ArticlePDF Available

Abstract and Figures

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.
Content may be subject to copyright.
A New DC-free Runlength Limited Coding
Method for Data Transmission and Recording
Kees A. Schouhamer Immink, IEEE Fellow.
Abstract—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 mbits are translated into codewords
of nbits using a conversion table. The codewords satisfy
a(d, k)runlength constraint in which at least dand 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 dand kare 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.
Index Terms—Constrained coding, runlength limited code,
Eight-to-Fourteen Modulation, EFM.
I. INTRODUCTION
Runlength limited (RLL) codes have been widely ap-
plied in well-known consumer electronics products such
as magnetic recording products and optical discs including
Compact Disc, DVD, and Blu-Ray Disc [1]. RLL codes
have recently been advocated in visible light communica-
tions (VLC) systems, where light intensity of solid-state
light sources, mostly LEDs, are varied [2]. Experimental
DNA-based storage architecture using RLL codes was im-
plemented by Church and others [3, 4, 5, 6].
Binary RLL sequences are characterized by two param-
eters, d+ 1 and k+ 1, which stipulate the minimum and
maximum runlength, respectively, where a runlength is the
number of consecutive like symbols in the sequence. In
RLL sequences, the occurrence of very short and/or long
runlengths are avoided. If the runlength is too short, inter-
symbol interference may become too excessive, resulting
in read or transmission errors. The maximum runlength
constraint ensures that adequate timing information can
be derived from the received signal. An RLL sequence
is usually generated by a transformation of a (d, k)-
constrained sequence, which has at least dand at most k
Kees A. Schouhamer Immink is with Turing Machines Inc, Willemskade
15d, 3016 DK Rotterdam, The Netherlands. E-mail: immink@turing-
machines.com.
zero’s between consecutive one’s. Modulo-2 integration of a
(d, k)-constrained sequences delivers an RLL sequence with
runlengths between d+ 1 and k+ 1.
Block codes have been used to translate user data into
a(d, k)-constrained sequence. In a block code format, the
user data is partitioned into blocks of mbits, which are
uniquely translated into nbits that conform the prescribed
dand krunlength constraints. The n-bit blocks are cascaded
to form a long sequence of symbols, and subsequently
forwarded to the recorder or transmitter. In order to satisfy
the (d, k)-constraint between the cascaded n-bit blocks, p-
bit merging blocks are inserted between consecutive n-bit
blocks. A seminal construction method presented by Tang
and Bahl [7], has p=d+2. Improved construction methods
which impose additional constraints on the codewords allow
p=d[1].
In addition, the low-frequency components of the encoded
signal should be kept as small as possible. Such a signal
is called a dc-free signal. A first reason for using said
dc-free signals is that recording or transmission channels
are not normally responsive to low-frequency components.
The suppression of low-frequency components in the sig-
nal is also highly advantageous, for example, when the
signal is read from an optical disc on which the signal
is recorded in the track, because then continuous tracking
control undisturbed by the recorded signal is possible. A
good suppression of the low-frequency components leads
to improved tracking with less disturbing audible noise.
For visible light communication it is desirable that the
intensity variation of the light is invisible to the users, that is,
annoying flicker should be mitigated [8]. This requirement
implies that the spectrum of the encoded signal should not
contain low-frequency components.
Eight-to-Fourteen-Modulation (EFM), a dc-free block
code with basic parameters (d= 2, k = 10), and p= 3, has
been used in the Compact Disc [1]. It is compulsory that
the p(=3)-bit merging words satisfy the (d= 2, k = 10)
runlength constraints imposed for the cascaded sequence.
They are further selected to minimize the low-frequency
content of the encoded sequence.
An improved method for suppressing the low-frequency
components of RLL block codes is described in [9]. In said
article, the authors describe a method where the selection
of a p-bit merging word does not only depend on a single
upcoming codeword, but where in contrast the selection is
made using q,q > 1upcoming codewords. From the article
cited, it can be concluded that this look-ahead strategy
improves the quality of the low-frequency suppression. A
significant disadvantage of said strategy is the difficulty of
implementing it as the number of operations, such as adding,
comparing, buffering, and so on, grows exponentially with
the number of codewords involved in the selection process.
