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Abstract and Figures

Codes were designed for optical disk recording system and future options were explored. The designed code was a combination of dc-free and runlength limited (DCRLL) codes. The design increased minimum feature size for replication and sufficient rejection of low-frequency components enabling a simple noise free tracking. Error-burst correcting Reed-Solomon codes were suggested for the resolution of read error. The features of DCRLL and runlength limited (RLL) sequences was presented and practical codes were devised to satisfy the given channel constraints. The mechanism of RLL codes supressed the components of the genarated sequences. The construction and performance of alternative Eight to fourteen modulation (EFM)-like codes was studied.
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A Survey of Codes for Optical Disk Recording
Kees A. Schouhamer Immink, Fellow, IEEE
Abstract—We report on 20 years of development of codes for
optical disk recording systems. A description of the state-of-the-art
and feasible options for future extensions and improvements are
Index Terms—Constrained code, dc-free code, EFM, optical
recording, runlength-limited code.
OPTICAL recording, developed in the late 1960s and early
1970s, is the enabling technology of a series of very suc-
cessful products for digital mass data storage systems such as
compact disk (CD), CD-ROM, CD-R, DVD, and many other
products that are still in the offing. Eight to fourteen modu-
lation (EFM) developed by Immink and Ogawa in the early
1980s [1] was adopted as the recording code for the CD. Al-
most 15 years later, the DVD, the successor of the CD, was
developed. The DVD uses EFMPlus [2], a code with the same
basic parameters as EFM but a slightly (6%) higher rate. No-
tably, spectral shaping and runlength-limited (RLL) codes have
found widespread usage in consumer-type mass storage sys-
tems such as CD, DAT, DVD, and so on [3]. The design of
codes for optical recording is essentially the design of combined
dc-free and runlength-limited (DCRLL) codes. Table I gives a
survey of recording codes currently in use by consumer-type
optical recording products. An RLL code is very useful in op-
tical recording, where replicas are made for mass distribution.
The replication of disks with very small pits and lands turns out
to be very difficult, leading to unacceptably high bit error rates.
The minimum pit size of RLL sequences is larger than those of
uncoded counterparts so that a higher density can be obtained
without sacrificing the reliability. A dc-free code makes it pos-
sible to use simple servo systems that extract tracking informa-
ations. Two design considerations include increased minimum
feature size for replication and sufficient rejection of low-fre-
quency components to enable a simple noise-free tracking. As
the reading of disks is virtually noiseless, other properties, such
as, for example, robustness against additive noise play a minor
role. Read errors are mostly caused by imperfections of the
disk and can be resolved by sophisticated error-burst correcting
Reed–Solomon codes [7].
We start, in the next sections, with an outline of the properties
of DCRLL sequences. Thereafter, it will be shownhow practical
will be shown, among others, that industry-standard RLL codes
can be supplemented by a simple mechanism with which the
Manuscript received June 20, 2000; revised August 1, 2000.
The author is with the Institute for Experimental Mathematics, 45326 Essen,
Germany (e-mail:
Publisher Item Identifier S 0733-8716(01)01767-X.
Device Code Type Ref.
Compact Disc EFM RLL, dc-free [4]
MiniDisc EFM RLL, dc-free [5]
DVD EFMPlus RLL, dc-free [2]
DVR (1,7)PP RLL, dc-free [6]
lf-components of the generated sequences can be suppressed. In
the remaining part of this article, we will study the construction
and performance of alternative EFM-like codes.
We start in the next section, with the definition of RLL
sequences, and the computation of a number of basic properties
of such sequences.
A RLL sequence is a string of symbols of ones and
zeros with at least and at most zeros between consecutive
ones. Channel codes are needed to translate arbitrary data into
sequences. In general, a sequence is not employed
in optical or magnetic recording without a simple coding step.
Asequence is converted to an RLL channel sequence in
the following way. Let the channel signals be represented by
a bipolar sequence . The channel signals
represent the positive or negative magnetization of the recording
medium, or pits or lands when dealing with optical recording.
The logical ones in the sequence indicate the positions of
a transition or of the corresponding RLL
sequence. The sequence
would be converted to the RLL channel sequence
The mapping of the waveform by this coding step is known as
precoding. It can readily be verified that the minimum and max-
imum distance between consecutive transitions of the RLL se-
quence derived from a sequence is and symbols,
respectively; or, in other words, the RLL sequence has the virtue
that at least and at most consecutive-like symbols
(runs) occur.
An encoder translates arbitrary user (or source) information
into, in this particular instance, a sequence that satisfies given
constraints. On the average, source symbols are trans-
lated into channel symbols. What is the maximum value of
that can be attained for some specified values of the
minimum and maximum runlength and ? Using the basic
techniques developed by Shannon presented, for example, in
0733–8716/01$10.00 © 2001 IEEE
Fig. 1. RDS versus time. Input symbols are translated into the write signal
and the channel bits . In this example, the RDS assumes at most seven values.
[3, Ch. 2], it is fairly straightforward to compute the maximum
value of , called capacity, of encoders that generate sequences
with a constraint on the minimum and maximum runlength. The
capacity of RLL sequences is [3, Ch. 4]
where is the largest real root of the characteristic equation
RLL sequences used in optical disk recording systems should
satisfy the additional requirement that the low-frequency com-
ponents are sufficiently small. Sequences with such a property
are usually called dc-free sequences. The running digital sum of
a sequence, in short, RDS, plays a significant role in the analysis
and synthesis of codes whose spectrum vanishes at the low-fre-
quency end. Let
be a binary sequence. The (running) digital sum is defined as
Fig. 1 portrays the various signals. Chien [8] studied bipolar se-
quences , that assume a finite number of sum
values; that is, at any instant , the RDS of such a sequence
meets the condition
where and are two (finite) constants, . Se-
quences that have a bound to the number of assumedsum values
are termed (-constrained) or RDS-constrained sequences. The
total number of sum values a sequence assumes, denoted by
is often called the digital sum variation (DSV). Pierobon [9]
showed that the power density function of an encoded sequence
vanishes at zero frequency if, and only if, the encoder is
a finite RDS encoder. The capacity of “pure”
dc-free sequences; i.e., sequences that assume a maximum of
sum values were derived by Chien [8]
The capacity of dc-free RLL sequences has been computed by
Norris and Bloomberg [10].
