Content uploaded by Kees Schouhamer Immink
Author content
All content in this area was uploaded by Kees Schouhamer Immink on Sep 22, 2021
Content may be subject to copyright.
IEEE Transactions on Consumer Electronics, Vol. 55, No. 3, AUGUST 2009
Contributed Paper
Manuscript received June 21, 2009 0098 3063/09/$20.00 © 2009 IEEE
1360
Abstract — Two-dimensional error correction codes (2D-
ECCs) have been the cornerstone of all three generations
of optical recording - CD, DVD and BD. Research into
powerful error correction methods is paramount for the
development of high-capacity optical recording systems. A
Reed-Solomon product-code (RS-PC) for DVD systems
performs error and erasure decoding by giving and taking
erasure information between two ECCs. In this paper, we
will present a new error correction method that performs
erasure decoding using the only erasure information
supplied from a modulation code decoder – more
specifically, the EFMPlus code for DVD systems. We will
evaluate the decoding efficiency of the new error correction
method under a channel environment with various error
types.
Index Terms— Erasure decoding, RS-PC, EFMPlus code
and DVD systems.
I. INTRODUCTION
Due to increasing demand for high-quality consumer
products, optical storage systems such as DVD systems
[1] and BD systems [2] have been developed to provide
higher storage capacity by leading industrial consortia.
One solution for achieving higher storage capacity is a
powerful error correction technique. In order to correct
the errors that may be included in the output stream of
a modulation code [3] decoder, optical recording
systems utilize 2-dimensional error correction codes
(2D-ECCs).
The 2D-ECCs are composed of two ECCs and
perform error and erasure decoding [4] by exchanging
erasure information between two ECCs. The 2D-ECCs
use a Reed-Solomon (RS) code [4] as an error
correction code. The reason is to increase their error
correction capability using erasure decoding of the RS
code. When the erasure decoding is employed, an RS
code with t error correction capability [4] is capable of
correcting v errors and e erasures, where 2v+e ≤ 2t. In
other words, the number of maximum correctable
errors by an RS code is t, while the number of
Jun Lee is with Digital Storage Research Laboratory, LG Electronics in
Korea (e-mail: leejun28@lge.com).
Kees A. Schouhamer Immink is with Institute for Experimental
Mathematics, Ellernstrasse 29-31, Essen, Germany (e-mail:
immink@turing-machines.com).
maximum correctable erasures by RS code is 2t. This
implies that the performance of the 2D-ECCs depend
on how efficient the used erasure decoding is.
The use of a modulation code in optical recording
systems is essential for the reduction of inter-symbol
interference, timing recovery and servo tracking. The
decoder takes the output stream of a detector as its
input. Under the decoding algorithm of the modulation
code like the slide-block algorithm [3], the decoder
decodes the output stream of a detector by searching a
look-up table. If the input of the decoder does not exist
in a look-up table, the decoder declares erasure to the
corresponding output and then assigns a pre-defined
value, which is one of the elements of a Galois field, to
the erased position. The resulting output stream
contains the errors and erasures. This erasure
information can play a significant role in improving the
error correction capability for RS decoders. However,
under the conventional erasure-decoding rule of 2D-
ECC, the 2D-ECC accomplishes the error and erasure
decoding without using this erasure information
stemming from the modulation code decoder. Also, it
is possible that the 2D-ECC exchanges the incorrect
erasure information with a high probability between
two ECCs.
This paper proposes a new error correction method
that performs error and erasure decoding using the only
erasure information supplied from the modulation code
decoder. The main goal of this paper is to increase
error correction capability by improving the erasure
decoding method of conventional 2D-ECC. This
method requires no exchange of erasure information
between two ECCs, and the erasure information only
stems from the modulation code decoder. The erasure
information may be more reliable than that of
conventional 2D-ECC because the 2D-ECC is just
designed to correct errors and erasures included in the
output stream of the modulation code decoder. The
performance of the proposed erasure decoding is
evaluated under a DVD system. Thus, the modulation
code is the EFMPlus code [5] and the 2D-ECC is a
Reed-Solomon product-code (RS-PC) [6][7].
