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J. Lee and K. A. S. Immink: DC-free Multimode Code Design Using Novel Selection Criteria for Optical Recording Systems

Contributed Paper

Manuscript received December 1, 2008 0098 3063/09/$20.00 © 2009 IEEE

553

Abstract — DC-free run-length limited codes have been the

cornerstone of all three generations of optical recording, CD,

DVD and BD. Research into very efficient coding methods is

paramount for the upcoming fourth generation. Guided

Scrambling (GS) is an efficient coding method that has been

reported in the literature. Under GS rules, a user word is

translated into a plurality of possible candidate words, and

among the candidate words the encoder selects the codeword

with the least low-frequency spectral content. In our paper, we

will present results of our attempts to improve the performance

of GS-based codes. We will present new selection criteria and

evaluate their performance and complexity. Specifically, we

will evaluate the new selection criteria to the 2/3(1,7) parity

preserving code used in Blu-Ray Disc.

Index Terms — Selection Criterion, GS, DC-free RLL code

I. INTRODUCTION

The design of codes for optical recording is essentially the

design of the combined DC-free and runlength-limited

(DCRLL) codes. An RLL constraint in optical recording plays a

crucial role for the reduction of channel impairments and clock

recovery. The DC-free property is for circumventing or reducing

interaction between data written on disk and the servo systems

that follow the track. In literatures [1][2], the design of DCRLL

codes can be accomplished by several design techniques and

has been mostly concentrated on byte-oriented DCRLL code

with the small codeword length. The data recording industry has

been moving towards detection scheme that can function well at

high code rate such as 16/17, 24/25 and 32/33. For certain

application, it is desirable that the code rate and codeword

length of a modulation code for optical recording are even

higher. However, unfortunately, the design of high-rate DCRLL

code satisfying all of two constraints is far from obvious, and

severely hampered by the large number of states of the finite-

state machine (FSM) which models the channel constraints

[3][4].

One possible solution for achieving high capacity adopts a

weakly constrained code, instead of perfectly RLL constrained

code, for designing recording code. Recently, multimode coding

scheme is issued for next-generation optical recording [4][5].

The coding scheme is one of methods for constructing weakly

constrained code with DC-free property. In multimode codes,

each source word is translated into codewords of a selection set

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).

consisting of L > 3 codewords. The encoder evaluates the

quality of each codeword in the selection set, and then transmits

the codeword with the least DC-contribution. There are two key

elements for multimode code design with DC-free property.

One is a scrambler for translating source words into their

corresponding selection sets, and the other is a good criterion for

evaluating the quality of the candidate codewords. The spectral

performance of the code greatly depends on both issues.

The best multimode coding scheme reported is guided

scramble (GS) [6]. Originally, GS scheme is designed for fiber

optic communication system required to DC-suppression, and

its application is limited to the transmission system over fiber

cables. In recent, its application is moving toward optical

recording system requiring DC-free property. GS scheme

exploits the linear shift feedback register as scrambler and

augmenting step for generating the distinct candidate codewords.

The DC-control of GS scheme can be achieved by developing

selection criterion, which is one of the key elements of

multimode code. The criteria developed can also be extended to

any multimode coding scheme. Immink and Patrovics [4]

assessed the spectral performance of the GS scheme under

conventional criteria. With the same redundancy, the simulation

results show that the performance of GS scheme with short

codeword length is almost the same irrespective the selection

criteria, while that with long codeword length is very sensitive

to the selection criteria. This fact reveals that the selection

criterion is indispensable for multimode code design with DC-

free property and certain application.

The criteria reported for evaluating the quality of the

candidate codewords are minimum running digital sum

(MRDS), minimum squared weight (MSW) and minimum

threshold overrun (MTO) [1][4][9]. The MRDS criterion that

selects a codeword with minimum absolute RDS at the end of

each codeword requires the simplest complexity, while its

spectral performance is degraded as the length of codeword is

increased. The MSW criterion that selects a codeword with the

minimum variance of RDS among candidate codewords can

achieve the best performance irrespective of the codeword

length, while its complexity is large because it requires the

squaring operation. The MTO criterion simply counts the

number of times that the absolute value of RDS in the codeword

is larger than the threshold predetermined by trial and error.