The capacity of an RLL sequence with a bounded RDS is
characterized by three parameters and and it will be
denoted by . We will not follow the derivation given
by Norris and Bloomberg, but will offer an alternative approach
in the next section that will make it possible to efficiently com-
pute the power density function of DCRLL sequences as well.
A. Capacity and Spectral Properties of DCRLL Sequences
Kerpez [11] presented a description of the combined
and constraint in terms of a variable length graph and its
adjacency matrix that requires a relatively small number,
, of states.
Let the DCRLL message be denoted by
. The RLL message is assumed to be
composed of runlengths of lengths taken from
the set of allowed runlengths . As the
sequence has limited DSV, we have
where . The above constraint can be described
in terms of the runlengths. The sequence is composed of a
cascade of runlengths whose symbols have alternate polarity.
Transitionsofthepolarityofthesequence ,i.e.,instantswhere
, occur therefore at . We simply find
where the sequence , . In other words,
the DSV constraint is equivalent to
for all
Thus, a sequence satisfies the constraint if
and only if the sequence of runlengths satisfies, for all
The general form of the adjacency matrix for the
constraint, derived from (6) and (7), has a regular struc-
ture. The matrix has size and is
constant on the anti-diagonals. If the value of is nontrivial, i.e.,
, the lower right of the diagonal of the matrix is
zero, whereas in the case of , the lower right corner
is filled. Using the above adjacency matrix it is now straight-
forward to compute the capacity and the spectrum of the max-
entropic sequence for large values of and . A maxentropic
0 1 .6358 .6551 .6662 .6731 .6778
0 2 .7664 .8032 .8244 .8378 .8468
0 3 .7925 .8416 .8704 .8887 .9012
0 4 .8495 .8832 .9048 .9196
0 5 .8858 .9094 .9256
0 6 .9103 .9273
0 7 .9276
1 2 .3471 .3705 .3822 .3889 .3931
1 3 .4248 .4746 .5000 .5145 .5237
1 4 .5018 .5390 .5608 .5746
1 5 .5497 .5772 .5947
1 6 .5816 .6020
1 7 .6039
2 3 .2028 .2457 .2625 .2709 .2757
2 4 .3089 .3471 .3666 .3777
2 5 .3723 .4024 .4199
2 6 .4135 .4366
2 7 .4418
3 4 .1568 .1903 .2035 .2101
3 5 .2434 .2744 .2902
3 6 .2972 .3224
3 7 .3333
Fig. 2. Power spectral density function of a maxentropic dc-balanced, RLL
sequence. DSV , and runlength parameters and .
sequence is assumed to be generated by a Markov source whose
transition matrix is chosen such that the entropy of that source
equals capacity. Spectral and other properties of maxentropic
sequences are assumed to be a sound predictions of sequences
generated by efficient encoders. Table II shows the results of
computations for various values of DSV and runlength param-
eter The following examples may serve to illustrate the theory.
Fig. 2 shows the power spectral density function of maxentropic
sequences with , and the maximum runlength
as a parameter. Apparently, the influence of the maximum
runlength parameter is drastic. Most noticeable is the fact that
the curves become more peaked with decreasing maximum run-
lengthparameter .Fig.3showsthespectrumfortheparameters
Fig. 3. Power spectral density function of a maxentropic dc-balanced RLL
sequence (logarithmic axes). Runlength parameters and with
as a parameter. By way of example, the cutoff frequency is shown for ,
, and .
, and , and with a log-
arithmic frequency-axis and a vertical (dB) axis, where a
decibel is defined by . The choice of the log axes
clearly shows the parabolic relationship
between power and frequency in the low-frequency range. The
low-frequency power increases with 6 dB per octave (or 20 dB
per decade) frequency increase. We need a sound yardstick for
measuring the low-frequency properties of DCRLL sequences.
The spectral width is usually quantified by a parameter called
cutoff frequency [3, Ch. 9]. Braun [12] defined the cutoff
frequency of DCRLL sequences, denoted by ,by
where denotes the spectral density at zero frequency
of the maxentropic constrained sequence. For and
, the parameters used in Fig. 3, we find
Braun also studied the relationship between redundancy and
cutoff frequency. He defined the extra rate loss, ,as
the difference between the capacities of the pure RLL channel
and the DCRLL channel, or
The parameter quantifies the extra rate loss that
results from the additional constraint on the RDS . Braun
showed that maxentropic sequences have the property that
there is, in good approximation, a linear relationship between
cutoff frequency and the extra rate loss . The relationship
found is given by
The constant of proportionality between cutoff frequency and
extra rate loss is independent of the and constraints.
Fig. 4. Strategy for minimizing the RDS.
The constant was derived for pure RDS constrained sequences
and is valid if in addition and constraints are imposed. Com-
puter simulations revealed that the above relationship appears to
be accurate to within 5% for .
In the next section, we will discuss various design methods
for constructing DCRLL codes that have emerged in the litera-
The main parameters of EFM are , , and rate
. Detailed information on code tables and so on can
be found in the patent granted to Immink and Ogawa [1]. The
8-bit source data are translated into a 14-bit -constrained word.