In [10], Immink describes a type of constrained codes,
termed weakly constrained codes. Weakly constrained codes
fail to comply with the (d, k)-constraints as they produce
sequences that violate the prescribed constraints with (low)
probability. It is argued that if the channel is not free
of errors, it is pointless to feed the channel with per-
fectly constrained sequences. Violation of prescribed (d, k)-
constraints offers an additional degree of freedom that can
be exploited to reduce the low-frequency components. It is
known that violations of the (d)-constraint, i.e., runs of ‘0’s
less than d, are prone to error resulting from inter symbol
interference. A violation of the (k)-constraint could easily
result in loss of clock synchronization, which, in turn, could
lead to a burst of errors. The method is therefore not very
effective as the frequency of violations of the dk-constraint
must be small as they will inevitably lead to bit detection
errors at the receiver’s site.
Information recording has a constant need for increasing
the reading and writing speed. The aim of increased reading
speed, however, requires higher servo bandwidth of the
tracking mechanism, which, in turn, sets more severe restric-
tions on the suppression of the low-frequency components
in the recorded signal. Improved suppression of the low-
frequency components is also advantageous for suppressing
audible noise arising from the tracking mechanism. For
visible light communication systems, it is desirable that
the intensity variation of the light, flicker, is invisible to
the users. For this reason, it is desirable to make as many
efforts to prevent the encoded signal from containing low-
frequency components.
In this paper, we present a new construction method
for designing weakly constrained (d, k)constrained block
codes. The n-bit codewords obey the (d, k)-constraint, but
the merging words are not required to obey the mandatory
(d)-constraint. Violation of the prescribed d-constraint has a
bearing on the error rate of the merging bits (and not the n-
bit data). But as the p-bit merging words are skipped by the
decoder, the (d)-constraint violations are harmless and as a
result the data error rate is not affected. Violation of (d)-
constraint of the p-bit merging words offers a greater degree
of freedom for selecting the merging words, which has a
bearing on the low-frequency content of the encoded data
stream. The extra freedom for selecting the p-bit merging
words, makes it possible to significantly reduce the low-
frequency content of the encoded signal. We exemplify the
new method by the design of an alternative and EFM-
compatible coding method. The new method violates the
regular EFM rules as the prescribed d(=2)-constraint is not
obeyed in the 3-bit merging words. The spectral perfor-
mance of the new coding method has been appraised by
computer simulations, and we found that the new method
performs around 4 dB better in the low-frequency range
than the conventional EFM method.
We start in Section II with a description of the prior art.
A description of the new method is given in Section III.
Section IV concludes the paper.
II. DE SC RI PT IO N OF T HE P RIOR ART
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 self-
clocking, 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. In addition, the signal should
be ‘dc-free’, that is the low-frequency components of the
encoded signal should be kept as small as possible.
A. Eight-to-Fourteen-Modulation (EFM)
Eight-to-Fourteen-Modulation (EFM) developed by Im-
mink 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 informa-
tion words into a series of n(=14)-bit codewords, and
where p(=3) merging bits are inserted between consecutive
codewords. Respective codewords of 14 bits satisfy the
conditions that at least d(= 2) and at most k(=10) ‘0’s are
placed between two consecutive ‘1’s.
Under EFM rules, in order to satisfy this condition also
between codewords, 3-bit merging words are used. It is
easily verified that only four 3-bit merging words of the
eight possible 3-bit merging words are permitted to be
used, namely the words ‘001, ‘010’, ‘000’, and ‘100’.
The remaining 3-bit merging words, namely ‘111’, ‘011’,
‘101’, and ‘110’ cannot used as they violate the prescribed
d(=2)-constraint. One of the four allowed merging words
is selected such that the bit string obtained after cascading
alternate codewords and merging words firstly satisfies the
(d, k)-constraint, and secondly that in the corresponding
modulo-2 integrated signal the running digital sum (RDS)
value remains substantially constant. The RDS at a specific
instant is understood to mean the difference between the
number of bit cells having the high signal value and the
number of bit cells having the low signal value, calculated
over the encoded signal portion situated before this specific
instant. A substantially constant running digital sum value
means that the frequency spectrum of the signal does not
comprise frequency components in the low frequency range.
