Extremely Efficient Dc-free RLL codes for Optical Recording

Abstract

We report on new DC-free runlength-limited codes (DCRLL) intended
for the next generation of DVD. The efficiency of the newly developed
DCRLL schemes is extremely close to the theoretical maximum, and as a
result, significant density gains can be obtained with respect to prior
art coding schemes

Full text

910
IEEE
Transactions
on
Consumer Electronics,
Vol.
47,
No.
4,
NOVEMBER
2001
EXTREMELY
EFFICIENT DC-FREE RLL CODES FOR OPTICAL RECORDING
Kees A. Schouhamer Immink, Jin-Yong Kim, Sang-Woon Suh and Seong Keun Ahn
AESTRACT
We will report on new dc-free runlength-limited codes
(DCRLL) intended for the next generation
of
DVD. The
efficiency of the newly developed DCRLL schemes is ex-
tremely close to the theoretical maximum, and as a result,
significant density gains can be obtained with respect to
prior art coding schemes.
Keywords: optical recording, capacity, constrained code,
runlength-limited, RLL sequence,
(d,
k)
sequence, dc-free
code
I. INTRODUCTION
Optical recording, developed in the late 60s and early
70s, is the enabling technology of a series of very success-
ful products for digital consumer electronics systems such
as Compact Disc (CD), CD-ROM, CD-R, DVD, and many
other products that are still in the offing. Notably spec-
tral shaping (dc-free) and runlength-limited (RLL) codes
have found widespread usage in consumer-type mass stor-
age systems such as Compact Disc, DAT, DVD, and
so
on
[l].
The design of codes for optical recording is essen-
tially the design of combined
dc-free
and
runlength limited
(DCRLL) codes. Eight to Fourteen Modulation (EFM) de-
veloped by Immink
&
Ogawa
in
the early eighties [2] was
adopted as the recording code for the Compact Disc
(CD).
EFMPlus [3]; used in the DVD, is a code wit,h the same
basic parameters as
EFM
and a useful six percent higher
efficiency. Table
I
gives a survey of recording codes, which
are part of consumer-type optical recording products.
TABLE
I
Survey
of
recording codes and their application area
Device Code Type d,k Ref.
CD EFM DCRLL
1,lO
[2]
MiniDisc EFM DCRLL
1,lO
DVD EFMPlus DCRLL
1,10
[3]
DVR (1,7)PP DCRLL 1,7 [4]
Kees
A.
Schouhamer Immink is with Turing Machines Inc,
15
W. Alexanderlaan, 5664
AN
Geldrop, The Netherlands. E-mail:
immink@turing-machines.com.
Jin-Yong
Kim,
Sa,ig-Woon Suh,
Seong Keun Ahn are with DCT Team, Multi-Media Labs, LG Elec-
tronics Inc., 16 Woomyeon-Dong, Seocho-Gu, Seoul 137-724, Korea
11. RUNLENGTH-LIMITED CODES
Binary sequences generated by
a
(d,
k)
RLL encoder have
at least
d
and
at
most
k
’zero’s between successive ’one’s.
Let the integers
m
and
n,
denote the information word
length and codeword length, respectively. The
code rate,
R
=
m/n,
is
a measure
of
the code’s efficiency. The maxi-
mum rate
of
an RLL code, given values of
d
and
k,
is called
the
Shannon capacity,
and
it
is denoted by
C(d,
k).
As
an
TABLE I1
Capacity
C(1,
k)
and
C(2,
k)
as
a
function of
k.
k
C(1,k) C(2,k)
7
0.6793 0.5174
8 0.6853 0.5293
9 0.6888 0.5369
10
0.6909 0.5418
11
0.6922 0.5450
cc
0.6942 0.5515
example, Table
I1
tabulates
C(d
=
1,k) and
C(d
=
2,k)
for relevant values of
k.
We may observe, for example, that
for
d
=
1
and
k
=
7 the Shannon capacity, C(117), has a
value of 0.6793. Thus, an encoder that translates arbitrary
sequences
into
sequences
that have
at
least
d
=
1
and at
most
IC
=
7
0’s
between successive
l’s,
cannot have
a
rate
larger than 0.6793.