The 14-bit words are concatenated with 3-bit words, merging
words. The 3-bit mergings words are selected by the encoder
such that the minimum and maximum runlength are guaranteed.
There are instances, however, where the merging word is not
uniquely governed by the minimum and maximum runlength re-
quirements. This freedom of choice is used for minimizing the
power density at the low-frequency end, as will be explained
with Fig. 4. Fig. 4 shows an example of the merging process.
Eight user bits are translated into 14 channel bits using a look-up
table. The 14 bits are merged by means of three merging bits in
such a way that the runlength conditions continue to be satisfied.
For the case shown in Fig. 4, the condition that there should be at
least two zeros between ones requires a zero at the first merging
bit position. There are, thus, three alternatives for the merging
bits: 000, 010, and 001. The encoder chooses the alternative
that gives the lowest absolute value of the RDS at the end of a
new codeword, i.e., 100 in this case. In the experimental phase
of the CD [13], it was learned that the suppression of low-fre-
quency components, when only two merging bits are used, is not
sufficiently effective. Thus, the number of merging bits was in-
creased to three, so providing a greater degree of freedom to set
oromittransitionsinthemergingbits.With threemergingbitsin
65% of the block catenations, a transition can be set or omitted
freely. The more effective low-frequency control is achieved at
the expense of 1/17 of the information rate.
Fig. 5. Spectrum of classic EFM. The straight line is a least-squares mean
estimate of the low-frequency part of the spectrum.
In principle, better suppression of the low-frequency compo-
nents can be obtained, without offending the agreed standard for
the CD system, by applying improved merging strategies. For
example, by looking more than one symbol ahead, because min-
always contribute to longer-term minimization. Improvements
of 6–10 dB have been reported [14]. The look-ahead strategy
is not used in present equipment. The power spectral density
(PSD) function of classic EFM has been obtained by computer
simulation. Results are plotted in Fig. 5.
The CD and its extensions CD-ROM and CD-V, introduced in
the early 1980s, have become a very successful medium for the
distribution and storage of audio, MPEG-1 video, and other dig-
ital information. Its storage capacity, 680 MByte, is insufficient
for graphics-intensive computer applications and high-quality
digital video programs. An extension of the CD family, the dig-
ital versatile disk (DVD), is a new optical recording medium
with a storage capacity seven times higher than the conven-
tional CD. Most of the storage capacity increase is due to im-
proved quality of the light source (red instead of infrared light)
and the objective lens. The storage capacity of the DVD is also
increased by a complete redesign of the logical format of the
disk including a more powerful Reed–Solomon product code
(RS-PC) and recording code (EFMPlus). The details of the con-
struction of the rate 8/16, (2,10) EFMPlus code, a sliding-block
code with suppressed lf-content, will be discussed in the
next section.
A. Design Outline
Under EFM rules, the data bits are translated eight at a time
into 14 channel bits, with runlength parameters and
. In this section, we will detail a code with the same runlength
constraints as EFM, called EFMPlus,1having a 6% higher rate
than classic EFM. EFMPlus has been adopted in the industry
standard of the DVD as the channel modulation scheme. The
1The name EFMPlus is slightly confusing as the acronym EFM stands for
eight to fourteen modulation. In EFMPlus, there is no such mapping, but the
constraints are the same as in classic EFM.
351 0.0246 2
353 0.0237 3
354 0.0232 4
389 0.0075 8
391 0.0067 10
397 0.0041 13
398 0.0037 17
406 0.0000 102
most important design issues of the DVD were that critical
parameters such as lf-content and timing should definitely not
be compromised. Said parameters are critical as they affect
the servos and the timing recovery, which are the Achilles’
heels of the optical recording system. EFMPlus is a rate 8/16,
sliding-block code with the same runlength parameters as
EFM. Dc-control is performed with the surplus words that
leave each encoder state. The ACH algorithm is run for a
code size that is as large as possible within the complexity
constraints. The code size is the number of source words
(not necessarily a power of two) that can be accommodated
by the encoder. The additional source words ( 256) that are
made possible in this fashion are employed as alternatives for
dc-control (see the next section for more details). The com-
plexity of a sliding-block encoder and decoder is essentially
governed by the maximum value (weight) of an element of the
approximate eigenvector. Table III shows the maximum value
(weight) as a function of the code size . In addition, we
listed the parameter , which denotes the relative redundancy,
. Note that the maximum
code size that can be accommodated for , , and
is 406.
For the given code parameters, we note that for code size
, the maximum weight is two. A one-round split is
sufficient to construct the encoder. We also notice in Table III
that the maximum weight grows very rapidly with increasing
code size . After many trials and considering the diminishing
returns, it was decided for a code size . After an
initial merging of the states, we obtain a three-
state FSM. After a single-state split, this three-state FSM can
be transformed into a four-state encoder. Each of the four states
of the EFMPlus encoder is characterized by the type of words
that enter, or leave,the given state. The states and word sets are
characterized as follows.
Words entering State 1 end with trailing zeros,
Words entering State 2 and 3 end with trailing zeros,
trailing zeros.
Words entering State 4 end with trailing zeros
trailing zeros.
The words leaving the states are chosen in such a way that the
concatenation of words entering a state and those leaving that
state obey the channel constraints. For ex-
ample, words leaving State 1 start with a runlength of at least
two and at most nine zeros. In an analogous manner, we con-
clude that words leaving State 4 start with at most one zero.
Obviously, the sets of words leaving State 1 or 4 have no words
in common. Words emerging from State 2 and 3 comply with
the above runlength constraints, but they also comply with other
conditions. Words leaving State 2 have been selected such that
the first (msb) bit, , and the thirteenth bit, , are both equal
to zero. Words leaving State 3 have . With a com-
puter, it can easily be verified that from each of the states, at
least 351 words are leaving. An encoder is constructed by as-
signing a source word to each of the 351 edges that leave each
state. The encoder requires accommodation for only 256 source
words. The excess, 95, words have been used for suppressing
the low-frequency power (see the next section), the dc-control.