There are instances where the merging word is not uniquely
governed by the minimum and maximum runlength require-
ments. This freedom of choice is utilized for minimizing
the power density at the low-frequency end. By deciding
the merging words according to above rules, low-frequency
components of the encoded signal can be reduced. Decoding
of EFM signals is very simple. The 3-bit merging words
RDS
t
010
001
000
0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1
1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0
data bits
channel bits
XMM=000
XMM=010
XMM=001
X M M
Fig. 1. Strategy for minimizing the running digital sum (RDS) in
EFM. Two 8-bit user words are translated into 14-bit codewords
using a look-up table. The 14-bit codewords, in turn, are cascaded,
‘merged’, using a 3-bit merging word in such a way that the
runlength conditions continue to be satisfied for the cascaded
sequence.
are skipped by the decoder, and the 14-bit codewords are
translated, using a look-up table into the information bytes.
Figure 1 shows an example of the merging process. Eight
user bits are translated into 14 channel bits using a look-
up table. The 14-bit codewords are cascaded, ‘merged’,
by means of 3-bit merging words in such a way that the
runlength conditions continue to be satisfied. For the case
shown, the condition that there should be at least two
‘zero’s between ‘one’s requires a ‘zero’ at the first merging
bit position (denoted by X). There are thus only three
alternatives for the merging words, namely ‘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 ‘000’ in this case.
III. DES CR IP TI ON O F TH E NE W METHOD
A possible solution to the problems inherent in the prior
art is based on the observation that prior art methods are
overly restrictive in the choice of the merging words as
only those merging words are allowed that when alternate
merging words and codewords are cascaded the prescribed
(d, k)-constraint is satisfied. The codewords obey both (d)-
and (k)-constraint in force, but the merging words are not
required to obey said d-constraint. It is known that runs of
‘0’s smaller than dare prone to error resulting from inter
symbol interference. However, as the merging words are
skipped by the receiver, the (d)-constraint in the merging
words can be violated without compromising the reliability
of the received codewords. Then, as a result of the increase
of the size of the set of merging words from which can
be selected, the low-frequency components of the encoded
TABLE I
MERGING OPERATION, EXAM PLE 1 .
14-bit word Merging bits Next 14-bit word RDS
01001000100100 000 00100000000100 4
01001000100100 001 00100000000100 10
01001000100100 010 00100000000100 8
01001000100100 011 00100000000100 2
01001000100100 100 00100000000100 6
01001000100100 101 00100000000100 0
01001000100100 110 00100000000100 2
01001000100100 111 00100000000100 8
signal can significantly be reduced with respect to signals
generated under the rules of prior art.
Consecutive n-bit codewords are alternated with p-bit
merging words. The encoder generates a set of allowed p-
bit merging words for use between consecutive codewords
so that the sequence comprised of alternate codewords and
merging words satisfies the conditions that between the
leading ‘1’ in the merging word and the trailing ‘1’ in the
codeword preceding the merging word, and the trailing ‘1’
in the merging word and the leading ‘1’ in the codeword
following the merging word are at least d‘0’s. In a second
aspect, the encoder selects from said set of allowed merging
words that merging word that yields the cumulative dc im-
balance nearest zero in the catenation of the codeword and
that merging word after modulo-2 integration. For example,
in the EFM code, where d= 2, k = 10, n = 14, m = 8,
and p= 3, there are four 3-bit merging words of the
eight possible merging words allowed, namely ‘001’, ‘010’,
‘000’, and ‘100’. By way of example, the remaining 3-bit
merging words, namely ‘111’, ‘011’, ‘101’, and ‘110’ are
allowed to be used. There are, however, three restrictions:
firstly, in the cascade of alternate 14-bit codewords and
3-bit merging words the k(=10) constraint should not be
violated, and secondly, in order to safeguard the reliability
of the codewords, the number of consecutive ‘0’s at the
beginning or end of the two codewords joining the merging
word should be at least d.