The paper is organized as follows. In Section 2, we
overview the RS-PC for DVD system and introduce the
problems inherent in its erasure decoding methods. In
Section 3, we describe a new erasure decoding method.
In Section 4, simulated results are shown. Finally, the
conclusion is given in Section 5.
An Efficient Decoding Strategy of 2D-ECC
for Optical Recording Systems
Jun Lee and Kees A. Schouhamer Immink, Fellow, IEEE
J. Lee and K. A. Schouhamer Immink: An Efficient Decoding Strategy of 2D-ECC for Optical Recording Systems
1361
Fig. 1. RS-PC structure for DVD systems
II. RS-PC FOR DVD SYSTEMS
Erasure decoding technique plays a significant role in error
correction systems because it can correct twice as many
erasures as it can errors (e + 2v ≤ 2t). For erasure decoding,
optical recording systems adopt a 2-dimensional structure
with two ECCs. Each of the two ECCs provides erasure
information to the other. Based on that erasure information,
ECCs can perform erasure decoding in addition to error-
only decoding. Thus, the accuracy of the erasure
information supplied is a key factor in deciding the
performance of the 2D-ECCs. This Section simply
introduces the conventional error and erasure decoding
method of the RS-PC, and describes its drawbacks.
The RS-PC is illustrated in Figure 1. Each row of
information is encoded by RS (n=182, k=172, tI=5) code
(namely, inner code) over GF (28), where n and k are the
length of the codeword and information respectively. All
columns are encoded by RS (208, 192, tO=8) code (namely,
outer code).
Error and erasure decoding consists of two steps. First,
RS-PC decodes each row (column) by inner code (outer
code) and then, if the number of error bytes is over 5 (8),
such rows (columns) result either in a mis-correction or in a
decoding failure. If it is a decoding failure, the RS-PC
declares erasures to the codeword (182 bytes or 208 bytes)
in that row (column). Second, after mapping the erasure
information to error-position over outer code (inner code),
outer code (inner code) performs the error and erasure
decoding about all columns (rows).
The drawbacks of RS-PS are given as follows. In the
first decoding process, the inner code (outer code) can just
perform error-only decoding. In addition, if the number of
error bytes in each row (column) exceeds 5 (8), inner code
(outer code) declares the erasure to the codeword (182
bytes or 208 bytes) in such row (column). Note that the
symbols included in the erased row (column) may or may
Fig. 2. The incorrect erasure declaration under the conventional
decoding rule of RS-PC.
not be in error. In this case, it is possible that the inner
code(outer code) supplies the incorrect erasure information
to the outer code (inner code) and then outer code (inner
code) unreliably performs the error and erasure decoding.
Outer code also can supply inaccurate erasure information
to inner code in the same manner. If the symbol error rate
after detection is high, phenomena like the above will more
frequency happen and the decoding efficiency of the RS-
PC will decrease. In the RS-PC, the approach of iterative
error correction between inner code and outer code is
possible. However, under conventional erasure decoding
methods for RS-PC, the approach does not induce the
improvement of performance. Figure 2 shows incorrect
erasure declarations under the conventional error correction
of RS-PC. In Figure 2, vI and vO are the number of error
bytes included in the shown row and column respectively,
and eI and eO are the number of erasures declared in the
shown row and column respectively. In Figure 2, inner
code and outer code declare erasure to the shown row and
column if 2vI + eI > 10 (=2tI) and 2vO + eO > 16(=2tO),
respectively. For better decoding efficiency of error
correction systems, the research of a technique for
supplying more accurate erasure information is essential.
III. A NEW ERROR CORRCTION TECHNIQUE
The output stream of the modulation code decoder may
contain the errors and erasures, referred to as a priori
information. This output stream is rearranged for the
decoding-unit for 2D-ECC, and then it is fed to the 2D-
ECC. The RS-PC treats the a priori information as error
and performs error and erasure decoding based on the
erasure information generated by two ECCs in the error
correction process. This a priori information may be more
accurate than that of the RS-PC because the RS-PC is just
IEEE Transactions on Consumer Electronics, Vol. 55, No. 3, AUGUST 2009
1362
Fig. 3. A new error and erasure correction strategy for RS-PC
designed to control the errors and erasures contained in
the output stream of the modulation code decoder. Thus,
for erasure decoding, the consideration of this a priori
information can be expected to improve the decoding
efficiency of RS-PC. This method performs the erasure
decoding using the only a priori information without
exchanging the erasure information between two ECCs.