More details can be found in [15].
The encoder defined above can freely accommodate 351
source words. In order to make it possible to use a unique 26-bit
sync word, seven candidate words were barred, leaving a code
size of 344. As we only need accommodation for 256 source
words, the surplus words can be exploited for minimizing the
power at low frequencies. The suppression of low-frequency
components, or dc-control, is done by controlling the RDS.
The 88 surplus words are used as an alternative channel
representation of the source words . The full encoder
is described by two tables called main and substitute table,
respectively. The source words can be represented
by the designated entries of the main table or, alternatively, by
the entries of the substitute table. For source words ,
the encoder opts for that particular representation from the
main table or the substitute table that minimizes the absolute
value of the RDS.
The DVD standard requires an extra rule for dc-control. If the
encoder is in State 1, the encoder may use the codeword ,
, as an alternative for dc-control, provided the
runlength constraints are not violated. Similarly, if the encoder
is in State 4, it may use the codeword , ,
as an alternative. In other words, codewords pertaining to States
1 and 4, i.e., and , both in the main and substi-
tute tables, may be used as alternatives for dc-control, provided
the runlengths constraints are strictly obeyed. State swapping is
allowed as decoding can be accomplished unambiguously. The
state swapping offers a 2–3-dB extra reduction of the lf power.
It is of some interest to consider the possibility of redesigning
the EFM code and its variants of various codes rates and to com-
pare the spectral performance.
The EFM code was designed in 1980 before efficient design
algorithms, such as ACH and so on, were developed. A second
handicap of the EFM design is that at the time of its conception,
every gate used for decoding was one too many.2Let us now
for academic interest ignore for the time being the complexity
issue, and start from scratch. Essentially, EFMPlus is a redesign
of EFM with a rate 8/16 instead of 8/17. Decoding of EFMPlus
requires 1000 instead of the 52 gates of EFM.
An obvious alternative of the rate 8/16, EFMPlus code would
have been EFM with two instead of three merging bits. The dc-
2Note that this requirement was not imposed for the encoding hardware, as it
was anticipated that there would be a very limited number of master and replica-
tion plants. Who, at that time, could envisage that there would be EFM encoders
in the households in CD-R and CD-RW players as computer peripheral.
Code (dB) Sum var.
EFM 16 8/17
EFMPlus 19 8/16
EFMPlus* 24 8/16
EFM16a 66 8/16
EFM16b 27 8/16
EFM15 220 8/15
content of the alternative code, EFM16a (the name we shall use
for the code with two instead of three merging bits), can easily
be assessed by computer simulation, and the results are shown
in Table IV. The dc-content can be reduced significantly by a re-
assignment of the various words that takes into account the fol-
lowing observation. Observe, for example,that in EFM16a, the
16-bit words 0001000100001000 and 1001000100001000 are
alternative channel representations. It can easily be verifiedthat
the disparity of both words (after precoding, of course) is zero.
This, in fact, means that the encoder has no real option to in-
crease or decrease the RDS with the transmission of those code-
words. Obviously, it would be much better if we could redesign
the code in such a way that as many source words as possible
would have channel representations of zero-disparity. Nonzero-
disparity codewords of opposite signs should be paired, whereas
zero-disparity codewords may remain single.
It is a straightforward exercise, using Gu and Fuja’s method
tics. We may construct a block-decodable code with a source
size of 260 instead of 257 words. A typical result, note there are
many possibilities, called EFM16b, offers 8 dB (see Table IV)
more reduction at the low-frequency end than does EFM16a.
This is a significant improvement, in particular, as the only dis-
advantage is the extra gate count required for decoding. Note
that the EFM16b code requires a full decoding array of 16 bits
instead of 14 bits as in EFM16a. An advantage with respect to
EFMPlus, which requires a sliding-block decoder of length two,
is the absence of error propagation. On the other side of the bal-
ance, we have a 3-dB extra reduction of EFMPlus’s lf-content
(see Table IV).
As , at least in theory, it is possible to
construct a rate 8/15 (2, 9) code. The EFM15 code [17] is an
example of a rate 8/15, (2, 14) DCRLL code. An alternative
rate 8/15 construction [18] is possible that requires, in contrast
with classic EFM, only one merging bit. We could, in principle,
employ the same 14-bit word assignment as in classic EFM. For
an example of such a construction, the reader is referred to the
U.S. Patent granted to Tanaka et al. [19].
EFM15, which is very similar to EFMPlus, has a codeword
encoder states, and was constructed using the ACH algorithm
after a single split. The number of words that can be accommo-
dated depends on the state, and is at most 270. This leaves at
most spare words that can be used for dc-con-
trol. Pairing of the alternative representations has been accom-
plished in such a way that the words that form a pair differ in
Fig. 6. Sum variance of maxentropic DCRLL sequences with parameters
and and the digital sum variation as a parameter. As a comparison,
we plotted the rate and sum variance of EFM and EFMPlus.
a single position, i.e., have unity Hamming distance. This has
the advantage that the decoding operation is simplified and that
the alternative representations have an odd or even number of
ones, which, as was observed experimentally, has a beneficial
effect upon the quality of the dc-control. Further details, such
as coding tables and so on, of EFM15 can be found in the U.S.
Patent description [17].
The spectral performance of the various members of the EFM
of the simulations have been collected in Table IV.