Information recording has a constant need for enhancing
the information density on the record carrier, and a possible
solution to this end is an increase of the rate of the code.
111.
VERY
EFFICIENT
CODING
SCHEMES
For
ease of presentation we will first focus on the design
of RLL codes with
d
=
1. Later we will extend the ideas
to the design of codes with
d
=
2.
Rate 213, (1,7) codes are known in the art for more than
a quarter of a century, see for example [5, 61. The code
rate, 213, of the (1,7) code is slightly less than the Shannon
capacity,
0.6793,
and the code is therefore
a
highly efficient
one. The efficiency of an RLL code
is
usually measured by
a quantity called
code eficiency,
77,
defined by
There are only two approaches for constructing
a
(1,k)
RLL code, whose rate is larger than two-thirds. Firstly, we
may relax the maximum runlength
k
to
a
value larger than
7.
Note that a (1,7) code was first put to practical use in
Original manuscript received June
25,
2001
Revised manuscript received September 26, 2001
0098
3063/00
$10.00
@
2001 IEEE

Immink: Extremely
Efficient Dc-free RLL codes
for
Optical
Recording
91
1
the early seventies, and that since the advent of hard-disk
drives
(HDDs),
significant improvements in signd process-
ing for timing recovery circuits have made it possible to
employ codes with a much larger maximum runlength
IC.
Secondly, on top of that we may endeavor to design a more
efficient code.
The efficiency of the rate
2/3, (1,7)
code
is
0.6667/0.6793
=
0.981,
which reveals that we can
at
most gain
1.9%
in
rate by an alternative, more efficient, code redesign.
If
we
fully relax the
k
constraint, i.e. set
k
=
00,
we can at most
gain
3.97%
in code rate. In other words, a viable improve-
ment in code rate of
a
(d
=
1)
encoder ranges from
1.9
to
3.97%.
To the best of the author's knowledge, extremely
efficient
(d
=
1)
codes having
a
rate exceeding two-thirds
have not been reported in the literature. In the sequel of
the paper, we will systematically design such extremely effi-
cient codes. We start, in the next subsection, with
a
simple
problem, namely finding integers
m
and
n
that improve the
rate,
213,
of
the industry standard code.
A.
Suitable integers
m
and
n
for
d
=
1
We will start with
a
simple, but very illuminating exer-
cise, namely
a
search for pairs of integers
m
and
n
that
are suitable candidates for a coding rate exceeding
213.
All pairs of integers
2/3
<
m/n
<
C(l,co),
n
<
50,
are
shown in Table
111.
Surprisingly there are just six
m
and
n
pairs whose quotient is larger than
213.
We omitted trivial
pairs, such as
18
and
26
etc., that are multiples
of
given
smaller pairs. Perusal of the table reveals that the code
rate
m/n
=
9/13
is
highly attractive as it is just
0.28%
below the Shannon capacity
C(1,co).
The fact that the
quotient
9/13
is
less
than
capacity
does
not
mean that
a
code with that, rate can be
practically
constructed.
TABLE
111
Integers
m
and
n
such that 2/3
<
R
=
m/n
<
C(1,oa).
The
quantity
11
=
R/C(l,
a)
expresses the code efficiency.
m
n
1-q%
34 49 0.0525
9
13
0.2786
11 16 0.9711
13 19 1.4449
15 22 1.7895
17 25 2.0514
B.
Encoder description
We start with
a
few ubiquitous definitions. The encoder
has
r
states, which are divided into two state subsets of a
first and second type. The state subsets are
of
size
1-1
and
TZ(=
r
-
rl),
respectively.
A
codeword is
a
binary string of
length
n
that satisfies the
d
=
1
constraint. The encoder
state-transition rules are easily described. Codewords that
end with a
'O',
i.e., codewords in subsets
Eo0
and
El0
may
enter any of the
r
encoder states. Codewords that end with
a
'1'
may be followed by codewords in the
r1
states of the
first type only. With the above model we were able to con-
struct many new codes including
a
rate
9/13, (1,14)
code.