Table I shows schematically the process of generating
the set of allowed merging words, the computation of
the corresponding RDS, and the selection of the merging
word that yields the least dc-imbalance. We show the
concatenation of the 14-bit codewords ‘01001000100100’
and ‘00100000000100’, where for illustrative purposes it
is assumed that the RDS at the end of the first codeword
‘01001000100100’ equals +5. For the specific case in hand
all possible 3-bit merging words can be used without vio-
lating the prescribed constraints. Table I shows all possible
3-bit merging words, and it shows the resulting RDS after
the merging word and codeword have been catenated and
integrated modulo-2. The encoder selects that particular
merging word resulting in an RDS nearest zero, i.e. it
selects ‘101’. The RDS after cascading the merging words
‘101’ and the codeword ‘00100000000100‘ is thus 0. In this
TABLE II
MERGING OPERATION, EXAMPLE 2.
14-bit word Merging bits Next 14-bit word RDS
01001000100100 000 01000001001001 4
01001000100100 001 01000001001001 Not allowed
01001000100100 010 01000001001001 8
01001000100100 011 01000001001001 Not allowed
01001000100100 100 01000001001001 6
01001000100100 101 01000001001001 Not allowed
01001000100100 110 01000001001001 2
01001000100100 111 01000001001001 Not allowed
manner the dc-level of the encoded signal is maintained at
a substantially constant level and the frequency spectrum
of the encoded signal will show suppressed low-frequency
components. Note that prior art EFM encoders, where the
merging bits obey the prescribed (d)-constraint, will select
the merging word ‘000’, which will lead to a larger RDS,
namely +4. This example shows that signals obtained in
accordance with the invented method show a more constant
dc-level of the encoded signal than those generated by prior
art methods.
As a further illustration, Table II shows the process of
generating all 3-bit merging words in the case codewords
‘01001000100100’ and ‘01000001001001’ are catenated.
Merging words ‘001’, ‘011’, ‘101’, and ‘111’ are not
allowed as the trailing ‘1’ of the merging word and the
leading ‘1’ of the codeword ‘01000001001001’ are less than
d(=2) ‘0’s apart. If it is assumed that the RDS at the end of
the codeword ‘01001000100100’ equals +5, then the RDS
after a candidate merging word and the 14-bit codeword
have been catenated and integrated modulo-2 is listed in
Table II. The encoder selects the merging word resulting in
the RDS nearest zero, i.e. it selects ‘110’, so that the RDS
after cascading the merging words ‘110’ and the codeword
‘01000001001001’ is thus +2. Note that a conventional EFM
encoder, where the merging words must obey the prescribed
(d)-constraint, will select the merging word ‘000’, which
will lead to a larger RDS, namely +4.
A. Results
The new coding method, as shown in Table II, may
select merging words leading to a smaller RDS, which
has a bearing on the low-frequency content of the encoded
data stream. The spectral performance of the new method
has been appraised by computer simulations, where a long
series of random data was encoded using the new merging
protocol. Figure 2 shows the power density function, or
spectrum, of a long stream of random data encoded by
classic EFM and that obtained by the new coding method
versus the relative frequency f. Perusal of the diagram
reveals that the new method improves the low-frequency
content by around 4 dB.
10-4 10-3 10-2 10-1
Frequency f (log)
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
Spectrum (dB)
EFM
new method
Fig. 2. Spectrum of classic EFM and the new method (dB) versus
relative frequency f(log axis).
IV. CONCLUSIONS
We have presented a new coding method used for record-
ing and transmission an audio or video signal, computer
data, etc on a recording medium or by visible light. Data
words of mbits are translated into codewords of nbits
in accordance with a prescribed conversion table. The n-bit
codewords satisfy a (d, k)-constraint in which at least d‘0’s
and not more than k‘0’s occur between consecutive ‘1’s.
The n-bit codewords alternate with p-bit merging words
which do not need to satisfy the (d)-constraint. They are
selected such that between the leading ‘1’ in the codeword
following the merging word and the trailing ‘1’ in the
merging word are at least d‘0’s, and further that between
the trailing ‘1’ in the codeword preceding the merging
word and the leading ‘1’ in the merging word are at least
d‘0’s. The merging word that satisfies said conditions,
yielding the lowest dc imbalance of the encoded signal
obtained after modulo-2 integration of the catenation of
the alternate codewords and merging words is selected. The
spectral performance of the new method has been appraised
by computer simulations for the EFM (Eight-to-Fourteen
Modulation) parameters, namely d= 2, k = 10, p = 3,
where a long series of random data was encoded using the
new merging protocol. The low-frequency content of the
signal generated by the newly presented method is around
4 dB lower in the relevant low-frequency range than that of
the conventional EFM method.