The lf-suppression, as presented in Table IV, is measured at
, where the channel bit frequency Hz. If we wish
to compare coding schemes of a different rate, it is standard
practice to compare the lf-suppression at, say, 0.0001 times the
user bit frequency . As the frequency Hz is assumed
to be in the range of frequencies, where the spectrum has
a parabolic shape, the lf-suppression at can be found by
multiplying the lf-suppression measured at by .For
example, if , we have to subtract dB from
the numbers shown in Table IV to obtain the lf-suppression at
, where Hz. A comparison of the properties of
sequences generated under the rules of EFM and EFMPlus with
those of maxentropic sequences is shown in Fig. 6. As we can
observe, theory predicts there is some room for improvement.
For codes of the same rate as EFM and EFMPlus, we could,
in theory, construct codes that generate sequenceswith a factor
of three smaller sum variance or, alternatively, a 10-dB extra
lf-content suppression.
If, on the other hand, we stipulate that the sum variance and,
thus, the lf-content of EFMPlus is adequate, we may conclude
from Fig. 6 that a rate 0.53 ( ) is possible with the sum
variance of EFM. The performance of the rate 8/15, code,
EFM15 [17], listed in Table IV, is a far cry from the theoretical
bound. Braun et al. [20] and Immink [21] presented coding
schemes using long block codes with enumerative coding that
are very close to the predicted maxentropic performance. The
typical codeword length in their constructions is about 1000
bits, and the hardware required for encoding and decoding is
about 5 kB. Other EFM-like codes have been presented by
Roth [22].
The design of any constrained code can, at least in principle,
be systematically accomplished by the design techniques that
have been developed over the years. Unfortunately, the design
of a DCRLL code with a rate close to the Shannon capacity
of the constrained channel, is severely hampered by the large
number of states of the finite-state machine (FSM), which
models the channel constraints at hand. The large number of
states of the underlying FSM, can, at least in principle, be
handled by buying a sufficiently large computer, but the insight
required is too easily lost. The design of DCRLL codes is
therefore (still) the province of a plurality of ad hoc methods,
for example, [23]–[26]. Basically, there are two systematic
design approaches that emerged in the literature.
The first method uses the ACH algorithm to design an RLL
code. In the final stage of the ACH algorithm, we end with a
graph with the property that from any state of the graph, there
are at least ( is assumed to be the source word length) out-
going edges. There are (hopefully) states with a larger number
of outgoing edges. These surplus edges are used as alterna-
tive codewords that can be used for dc-control. The rate 8/16,
(2,10) EFMPlus code, discussed in Section IV, is an example of
a DCRLL code used in practice (DVD) that was designed ac-
cording to these guidelines.
In the second method, dc-control is effectuated by multi-
plexing the source data or the encoded data with dc-control
bits. A given, state-of-the-art RLL code, for example, the
rate 2/3, (1,7) code, is used to generate RLL sequences. The
sequences generated under the coding rules of said code are
multiplexed with channel bits for minimizing the low-frequency
components, the dc-control. The user data or, alternatively, the
encoded data are partitioned into segments of bits. Between
two consecutive -bit segments , dc-control bits are inserted,
and the dc-control bits, in turn, are chosen to minimize the
low-frequency components. In the experimental phase, we
have the freedom to select the parameters and such that the
required dc-suppression is reached. There is, in other words, no
need to redesign the constituent RLL code.
The success of the design method depends on various fac-
tors, such as, for example, how much lf-suppression is required.
In most of the practical cases that we encountered, an extra re-
dundancy for the dc-control of 2–3% was sufficientto yield the
required dc-suppression. In that case, codes using multiplexing
methods offer an excellent performance and flexibility. In the
next section, we will present a description of the first design
method, where dc-control bits are multiplexed with the user or
channel data.
A. Dc-Control on Data Level versus Coded Level
Assume the and constraints are given and that an ef-
ficient code has been found in the literature or, alternatively,
constructed using the various methods offered in the literature.
A straightforward method for extending a standard code
with dc-suppression is to add (stuff) redundant bits, which can
be chosen to reduce the power at low frequencies. Essentially,
there are two approaches with which a encoder can be
extended with multiplexed dc-control: multiplexing can be done
at two levels, namely, at the source data level or at the channel
data level. Between segments of source data or between seg-
ments of encoded data , dc-control bits are inserted. In both
multiplex formats, the dc-control bits are chosen to minimize
the low-frequency components of the channel sequence gener-
ated. This can be accomplished by tallying the RDS at the end
of each candidate segment. The encoder transmits that candi-
date segment whose RDS is closest to zero. At the receiver site,
the added dc-control bits, either on the data or channel level, can
easily be skipped by the decoder. The two multiplex approaches
of dc-control have various distinct features. The dc-control
bits can be freely chosen if they are multiplexed at source data
level. Then, the encoder has possible sequences to be tried.
If, on the other hand, the dc-control bits are multiplexed with
the sequence, the new multiplexed sequence so gener-
ated has to obey the constraints in force, and as a re-
sult, the number of candidate sequences to be tried is less than
. For the dc-control to be effective under all worst-case cir-
cumstances, it should guarantee that an (almost) entire segment
of modulated data bits can be inverted or not inverted. We
can easily verify that if the dc-control bits are multiplexed with
the sequence, that in order to guarantee said worst-case
performance, we require at least dc-control bits. Then,
the maximum runlength at the segment boundaries will increase
from to . A similar method has been proposed by Odaka
[27], Coppersmith and Kitchens [28], and Patel [29]. When, on
the other hand, the dc-control bits are multiplexed on the source
level, the matter of worst-case performance is much more in-
volved. The encoded segments are both a function of the source
data and the encoder state at the start of the segment. It is there-
fore not recommended to use an industry-standard code.
A possible solution, using the parity preserving word assign-
ment, will be discussed in the next section.