Clearly this new code improves the rate of the traditional
rate
2/3, (1,7)
code by
a
factor
of
27/26
(=
1.038)
without
seriously compromising the timing regeneration.
IV.
EFFICIENT
d
=
2
CODES
Up till now we have concentrated on the design of effi-
cient
d
=
1
codes, and as both code parameters,
d
=
1
and
d
=
2,
are of great practical interest for optical recording,
we will now repeat the exercise for the case
d
=
2.
A.
Suitable integers
m
and
n
ford
=
2
RLL
codes with minimum runlength parameter
d
=
2
have been widely published. The highest reported rate of
such a
(d
=
2)
code is
8/15l.
Table I1 tabulates
C(2,
IC)
as
a function of
k,
and from this table the reader can easily
discern the head room available for the design of a code of
rate
R
=
m/n
>
8/15.
The rate
8/15
is, see Table
11,
3.3%
below channel capacity
C(2,
00).
Table IV shows values of
m
and
n,
where
8/15
5
m/n
<
C(2,co)
and
n
<
50.
The
pairs of integers are ordered according to their efficiency
R/C(2,co).
Clearly, the quotients
11/20, 6/11,
and
7/13
TABLE
IV
Integers
m
and
n
such that 8/15
<
R
=
m/n
<
C(2,
w).
The
quantity
r)
=
R/C(2,
oa)
expresses the code efficiency.
m
n
1-~%
11 20 0.2720
17
6
19
13
20
7
15
8
31
11
35
24
37
13
28
15
-
0.5644
1.0962
1.5672
1.7830
1.9872
2.3642
2.8623
3.2940
are suitable candidate rates for the creation
of
small
(d
=
2)
codes.
B.
Encoder descraption
In this section we will describe
a
finite-state encoder that
generates sequences that satisfy the
d
=
2
constraint (note
that the
k
constraint will be ignored for
a
while). The
encoder is assumed to have
T
states, which are divided into
three state subsets
of
states
of
a
first, second, and third
type. The state subsets are
of
size
TI,
TZ,
and
r3(=
'r
-
r1
-
TZ),
respectively. Codewords that end with the string
'00'
may enter any of the
r
encoder states. Codewords
that end with a
'10'
may not be followed by codewords in
a state of the third type. Similarly, codewords that end
with a
'1'
may only be followed by codewords belonging
to states of the first type. Table V summarizes the new
'At press time, the author became aware that Kim
(71
has been
granted a
US.
Patent
on
an example
of
a rate 7/13, (2,25) code.

912
IEEE Transactions on Consumer Electronics,
Vol.
47,
No.
4,
NOVEMBER
2001
-15
-20
RLL codes,
d
=
1
and
d
=
2, we have found.
As
we can
see, the efficiency of the majority of the new codes is just
a few tenths of a percent below capacity.
At
this junction,
TABLE
V
Survey
of
newly developed codes.
-
~
m
n
d
k
states
11
=
R/C(d,k)
11
20
2
23 9 0.9975
7
13
2
11
9 0.9880
6
11
2
15 9 0.9915
9 13
1
14 13 0.9979
9
13
1
18
5
0.9973
11
16
1
10 13 0.9951
we have completed the description of the new RLL codes,
and we are in the position to describe how we can turn the
newly developed RLL codes into DCRLL codes.
V.
GUIDED
SCRAMBLING
There are various methods to transform an RLL code
into a DCRLL code [l] by adding redundant dc-control bits,
which are chosen by the encoder to optimize the spectral
performance of the generated sequence. Obviously, we can
multiplex, either at data
or
channel level, the data stream
with the dc-control bits. Alternatively,
a
promising method
for adapting an RLL code is
Guided Scrambling (GS)
[l].
In
GS,
each information word can be represented by a member
of
a
selection set consisting of
L
=
2P,
p
2
1,
codewords.