REFERENCES
[1] K. A. S. Immink, “Runlength-Limited Sequences,Proceedings of
the IEEE, vol. 78, no. 11, pp. 1745-1759, Nov. 1990.
[2] A. R. Ndjiongue, H. C. Ferreira, and T. M. N. Ngatched, Visible Light
Communications (VLC) Technology, Wiley Encyclopedia of Electrical
and Electronics Engineering, 2015.
[3] G. M. Church, Y. Gao, and S. Kosuri, “Next-generation digital
information storage in DNA,Science, vol. 337, no. 6012, pp. 1628-
1628, 2012.
[4] D. Limbachiya, M. K. Gupta, and V. Aggarwal, “Family of Con-
strained Codes for Archival DNA Data Storage,IEEE Commun.
Letters, vol. 22, no. 10, pp. 1972-1975, August 2018.
[5] M. Blawat, K. Gaedke, I. Hutter, X. Cheng, B. Turczyk, S. Inverso,
B. W. Pruitt, and G. M. Church, “Forward Error Correction for DNA
Data Storage,” International Conference on Computational Science
(ICCS 2016), vol. 80, pp. 1011-1022, 2016.
[6] K. A. S. Immink and K. Cai, “Design of Capacity-Approaching
Constrained Codes for DNA-based Storage Systems,IEEE Commun.
Letters, vol. 22, pp. 224-227, Feb. 2018.
[7] D. T. Tang and L. R. Bahl, “Block Codes for a Class of Constrained
Noiseless Channels,” Information and Control, vol. 17, pp. 436-461,
1970.
[8] M. Oh, “A Flicker Mitigation Modulation Scheme for Visible Light
Communications”, 2013 15th International Conference on Advanced
Communications Technology (ICACT), PyeongChang, South Korea,
Jan. 2013.
[9] K. A. S. Immink and U. Gross, “Optimization of Low-frequency
Properties of Eight-to-Fourteen Modulation,” The Radio and Elec-
tronic Engineer, vol. 53, no. 2, pp. 63-66, Feb. 1983.
[10] K. A. S. Immink, “Weakly Constrained Codes,” Electronics Letters,
vol. 33, no. 23, pp. 1943-1944, Nov. 1997.
[11] K. A. S. Immink, “A Survey of Codes for Optical Disk Recording,
IEEE J. Select. Areas Commun., vol. 19, no. 4, pp. 756-764, April
2001.
Kees A. Schouhamer Immink (M’81-SM’86-
F’90) founded Turing Machines Inc., an inno-
vative start-up focused on novel signal process-
ing for DNA-based storage, where he currently
holds the position of president. He received a
personal Emmy award in 2004, the 2017 IEEE
Medal of Honor, the 1999 AES Gold Medal, the
2004 SMPTE Progress Medal, the 1999 IEEE
Masaru Ibuka Consumer Electronics Prize, the
Eduard Rhein Prize for Technology, and the 2015
IET Faraday Medal. He was inducted into the
Consumer Electronics Hall of Fame. He received an honorary doctorate
from the University of Johannesburg in 2014. He served the profession as
a member of the BoG of IEEE’s Consumer Electronics Society, and as
President of the Audio Engineering Society Inc., New York, in 2003.
... The 8B10B code has many embodiments [2,9], and is widely used in gigabit telecommunication systems and data storage media. Combinations of RLL and balanced codes can be found in data storage, energy harvesting, and communications codes [10,11,12,13]. ...