Under current DVD systems, this a priori
information cannot be utilized as error-position
information for RS-PC erasure decoding. The reason is
because the pre-defined value used for representing a
priori information is one of the elements over GF(28)
consisting of a codeword of error correction code. The
erasure decoding of the RS-PC using the only a priori
information can be realized by the following method.
The realization is possible by appending erasure–
indication bits to the output symbol of a modulation
code decoder. Thus, the EFMPlus code decoder outputs
9 bits, which include both the erasure-indication bit (1
bit) and its output symbol (8 bits), instead of just the 8
bits. If the erasure indication bit among the 9 bits is set
to 1, it means that the symbol at that position is erased.
A pre-defined value for expressing the a priori
information is no longer one of elements over GF (28)
and thus it is distinguished from elements consisting of
the RS codeword. For error correction, the RS-PC
searches for this pre-defined value in its decoding unit
and then maps it to the error position. Sequentially,
RS-PC can perform erasure decoding based on the only
error position. Based on this error position, repeatable
error corrections between inner code and outer code are
possible and this approach induces an incredible
performance gain compared to the same approach of
RS-PC under conventional erasure-decoding rules.
Figure 3 shows the proposed erasure decoding
procedure. In Figure 3, the modulation code is the
EFMPlus code and its decoder outputs 8 bits after
taking 16 bits as its input. Under the given decoding
rule, the decoder decodes the output stream by
searching a look-up table. If the input of the decoder
does not exist in the look-up table, the decoder outputs
9 bits of a pre-defined value. The corresponding output
is referred to as the erased symbol, or E. In case the
input of the decoder is in error but it exists in the look-
up table, the decoder outputs 9 bits in which the
erasure indication bit is set to 0. The corresponding
output is referred to as an undetected error symbol, or
U. The output stream of the decoder contains the
erased symbol E, the symbol with an error U and the
symbol without error, or C. This output stream is
rearranged to 208 by 192 bytes and is input into the
RS-PC. Finally, RS-PC accomplishes the erasure
decoding based on the only erased symbol without
exchanging erasure information between the two ECCs,
and this decoding is repeatedly performed between
inner code and outer code.
IV. SIMULATION RESULTS
In simulation, the decoding block for RS-PC is
referred to as a frame, and the number of total frames
(T) used is 200. The number of total error bytes added
to the input of the modulation code decoder is SER ×
the frame size (208 by 192 bytes), where SER (%)
stands for Symbol Error Rate. The types of errors
tested are random errors (R, %), short burst (S%), and
long burst errors (L, %). In simulation, the length of R
is 1 byte, the length of S is between 5 and 40 bytes and
the length of L is between 40 and 182 bytes. In the
channel model of this work, the ratio of E to U depends
on the types of errors tested and their distribution. All
simulation figures show the ratio of E to U and a Lena
Image reflecting the given error-types and their
distribution at specific SERs. In the figures, the X-axis
means -10log10 (SER) and the Y-axis means the
uncorrected symbol error rate. Figures 4 and 5
represent the performance of RS-PC under (R =100%)
and (R =33%, S =33% and L =34%), respectively. From
simulation results, we can identify that RS-PC using the
proposed erasure decoding (in short, I (Improved)
RSPC) outperforms conventional RS-PC irrespective of
error types and their distributions. Simulation results
reveal that the proposed erasure decoding method
clearly overcomes the drawback of conventional erasure
decoding methods, while conventional RS-PC performs
erasure decoding by exchanging incorrect erasure
information with a high probability between inner code
and outer code. In the approach of repeatable error
correction between two ECCs, the RS-PC using the
proposed erasure decoding method achieves incredible
performance gains as the number of iterations increases,
while conventional RS-PC does not. This fact implies
that two RS-PC ECCs do not generate precise erasure
information under conventional erasure decoding even if
they employ repeatable error correction.