The encoder generates the selection set, and the "best"
(according to
a
predefined penalty function) codeword in
the selection set is selected
for
transmission. The RLL
codes, listed in Table
V,
will be employed in conjunction
with
GS
for achieving four goals:
spectral shaping;
rejection of long runs of
'0's:
k
constraint;
rejection of long transition runs of '01's
(d=l)
or
'001's
(d=2):
MTR
constraint;
rejection of predefined sync(hronization) patterns, sync
constraint.
The maximum runlength constraint,
IC,
imposed by the
GS
penalty function can be made smaller than that of the in-
ner RLL code.
It
has been found that constraining a long
repetition of minimum transition runs (MTR constraint),
'1010101
...'
(d=l)
or
'1001001001
...'
(d=2),
in conjunction
with Partial-Response (PR) detection is beneficial to the
system margins. Naturally, the
GS
method cannot fully
guarantee the
k
and MTR constraints, but, the probability
of
occurrence of such vexatious subsequences can be made
extremely small.
A.
Format
In the
GS
format, ml user bits are multiplexed with
p
redundant bits, which are
a
part of the input of the chan-
nel encoder. The
p
redundant bits are used to generate a
selection set of size
L
=
2p. Each member of the selection
set is generated and tested by the encoder with respect to
the penalty function. In the proposed coding format, the
channel encoder input comprises
p
redundant bits plus ml
user bits that from a
super
block. The integers
p
and
ml
are integers chosen such that
Km
=
p
+
ml,
(2)
where
K
is an integer that denotes the number of m-bit
information words in a super block. In a practical environ-
ment of a byte-oriented system, ml
is
preferably
a
multiple
of eight, i.e. ml mod 8
=
0.
Under the rules of the RLL
code, the
p
+
ml
=
Km-bit super block is translated into
Kn
channel bits. Thus, the overall rate,
R,,
of
the code is
B.
Results and comparison with prior art methods
The Power Spectral Density (PSD),
H(f),
and other rel-
evant characteristics can easily be measured using com-
puter simulation. As
a
typical example, we will show re-
sults obtained with the rate 9/13, (1,14) RLL code. Fig-
ure
1
shows the spectrum,
H(f),
versus (channel) fre-
quency,
f,
for
p
=
5,
k
=
10,
and
K
=
45. The overall
coderateis
R,
=
(Km-p)/Kn=
(45x9-5)/(45~13)=
0.68376. Note that the overall code is byte oriented as
Km
-
p
=
400 is
a
multiple of eight. In the runlength
51,
I
0.001
0.01
0.1
-25[
' ' '
0.0001
channel
frequency
1
Fig.
1.
Simulation results
of
a
PSD
function
of
a
(d
=
l,k
=
10)
code
of
overall rate
R,
=
0.68376.
The
straight
line
is
a 'best fit'
estimate
of
the low-frequency part
of
the spectrum.
We
simply
discern that
H(f
=
=
-24.3
dB
penalty function, we set the maximum 'zero' runlength to
k
=
10, which means that the code essentially behaves as
a
(d
=
1,
k
=
10) code. The spectrum,
H(f),
versus fre-
quency
f
has a parabolic shape in the low-frequency range,
which shows as a straight line as
a
result of the logarithmic
frequency axis used. We can employ the spectral density
at a, given, low frequency
as
the low-frequency (If) spec-
tral performance yard stick of a DCRLL code. Results are
shown in Figure
2
for
p
=
5 and
p
=
8.
In order to compare
our
results with the maximum theoret,ical performance of
DCRLL codes, we invoked the algorithms found in
[l,
pages
282-2861 which compute the
maxentropic
performance of

Immink: Extremely Efficient Dc-free
RLL
codes
for
Optical
Recording
913
.451
"
"
"
"
'
I
0
64
0
645
0.65
0.655
0.66
0
665
0.67
0.675
0
68
0.685
0.69
Fig. 2. The two upper curves show the If suppression, H(10-4), as
a
function
of
the overall code rate
R,.
The upper curve shows
results
for
p
=
5,
and the lower curve
for
p
=
8. The maximum
imposed runlength
for
both cases is
IC
=
10.
