.4. Some alternative readout modes and track formats are indicated. Methods for the generation of error signals for the radial and the vertical tracking are briefly discussed.
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The power spectral density (PSD) is the average power per unit frequency of encoded random data transmitted over a perfect channel. The one-sided PSDs of a number of channel codes of recent interest in digital magnetic recording are calculated from codeword dictionaries and state diagrams. Given here are:
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This paper describes a novel run-length limited code, termed 3PM. A group of three data bits is converted into six code bits which are represented by the presence or absence of signal transitions. At least two zeros are maintained between two consecutive ones, that is a minimum distance of three positions between transitions, resulting in great reduction of pulse crowding. The minimum distance is assured by a unique merging rule at the boundary of adjacent code words. This rule distinguishes the code from both fixed and variable length codes and results in very simple encoding and decoding algorithms. An actual 50% density increase has been accomplished in saturation recording by using the 3PM code in combination with other electronic techniques. The new code is used in a current ISS/Univac high density disk storage system, featuring 2500 bits/cm (6300 BPI) linear density, 10 Mbits/sec data rate, 338 MByte capacity and one bit in 10 billion raw error rate on conventional Mod-11 head/disk interface.
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Using a criterion of minimum average error probability we derive a method for specifying an optimum linear, time invariant receiving filter for a digital data transmission system. The transmitted data are binary and coded into pulses of shape pm s(t) . The linear transmission medium introduces intersymbol interference and additive Gaussian noise. Because the intersymbol interference is not Gaussian and can be correlated with the binary digit being detected, our problem is one of deciding which of two waveforms is present in a special type of correlated, non-Gaussian noise. For signal-to-noise ratios in a range of practical interest, the optimum filter is found to be representable as a matched filter followed by a tapped delay line--the same form as that of the least mean square estimator of the pulse amplitude. The performance (error probability vs. S/N ) of the optimum filter is compared with that of a matched-filter receiver in an example.