B. Codes with Parity Preserving Word Assignment
In order to make it possible to efficiently control the dc-con-
tent in the source date level mode, we havemade the assignment
between source words and codewords in such a way that the
parity of both the source word and its assigned codeword are the
same. The parity of an -bit word
(either source words or codewords), is defined by
In other words, if the source word has an even (or odd) number
of ones, then its channel representation also has an even (or odd)
number of ones. A code with a parity preserving assignment has
the virtue that when it is used in conjunction with dc-control bits
at the data level, that setting an even(or odd) number of ones at
the data level will result in an even (or odd) number of ones at
the code level. This leads, as we will demonstrate shortly, to an
efficient dc-control.
Data Code
00 000
01 010
10 100
1100 001010
1101 001000
1110 101010
1111 101000
Data Code
10 0100
01 1000
001 001000
000 100100
111 000100
1101 00001000
1100 00100100
Data Code
00 101
01 100
10 001
11 000
Data Code
11.11.11 000.010.010
11.11.10 001.010.010
01.11.10 101.010.010
01.11.11 100.010.010
An example of a variable length rate 2/3, code
that complies with the parity preserving property is shown in
Table V. It can easily be verified that indeed the assignment is
parity preserving.
A parity preserving assignment of a rate 2/3, (1,8) code, first
presented by Kahlman and Immink [30], is based on the look-
ahead rate 2/3, (1,7) code described by Jacoby and Kost [31].
Tables VII–IX show the encoding of the new code parity pre-
serving code. The full coding table of the code consists of a
main table and two substitute tables instead of a single substi-
tute table. It can easily be verified that the assignment is indeed
parity preserving. The code was found by trial and error, as no
approach is (yet) available for systematically constructing codes
with a parity preserving word assignment.
Data Code
00.00 100.010
00.01 101.010
10.00 000.010
10.01 001.010
The systematic design of RLL codes with a parity preserving
word assignment is a challenging task. The above examples
show that it is indeed possible and that such codes offer a better
performance than do their counterparts. Block codes are by their
virtue of simplicity good candidates, but the complexity issue
will hamper their design. Variable length synchronous codes
seem to be promising candidates. It is not (yet) known how we
can design parity preserving codes with the ACH algorithm.
The difference between the quality of the alternative dc-con-
trol methods has been assessed by Wang et al. [32]. The
power density measured at a relatively low-channel frequency
was used as a quality criterion. Computer programs
have been written for simulating the two coding schemes,
where the dc-control bits are multiplexed at source or at
channel level, respectively. The code for the channel-level
multiplex is the standard, rate 2/3, (1,7) code, whereas the
source-level multiplex is the parity preserving, rate 2/3, (1,8)
code described in the previous section. The authors observed
that the parity preserving code performs 2 dB better than
does the standard rate 2/3, (1,7) code used with channel-level
multiplex in the range of dc-control redundancy of 1%–4%.
We have given a survey of channel codes for optical disk
recording systems. It has been shown that state-of-the-art codes
are very close to the bound set by the tenets of information
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U.S. Patent 4.501.000, Feb. 1985.
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vice, signal as well as record carrier,” U.S. Patent 5.696.505, Dec. 1997.
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11–15, 1999.
Kees A. Schouhamer Immink (M’81–SM’86–
F’90) was born in Rotterdam, The Netherlands. He
received the M.Sc. (EE) and Ph.D. degrees from the
Eindhoven University of Technology.
He is President and Founder of Turing Machines
Inc. and serves as a Guest Professor at the Institute
of Experimental Mathematics, Essen University,
Germany, and the National University of Singapore.
He has contributed to the design and development
of a variety of digital recorders such as the compact
disk, compact disk video, DAT, DCC, and recently,
the DVD. Immink was granted 35 U.S. patents, is (co)author of three books
and has written numerous papers in the field of digital recorders.
Dr. Immink is Vice-President of the Audio Engineering Society (AES),
a Governor of the IEEE Consumer Electronics Society, and Trustee of the
Shannon Foundation. He served as Program Chairman and Conference
Chairman of various international conferences over the years. He holds fel-
lowships of the AES, IEE, and SMPTE, and is an elected member of the Royal
Netherlands Academy of Arts and Sciences. For his part in the digital audio and
video revolution, he was honored with the AES Gold and Silver Medal, IEE
Thomson Medal, SMPTE Ponyatoff Gold Medal, IEEE Information Theory
Society Golden Jubliee Award for Technical Innovation, IEEE Masaru Ibuka
consumer electronics award, a Knighthood in the Order of Orange-Nassau,
and the IEEE Edison Medal “For a career of creative contributions to the
technologies of video, audio, and data recording.”
... Applications such as magnetic and optical recording systems are usually designed by combining two separate schemes which are an error-correction coding scheme and a modulation scheme [13]. To optimise the recording system, the coding and modulation are designed to be of high rate, low complexity, and be able to minimise the negative effects of AC coupling that can result into inter-symbol interference and error propagation [14]- [18]. To mitigate the effects of AC coupling, coding schemes that can perform spectral shaping are needed. ...
... (20) This therefore implies that any channel symbol combination in the removed column can not yield any notch value that is greater than (20). Both (19) and (20) thus proves (18). ...
... It should, however, be noted that (18) only holds for cases where δ = 1. As such, we have focused the evaluations done in this work to such cases and present limited results on cases where δ > 1. ...
Full-text available
In digital transmission systems that involve pulse amplitude modulation (PAM), channel coding is useful for spectral shaping by concentrating the frequency energy of the transmitted information towards a predetermined range of the frequency spectrum, or making it have low power content at such frequencies, so as to suit the frequency characteristics of the communication channel. We thus present a permutation coding system with injections that can exhibit spectral shaping at rational sub-multiples of the symbol frequency. We also present a mathematical expression that allows for the prediction of low energy positions in the codebook’s spectrum. Upper and lower bounds for the low energy spectrum were also determined. Due to the way the injections are introduced, it gives the scheme an advantage of achieving higher symbol rate, when compared with conventional permutation coding systems.