Then, it selects the codeword with minimum overrun. The

structure is simple compared to MSW, while it can select

codeword with bad quality because it randomly chooses one if

there are codewords with the same penalty. This paper suggests

the minimum peak RDS (MPRDS) criterion that is simple to

implement while its efficiency approaches that of the MSW

criterion. The scheme does not require the exhaustive search of

optimal threshold unlike MTO, and achieves the reasonable

DC-free Multimode Code Design

Using Novel Selection Criteria for Optical Recording Systems

Jun Lee and Kees A. Schouhamer Immink, Fellow, IEEE

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IEEE Transactions on Consumer Electronics, Vol. 55, No. 2, MAY 2009

554

performance irrespective of the number of candidate codewords

like MSW, and only requires simple components (adder and

comparator) while MSW requires squaring operator in addition

to that of conventional criteria for implementation. For

improving the performance of criteria, we also propose the sign

change (SC) aided criteria. SC criterion is appended to the

proposed and conventional criteria as sub-criterion, and then SC

aided criteria reduce the probability selecting codewords with

large DC-contribution among codewords with the same penalty.

Thus, SC aided criteria can achieve better DC-suppression than

those without SC. We also suggest the absolute RDS criterion

(ABSRDS). This criterion is the simplified version of MSW

because it uses absolute operation instead of the squaring

operation of MSW for computing RDS variation. The scheme

achieves the best performance among the proposed schemes. In

addition, we introduce the complexity reduction (CR) versions

of new and conventional criteria, which are CRMSW,

CRABSRDS, CRMPRDS and CRMTO. CR criterion sparsely

evaluates each codeword instead of checking at each bit of the

codeword. The scheme requires definitely less complexity than

the conventional schemes, and the performance loss is not

noticeable in the range investigated. For displaying certain

application of the proposed criteria, we apply the proposed

criteria to 2/3(1, 7) parity preserving (PP) code [7], and GS

scheme satisfying RLL constraints. For better DC-control of (1,

7) PP code, its encoding exploits look ahead (LA) algorithm that

looks ahead some codewords. From the simulation results, we

identify that the spectral performance of the proposed criteria

outperforms that of conventional criteria.

This paper is organized as follows. We firstly start with some

preliminaries in Section II. In Section III, we introduce the

conventional and proposed criteria, and analyze their spectral

performance. Section IV applies the proposed criteria to two

DCRLL coding for optical recording systems. Finally, Section V

remarks conclusion.

II. PRELIMINARIES

DC-free codes translate binary source sequences into binary

channel sequences with spectral null at zero frequency. The

amount of DC-content in channel sequences depends on the

range of running digital sum (or digital sum value), in short

RDS, of channel sequences. Let xi = {. . ., x-1, x0, . . ., xi, . . .}, xi

∈{-1, 1} be a binary sequence. The RDS zi is defined as

1

i

ijii

j

z

xz x

−

=−∞

==+

∑. (2.1)

The literatures show that if zi is bounded with small value, its

power spectral density (PSD) vanishes at zero frequency

[1][8]. Let the RDS zi of sequences meet the condition N1 ≤

zi ≤ N2 at any instant i, where N1 and N2 are two (finite)

constants, N2 > N1. The digital sum variation (DSV, N) is

defined as N = N2 - N1 + 1, and then sequences have DC-free

property if N is sufficiently small.

The channel capacity C(N) of maxentropic DC-free code

can be easily computed if N is given [1], and is the important

parameter for computing the efficiency of the implemented

code. The other quantity is sum variance. Sum variance plays

a significant role in the evaluation of the spectral property of

the sequences. The reason is because the smaller the sum

variance of sequences, the smaller its DC-content at low

frequency.