Under the more various channel environments, we also
tested a new erasure decoding method and the results have
J. Lee and K. A. Schouhamer Immink: An Efficient Decoding Strategy of 2D-ECC for Optical Recording Systems
1363
Fig. 4. Performance comparison at R=100%
Fig. 5. Performance comparison at R=33%, S=33% and L=34%
shown that the new method outperforms the conventional
method no matter the channel environment. This section
introduces two applications exploiting the proposed criteria
applying to GS scheme with RLL constraints and the 2/3 (1,
7) PP code.
V. CONCLUSION
We have proposed an efficient erasure decoding method
using the only erasure information provided from the
modulation code decoder. This new method definitely
overcomes the drawbacks of conventional erasure decoding
methods for DVD systems. The improvement of performance
is induced by independent erasure decoding of two ECCs. The
new method achieves high performance gains irrespective of
error types and their distribution, and can easily be applied to
optical recording systems such as BD systems with minor
modifications. Thus, we conclude that the proposed method
can be a candidate for next-generation storage systems
requiring more reliable error control systems.
REFERENCES
[1] “DVD specifications for rewritable disk,” Dec. 1996.
[2] “Blu-ray disk specifications for read-only format,” Nov. 2005.
[3] K. A. S. Immink, Codes for Mass Data Storage Systems, Shannon
Foundation Publishers, 1990.
[4] S. Lin and D. J. Costello, Error control coding : Fundamentals and
application (second edition), Prentice Hall, 2004.
[5] K. A. S. Immink, “EFMPlus: the coding format of the multimedia
compact disc,” IEEE trans. on consumer electronics, vol. 41, no. 3, pp.
491-497, Aug. 1995.
[6] W. Coene, H. Pozidis and et al, “Channel coding and signal processing
for optical recording systems beyond DVD,” IEEE trans. on magnetic,
vol. 37, no. 2, pp.682~687, March 2001.
[7] H. C. Chang, C. B. Shung and C. Y Lee, “A Read-Solomon product-
code (RSPC) decoder chip for DVD applications,” IEEE Journal of
solid-state circuit, vol. 36, no. 2, pp. 229~237, Feb. 2001.
BIOGRAPHY
Jun Lee received his B.S. and M.S. degree from
Dongguk University, Seoul, Korea in 1998 and
2000, respectively. Since March 2000, he has
been a Ph.D. student in Dept. of Electronic
Engineering at Dongguk University. In 2003, he
received Ph. D. degree and he joined the faculty
of Samsung Advanced Institute of Technology
(SAIT), Suwon, Korea, and he is currently
working with LG Electronics. His research
interests are signal processing and coding for
storage systems and communication theory.
Kees Schouhamer Immink received his PhD
degree from the Eindhoven University of
Technology. He was with Philips Research
Labs in Eindhoven from 1968 till 1998. He
founded and became president of Turing
Machines Inc. in 1998. He is, since 1994, an
adjunct professor at the Institute for
Experimental Mathematics, Essen University,
Germany. Immink designed coding techniques
of virtually all consumer-type digital audio and
video recording products, such as Compact Disc, CD-ROM, CD-Video,
Digital Audio Tape recorder, Digital Compact Cassette system, DCC,
Digital Versatile Disc, DVD, Video Disc Recorder, and Blu-ray Disc. He
received widespread recognition for his many contributions to the
technologies of video, audio, and data recording. He received a
Knighthood in 2000, a personal ‘Emmy’ award in 2004, the 1996 IEEE
Masaru Ibuka Consumer Electronics Award, the 1998 IEEE Edison Medal,
1999 AES Gold Medal, and the 2004 SMPTE Progress Medal. He was
named a fellow of the IEEE, AES, and SMPTE, and was inducted into the
Consumer Electronics Hall of Fame, and elected into the Royal
Netherlands Academy of Sciences and the US National Academy of
Engineering. He served the profession as President of the Audio
Engineering Society inc., New York, in 2003.