The curve denoted
by (1,7)PP gives results
of
a prior art code [SI.
(d,
k)
codes. The maxentropic performance sets
a
theoret-
ical limit to the performance of any implemented DCRLL
code. Figure 2 shows that the implemented codes operate
very close to the best theoretical performance.
For
p
=
5
the implemented codes are 2-3 dB, (for
p
=
8,
1-2 dB)
below the theoretical ceiling.
As
a further comparison we
plotted the performance of
a
prior art rate 2/3, (1,7) code
[4],
which is extended with dc-control bits on data sequence
level.
Figure
3
shows the
If
spectral performance
of
the rate
6/11, (2,15) code
in
conjunction with Guided Scrambling.
Results are given for
p
=
5
and
p
=
8.
As
reported in the
above
d
=
1
case, the combination of an efficient RLL code
and
GS
works quite satisfactorily as only 2-3 dB can be
gained with respect to the theoretical ceiling.
-10
1
l
0
525
0
53
0
535
0
54
o
545
-40
I
0
52
Overall
code
iale
Fig.
3. The two upper curves show the
If
suppression,
H(10-4),
as
a
function
of
the overall rate
R,.
The upper curve
is
for
p
=
5,
and
the lower curve is for
p
=
8.
The maximum imposed runlength for
both cases is
k
=
12.
As a comparison we plotted the theoretical
ceiling,
io-^),
of
maxentropic
(d
=
2,k
=
12) sequences.
VI.
CONCLUSIONS
We have studied the construction of extremely efficient
Iunlength-limited (RLL) codes. We have shown that there
is
a
very limited number of pairs of integers
m
and
n,
whose
quotient
m/n8
form
a
suitable coding rate for
(d
=
1)
and
(d
=
2) RLL codes that are more efficient than prior art
codes. Suitable values for the rate of
a
(d
=
1) code
are
9/13 and 11/16, while for
(d
=
2) codes we have 11/20,
7/13, and 6/11.
We have disclosed a novel technique for designing very
efficient RLL codes. Using the novel technique we con-
structed a series of new RLL codes, whose rate
i~
only a few
tenths below capacity.
For
example, we have found
a
13-
state rate 9/13,
(1,14)
RLL code, whose rate
is
only 0.2%
below channel capacity C(1,14).
In
addition, we have con-
structed a new rate 6/11, (2,15) code,
a
rate 11/20, (2,23)
code, and a rate 7/13, (2,ll) code.
The above, and other, RLL codes can be employed in
conjunction with Guided Scrambling
(GS)
,
or
other tech-
niques, to turn them into DC-free
RLL
codes, which sup-
press the low frequency (If) components. Under the rules
of the
GS
algorithm, a selection set of alternative candi-
date codewords
is
generated, and the candidate with the
least
If
spectral content
(or
other desirable attributes) is
transmitted. Results of computer simulations have shown
that the arrangement of the newly developed RLL codes
in conjunction with GS is extremely efficient in terms of
overall rate and spectral performance. With the newly de-
veloped rate 9/13,
d
=
l
code
as
an inner code, we have
achieved
a
4.5% better overall rate than possible with the
prior art (1,7)PP code, and with the newly developed rate
6/11,
d
=
2 code we have achieved
a
9.3% higher overall
rate than that of EFMPlus.
The new DCRLL codes perform quite well in absolute
terms as we have shown that only a few dB in spectral
performance can be gained with respect to the theoretical
ceiling.
REFERENCES
K.A.S. Immink,
Codes
for
Mass Data Storage
Systems,
ISBN
90-
74249-23-X, Shannon Foundation Publishers, Netherlands, 1999.
K.A.S. Immink and
H.
Ogawa, 'Method
for
Encoding Binary
Data',
US
Patent 4,501,000,
Feb.
1985.
K.A.S. Immink, 'EFMPlus: The Coding Format
of
the MultiMe-
dia Compact Disc',
IEEE
Trans. Consumer Electr.,
vol. CE-41,
pp. 491-497, Aug. .1995.