Code efficiency [1] is given by

2

2

(1 ( ))

(1 )

R

DS

CN

ERs

σ

=−

− (2.2)

where 1−C(N) and σ2RDS are the redundancy and sum variance

of maxentropic DC-free sequences, respectively, and R is the

code rate of the implemented code, and s2 is variance of RDS

values obtained at every bit position of sequences produced by

implemented code. It means how redundancy-sum variance

product of implemented code approaches to that of

maxentropic sequence. Maxentropic DC-free sequences

satisfy the following relationship between the sum variance

and the redundancy [1]

0.2326 <(1−C(N)) σ2RDS ≤ 0.25. (2.3)

Since the codeword length that we are targeting is very long

(greater than 50 bits), DSV is around 30. For large N, the

redundancy-sum variance product of maxentropic sequences

is approximately constant and equals 0.2326. Thus, E is given

by

2

0.2326

(1 )

ERs

≈

−. (2.4)

The efficiency in the equation (2.4) is used for discussing the

performance of the proposed criteria.

The paper applies the proposed criteria to GS scheme,

which is a multimode coding scheme, for examining their

performance. Figure 1 represents the operation procedure of

GS algorithm. In Figure 1, symbols T and ⊕ denote the shift

register and modulo-2 addition, respectively. The operation

process of GS algorithm is executed as follows. In the first

step, the source word X = {x1,…,xm}, xi ∈{0, 1}and i = 1,...,m,

is preceded by all the possible binary sequences of length

(r−1) to generate the L' = 2r-1 vectors of B={b1,…,bL'}, bj =

{b1,...,bn} and j = 1,...,L'. In the second step, each vector of

length n=m+r−1 consisting of B is provided to linear shift

feedback register. Then, set B' ={b'1,...,b'L'} is produced, In the

third step, the vectors in B' are preceded by both a one and a

zero, and are shuffled by the scrambler with polynomial x+1

again. Then, selection set C ={c1,...,cL}, L=2r, is produced.

Each vector of C is composed by modulo-2 addition values

between the current input and previous output of scrambler.

This step embodies the polarity bit principle. In the fourth step,

the given criterion selects and transmits codeword (cbest) with

the least DC-contribution out of candidate codewords. At

receiver end, the codeword is firstly descrambled by using x+1

polynomial, and then after removing the first bit, it is

descrambled. The original source word X is eventually

reconstructed by removing r-1 bits.

III. SELECTION CRITERIA

There are two key components for multimode code

design with DC-free property. The first one is the scrambler

for converting source words into their corresponding

selection sets, and the second one is the selection criterion,

or metric, for evaluating the quality of the candidate

codewords. The DC-control of multimode code can be

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J. Lee and K. A. S. Immink: DC-free Multimode Code Design Using Novel Selection Criteria for Optical Recording Systems 555

achieved by developing a better criterion. This section

offers an overview of the conventional criteria, it

introduces new criteria, and evaluates their performance.

A. Conventional Criteria

MRDS: MRDS is often called word-end RDS (WRDS).

MRDS is criterion that selects a codeword with minimum

absolute RDS at the end of each codeword. The scheme

computes the absolute RDS values of candidate codewords

and selects one with the minimum absolute RDS if there is

no other codeword with the same minimum absolute RDS.

Otherwise, it randomly selects one. The scheme requires

the simplest complexity, while its spectral performance is

degraded as the length of codeword is increased.

MSW: MSW is criterion that selects a codeword with

minimum squared weight. The squared weight (wsq) is

defined as the expectation of the squared RDS values at

each bit position of the codeword. The smaller wsq, the

smaller its DC-content at low frequency. MSW criterion

can achieve the optimal performance irrespective of the

codeword length, while its complexity is large because it

requires the squaring operation.

Fig. 1. The operation procedure of GS algorithm.

MTO: MTO criterion utilizes the parameter, RDS

threshold, denoted by T > 0, predetermined by trial and

error. MTO criterion counts the number of times that the

absolute value of the RDS is larger than T. Here, the

counted value is termed as the penalty of the codeword.

Then, it selects the codeword with minimum overrun. If

two or more codewords have the same penalty, one of them

is randomly chosen and transmitted. The scheme is simple

compared to MSW, while it can select codeword with bad

quality because it randomly chooses one if there are

codewords with the same penalty. Besides, the scheme also

needs the exhaustive search for a good optimal threshold.