Article
Full-text available
We present coding methods for generating ℓ-symbol constrained codewords taken from a set, S, of allowed codewords. In standard practice, the size of the set S, denoted by M=|S|, is truncated to an integer power of two, which may lead to a serious waste of capacity. We present an efficient and low-complexity coding method for avoiding the truncation loss, where the encoding is accomplished in two steps: first, a series of binary input (user) data is translated into a series of M-ary symbols in the alphabet M = {0, ... ,M - 1}. Then, in the second step, the M-ary symbols are translated into a series of admissible ℓ-symbol words in S by using a small look-up table. The presented construction of Pearson codes and fixed-weight codes offers a rate close to capacity. For example, the presented 255B320B balanced code, where 255 source bits are translated into 32 10-bit balanced codewords, has a rate 0.1 % below capacity.
Article
Full-text available
We consider coding techniques that limit the lengths of homopolymer runs in strands of nucleotides used in DNA-based mass data storage systems. We compute the maximum number of user bits that can be stored per nucleotide when a maximum homopolymer runlength constraint is imposed. We describe simple and efficient implementations of coding techniques that avoid the occurrence of long homopolymers, and the rates of the constructed codes are close to the theoretical maximum. The proposed sequence replacement method for k-constrained q-ary data yields a significant improvement in coding redundancy than the prior art sequence replacement method for the k-constrained binary data. Using a simple transformation, standard binary maximum runlength limited sequences can be transformed into maximum runlength limited q-ary sequences, which opens the door to applying the vast prior art binary code constructions to DNA-based storage.
Article
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.
Article
Full-text available
Digital information is accumulating at an astounding rate, straining our ability to store and archive it. DNA is among the most dense and stable information media known. The development of new technologies in both DNA synthesis and sequencing make DNA an increasingly feasible digital storage medium. We developed a strategy to encode arbitrary digital information in DNA, wrote a 5.27-megabit book using DNA microchips, and read the book by using next-generation DNA sequencing.
Article
Full-text available
The author reports on the performance of a new class of constrained codes, called weakly constrained codes. These codes do not strictly guarantee the imposed channel constraints, but rather generate codewords that violate, with a given (small) probability, the prescribed constraint. Weakly constrained codes are specifically of interest when it is desirable that the code rate R=p/q is very high, requiring codewords of length q>100
Article
Full-text available
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.
Article
Full-text available
Coding techniques are used in communication systems to increase the efficiency of the channel. Not only is coding equipment being used in point-to-point communication channels, but coding methods are also used in digital recording devices such as sophisticated computer disk files and numerous domestic electronics such as stationary- and rotary-head digital audio tape recorders, the Compact Disc, and floppy disk drives. Since the early 1970s, coding methods based on runlength-limited sequences have played a key role for increasing the storage capacity of magnetic and optical disks or tapes. A detailed description is furnished of the limiting properties of runlength-limited sequences, and a comprehensive review is given of the practical aspects involved in the translation of arbitrary data into runlength-limited sequences.
Article
DNA-based data storage systems have evolved as a solution to accommodate data explosion. In this letter, some properties of DNA codewords that are essential for an archival DNA storage are considered for the design of codes. Constraintbased DNA codes which avoid runs of nucleotides, have fixed GC-weight, and a specific minimum distance are presented. An altruistic algorithm which enumerates DNA codewords with the above constraints is provided. A theoretical bound on such DNA codewords is obtained. This bound is tight when there is no minimum distance constraint. IEEE
Conference Paper
LED (light-emitting diodes) lighting is steadily finding its way into the market of artificial illumination. An additional characteristic of LED lighting is the ability to accommodate switching times that are high enough to transmit data via the visible light it emit. This paper proposes a scheme for providing a data transmission with less flicker in VLC (visible light communication). The scheme utilizes a modulation using dual slope pulses. Due to its moderately increasing and decreasing pulse characteristic. This scheme can also be effectively used in an extremely low light condition. A recovery process in the receiver is proposed.
Article
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.
Forward Error Correction for DNA Data Storage
  • M Blawat
  • K Gaedke
  • I Hutter
  • X Cheng
  • B Turczyk
  • S Inverso
  • B W Pruitt
  • G M Church
M. Blawat, K. Gaedke, I. Hutter, X. Cheng, B. Turczyk, S. Inverso, B. W. Pruitt, and G. M. Church, "Forward Error Correction for DNA Data Storage," International Conference on Computational Science (ICCS 2016), vol. 80, pp. 1011-1022, 2016.