... Codes for optical disc recording are described in [11]. The (d, k) runlength constraint is imposed in all optical disc products as it is desirable that the system is selfclocking, which requires that consecutive transitions in the encoded signal should not be too far apart, and it is a further requirement that two transitions of the encoded signal should not be following too closely in order to limit inter symbol interference. ...
... Eight-to-Fourteen-Modulation (EFM) developed by Immink and Ogawa in the early 1980s was adopted as the recording code for the Compact Disc [11]. The EFM signal is obtained by converting a series of m(=8)-bit information words into a series of n(=14)-bit codewords, and where p(=3) merging bits are inserted between consecutive codewords. ...
Full-text available
This paper describes a new coding method based on binary (d, k) runlength constraints used for recording or transmitting an audio or video signal, computer data, etc. Data words of m bits are translated into codewords of n bits using a conversion table. The codewords satisfy a (d, k) runlength constraint in which at least d and not more than k '0's occur between consecutive '1's. The n-bit codewords alternate with p-bit merging words which in the prior art are selected such that the d and k are satisfied at the borders of consecutive codewords. We present a new coding method, where the codewords obey the (d, k)-constraint, but the merging words are not required to obey the (d)-constraint. The merging word that satisfies said conditions, yielding the lowest low-frequency spectral content of the encoded signal obtained after modulo-2 integration, is selected. The spectral performance of the new coding method has been appraised by computer simulations for the EFM (Eight-to-Fourteen Modulation) parameters, d = 2, k = 10, and p = 3. The low-frequency content of the signal generated by the newly presented coding method is around 4 dB lower in the relevant low-frequency range than that generated by the conventional EFM method.
... We find, using (8) and (12), that where ...
Full-text available
We investigate a new approach for designing spectral shaping block codes with a target spectrum, H_t(f), that has been specified at a plurality of frequencies. We analyze the probability density function of the spectral power density function of uncoded n-symbol bipolar code words. We present estimates of the redundancy and the spectrum of spectral shaping codes with specified target spectral densities H_t(f_i) at frequencies f_i. Constructions of low-redundancy codes with suppressed low-frequency content are presented that compare favorably with conventional dc-balanced codes currently used in data transmission and data storage devices with applications in consumer electronics.
... We think of each received 1 as an arrival, and assume that it triggers a dead-time period of d channel uses. This problem has been extensively studied in the literature on run-length limited (RLL) coding [12][13][14][15]; we shall elaborate on this later. The noiseless binary channel with dead time can be thought of as a model for direct-detection optical channel with number states containing zero or one photon as inputs. 1 Furthermore, as we shall see, it serves as a reference for comparison for the Poisson channel. ...
Full-text available
This paper studies the discrete-time Poisson channel and the noiseless binary channel where, after recording a 1, the channel output is stuck at 0 for a certain period; this period is called the “dead time.” The communication capacities of these channels are analyzed, with main focus on the regime where the allowed average input power is close to zero, either because the bandwidth is large, or because the available continuous-time input power is low.
... In data storage products, user data are written into physical attributes that can be either magnetic [1], electronic [2], optical [3], or even biological such as DNA [4]. Due to inevitable process variations, called noise, the magnitude of the physical attributes may deviate from their nominal values. ...
Full-text available
We report on the feasibility of k-means clustering techniques for the dynamic threshold detection of encoded q-ary symbols transmitted over a noisy channel with partially unknown channel parameters. We first assess the performance of k-means clustering technique without dedicated constrained coding. We apply constrained codes which allows a wider range of channel uncertainties so improving the detection reliability.
... Codes that avoid runs of the same nucleotide longer than m, m > 0, will be called m-constrained runlength limited (RLL) codes. In magnetic and optical recording practice the maximum runlength of a sequence of q-ary symbols is preferably described in terms of a k-constraint [10]. A k-constrained codeword has, by definition, at most k consecutive zero's between consecutive non-zero symbols. ...
Full-text available
We analyze codes for DNA-based data storage which accounts for the maximum homopolymer repetition length and GC-AT balance. We present a new precoding method for translating words with a maximum run of k zeros into words with a maximum homopolymer run m = k + 1, which is atractive for securing GC-AT balance. Generating functions are presented for enumerating the number of n-symbol k-constrained codewords of given GC-AT balance Various efficient constructions are presented of block codes that satisfy a combined balance and maximum homopolymer run.
In this paper, we present a deliberate bit flipping (DBF) coding scheme for binary two-dimensional (2-D) channels, where specific patterns in channel inputs are the significant cause of errors. The idea is to eliminate a constrained encoder and, instead, embed a constraint into an error correction codeword that is arranged into a 2-D array by deliberately flipping the bits that violate the constraint. The DBF method relies on the error correction capability of the code being used so that it should be able to correct both deliberate errors and channel errors. Therefore, it is crucial to flip minimum number of bits in order not to overburden the error correction decoder. We devise a constrained combinatorial formulation for minimizing the number of flipped bits for a given set of harmful patterns. The generalized belief propagation algorithm is used to find an approximate solution for the problem. We evaluate the performance gain of our proposed approach on a data-dependent 2-D channel, where 2-D isolated-bits patterns are the harmful patterns for the channel. Furthermore, the performance of the DBF method is compared with classical 2-D constrained coding schemes for the 2-D no isolated-bits constraint on a memoryless binary symmetric channel.