K.A.S.
Immink,
J.A.H.
Kahlman,
G.
van den Enden, T. Naka-
gawa,
Y.
Shinpuku,
T.
Narahara, and
K.
Nakamura, 'Apparatus
and method
for
modulation/demodulation with consecutive min-
imum runlength limitation', Patent Application WO 9963671A1,
Issued
Dec.
1999.
P.A. Franaszek, 'On Future-dependent Block Coding
for
Input-
restricted Channels',
IBM
J.
Res. Develop.,
vol. 23, pp. 75-81,
1979.
G.V.
Jacoby and R.
Kost,
'Binary Two-thirds Rate
Code
with
Full
Word Look-Ahead',
IEEE
Trans.
Magn.,
vol. MAG-20, no.
5,
pp. 709-714, Sept. 1984.
M.J. Kim, '7/13 Channel Coding and Decoding Method Using
RLL(2,25) code',
US
Patent 6,188,336, Feb. 2001.
K.A.S.
Immink, 'EFM coding: Squeezing the last bits',
IEEE
Trans. Consumer Electronics,
vol. CE-43, pp. 491-495,
Aug.
1997.

914
IEEE
Transactions
on
Consumer Electronics, Vol.
47,
No.
4,
NOVEMBER
2001
BIOGRAPHY
Kees A. Schouhamer Immink,
obtained
M.S.
and Ph.D degrees
at
the Eindhoven Univer-
sity
of
Technology. He is founder and president of
Turing Machines Inc. Since 1995, he is an adjunct
professor at the Institute for Experimental Math-
ematics, Essen University, Germany In addition,
he
is
affiliated with the National University of
Sin-
gapore.
He has contributed to the design and development
of
a wide variety
of
consumer-type audio and video recorders such
as the Laservision video disc, Compact Disc, Compact Disc Video,
DAT, DV, DCC, and DVD. He holds 52 issued and pending
US
patents in various fields.
Dr
Immink is an elected member
of
the Royal Netherlands Academy
of
Arts and Sciences (KNAW) and holds fellowships of the IEEE,
AES, SMPTE, and
IEE.
For his contributions to the digital audio
and video revolution, he received wide recognition such
as
a Knight-
hood from
Beatrix,
Queen
of
the Netherlands, the 1999 IEEE Edison
Medal, AES Gold Medal, IEEE Masaru Ibuka Consumer Electronics
Award, and the Golden Jubilee Award
for
Technological Innovation
awarded by the IEEE Information Theory Society in 1998.
He is vice president
of
the Audio Engineering Society
(AES)
and a
governor
of
the IEEE Consumer Electronics Society, and a member
of
the
IEEE
Fellows Committee.
Jin-Yong Kim
received his
B.S.
degree in elec-
nic engineering from Seoul National University
his
M.S.
degree in electrical engineering
IST
in 1985, and Ph.D degree in electri-
eering from Iowa State University in 1992
ely. Dr. Kim is currently employed
as
a
Fellow
at Digital Media Research Labo-
G Electronics, Seoul Korea.
Sang-Woon
Suh
was born in
Seoul,
Korea,
on May
20,
1964. He received the
B.S.
degree
in electronics engineering fIom Seogang Univeristy,
Seoul, Korea, in 1987, and the
M.S.
degree in In-
formation and Communication engineering form
Korea Advances Institute
of
Science and Technol-
ogy(KAIST), Korea, in
1997.
From 1987
-
1990,
he was with Samsung Electronics Korea
as
a En-
gineer. From
1990
-
present, he was with
LG
Electronic Inc
,
Korea
as
a
senior
Research
Engi-
neer.
His current research interests included Op-
tical Data Storage, modulation code
for
optical discs and physical
format
for
optical discs.
Seong-Keun Ahn
rereived the
B.S.
and M.S.
ree
in school
of
electrical engineering from
ul National University,Seoirl,Korea
in
1996 and
8,respectively. Mr. Ahn is currently a research
ineer
at.
Digital Media Laboratory,I,G Electron-