In this paper, we consider the problem of transmitting binary messages over data-dependent two-dimensional channels. We propose a deliberate bit flipping coding scheme that removes channel harmful configurations prior to transmission. In this method, user messages are encoded with an error correction code, and therefore the number of bit flips should be kept small not to overburden the decoder. We formulate the problem of minimizing the number of bit flips as a binary constraint satisfaction problem, and devise a generalized belief propagation guided method to find approximate solutions. Applied to a data-dependent binary channel with the set of 2-D isolated bit configurations as its harmful configurations, we evaluated the performance of our proposed method in terms of uncorrectable bit-error rate.
Full-text available
A method of converting a series of m-bit information words to a modulated signal. For each information word from the series an n-bit code word is delivered. The delivered code words are converted to the modulated signal. The code words are distributed over at least one group of a first type and at least one group of a second type. For the delivery of each of the code words belonging to the group of the first type the associated group establishes a coding state of the first type. When each of the code words belonging to the group of the second type is delivered, a coding state of the second type is established which is determined by an information word belonging to the delivered code word. When one of the code words is assigned to the received information word, this code word is selected from a set of code words based on the coding state. The sets of code words belonging to the coding states of the second type are disjunct. The DC and LF parameters of the modulated signal improve when in a coding state of the first type, by assigning a code word from a set of another state of the first type, while maintaining the dk-constraint. Selecting one of the sets of the first type results in the best momentary running DC value. The method can be applied to different coding state mechanisms.
Full-text available
The sound from a Compact Disc system encoded into data bits and modulated into channel bits is sent along the 'transmission channel' consisting of write laser - master disk - user disk - optical pick-up. The maximum information density on the disk is determined by the diameter d of the laser light spot on the disk and the 'number of data bits per light spot'. The effect of making d smaller is to greatly reduce the manufacturing tolerances for the player and the disk. The compromise adopted is d approximately equals 1 mu m, giving very small tolerances for objective disk tilt, disk thickness and defocusing.
Full-text available
A description is given of the eight to fourteen modulation system (EFM) designed for the Compact Disc Digital Audio System with optical read-out. EFM combines high information density and immunity to tolerances in the light path with low power at the low-frequency end of the modulation bit stream spectrum. In this modulation scheme, blocks of eight data input bits are transformed into fourteen channel bits, which follow certain minimum and maximum run-length constraints by using a code book. To prevent violation of the minimum and maximum run-length constraints a certain number of merging bits are needed to concatenate the blocks. There are cases where the merging bits are not uniquely determined by the concatenation rules. This freedom of choice thus created is used for minimizing the power of the modulated bit sequence at low frequencies. The paper presents the results of algorithms that were used to minimize this low-frequency content.
Full-text available
A system for block encoding words of a digital signal achieves a maximum of error compaction and ensures reliability of a self-clocking decoder, while minimizing any DC in the encoded signal. Data words of m bits are translated into information blocks ofn1 bits (n1 >m) that satisfy a (d,k)-constraint in which at least d "0" bits, but no more than k "0" bits occur between consecutive "I" bits. The information blocks are concatenated by inserting separation blocks of n2 bits there between, selected so that the (d,k)-constraint is satisfied over the boundary between any two information words. For each information word, the separation block that will yield the lowest net digital sum value is selected. Then, the encoded signal is modulated as an NRZ-M signal in which a "1" becomes a transition and a "0" becomes an absence of a transition. A unique synchronizing block is inserted periodically. A decoder circuit, using the synchronizing blocks to control its timing, disregards the separation blocks, but detects the information blocks and translates them back into reconstituted data words of m bits. The foregoing technique can be used to advantage in recording digitized music on an optical disc.
Full-text available
A device for encoding a stream of data bits of a binary source signal (S) into a stream of data bits of a binary channel signal (C), wherein the bit stream of the source signal is divided into n-bit source words (x1, x2), which device includes a converting circuit (CM) adapted to convert the source words into corresponding m-bit channel words (y1, y2, y3). The converting circuit (CM) is further adapted to convert n-bit source words into corresponding m-bit words, such that the conversion for each n-bit source word is parity preserving (table I). The relations hold that m>n, p>0, and that p can vary. Preferably, m=n+1. Further, a decoding device is disclosed for decoding the channel signal obtained by means of the encoding device.
In digital transmission systems, the transmission channel often does not pass d-c. This causes the well- known problem of baseline wander. One way to overcome this difficulty is to restrict the d-c content in the signal stream using suitably devised codes. It is shown that, for a d-c constrained code, the limiting efficiency is related to the number of allowable running digital sum states in a very simple way.
We derive the limiting efficiencies of dc-constrained codes. Given bounds on the running digital sum (RDS), the best possible coding efficiency η, for a K-ary transmission alphabet, is η = log2 λmax/log2 K, where λmax is the largest eigenvalue of a matrix which represents the transitions of the allowable states of RDS. Numerical results are presented for the three special cases of binary, ternary and quaternary alphabets.
We have developed a new error correction method (Picket: a combination of a long distance code (LDC) and a burst indicator subcode (BIS)), a new channel modulation scheme (17PP, or (1, 7) RLL parity preserve (PP)-prohibit repeated minimum transition runlength (RMTR) in full), and a new address format (zoned constant angular velocity (ZCAV) with headers and wobble, and practically constant linear density) for a digital video recording system (DVR) using a phase change disc with 9.2 GB capacity with the use of a red (lambda=650 nm) laser and an objective lens with a numerical aperture (\mathit{NA}) of 0.85 in combination with a thin cover layer. Despite its high density, this new format is highly reliable and efficient. When extended for use with blue-violet (lambda≈ 405 nm) diode lasers, the format is well suited to be the basis of a third-generation optical recording system with over 22 GB capacity on a single layer of a 12-cm-diameter disc.