B. Proposed Criteria

B.1. Two Main Criteria and One Sub-Criterion

MPRDS: In optical recording system, the width of the

spectral notch region from the zero frequency must be as

large as possible for servo signal, and the DSV value is

inversely proportioned to the notch width [1]. Thus, for

minimizing the DSV, MPRDS criterion selects the

codeword having minimum peak RDS. The peak RDS is

the maximum absolute RDS value in a codeword. This

scheme achieves good performance irrespective of the

length of candidate codewords like MSW and requires

simple operation (compare and update MPRDS value) for

implementation unlike MSW (square RDS value at each bit

position and calculate average).

ABSRDS: This criterion is the simplified version of MSW.

It exploits the absolute operation instead of the squaring

operation of MSW. Firstly, this criterion calculates the integral

of absolute RDS of bipolar recording sequence up to a given

position. As a result, the codeword with minimum absolute

RDS variation is selected. The scheme achieves better

performance that is close to that of MSW than MPRDS, and

its complexity is definitely simple compared to MSW.

SC: The (conventional and proposed) main criteria

randomly select and transmit one codeword if there are two

or more codewords satisfying the given criterion. The

random selection has the possibility that the codeword with

larger DC-content out of codewords with the same penalty

is chosen. If a criterion reducing this possibility is

collaborated with the main criteria, the performance

improvement of conventional criteria is obvious.

Frequent sign change of RDS in a codeword means that

the RDS values are near from the zero, in other words, the

DSV is small with high probability compared to the case of

less sign change. Thus, if the SC criterion is applied to main

criteria for investigating the quality of candidate codewords,

the criteria with SC can control DC content better than those

without SC. Figure 2 shows the operation procedure of

MPRDS/SC as an example. This criterion can be performed

by two steps. Firstly, the scheme computes the PRDS and

counts the number of SC of candidate codewords. Secondly,

the criterion selects one with large SC if there are codewords

with the same MPRDS, otherwise, it selects codeword with

MPRDS. The reason that SC is selected as a sub-criterion is

because it cannot guarantee that the DSV value is small

without the main criteria. The reasonable thought is

supported by simulation results.

B.2. Complexity Reduction Method

We introduce the complexity reduction (CR) versions of the

proposed and conventional criteria, which are CRMSW,

CRABSRDS, CRMPRDS and CRMTO. The CR criterion

evaluates the selection metric at regular intervals instead of

each bit position in the candidate codewords. If the interval is

equal to one, then it is just the criterion without CR. Thus, we

can save the computation time for selecting codeword using

the CR. The performance loss is not noticeable at the surveyed

intervals. The CR criterion is developed for reducing the

complexity of main criteria, and can be also applied to others

with SC. Let us simply overview CRMTO/SC explaining the

concept of CR. The scheme observes MTO penalty at regular

intervals, while it counts the number of SC at every bit

position. Then, it selects the codeword with minimum penalty.

If the penalty of two or more codewords is equal, one with the

largest SC is selected and transmitted.

C. Simulation Results

This section evaluates the performance of the proposed

criteria. Figure 3 shows the efficiency comparison among

the proposed and conventional criteria as the number of

redundancy bits changes.

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IEEE Transactions on Consumer Electronics, Vol. 55, No. 2, MAY 2009

556

In Figure 3, the connected points have the same

redundancy (1-R), codeword length r/(1-R), and selection

set of size 2r. From Figure 3, we can notice the following.

1. The MRDS/SC criterion is not efficient for long-term

low frequency minimization like MRDS even if it

outperforms MRDS irrespective of the number of

redundancy bits. The MTO/SC criterion is efficient for

long-term low frequency suppression, and its efficiency

outperforms the MTO criterion. In addition, the efficiency

Cadidate codewords

Compute PRDS

Count SC

Select codewords with MPRDS

Recording (or transmitting)

the codeword

Only one ?

yes

no Find one with

the largest SC

Fig. 2. Codeword selection procedure for MPRDS/SC criterion.

(a) Criteria without SC

(b) Criteria with SC

Fig. 3. The efficiency of the proposed criteria at (1-R)=1/56.

difference between MTO and MPRDS is clearly

noticeable, but the efficiency of MTO/SC really

approaches to that of MPRDS/SC. The results imply that

MTO can select a lot of codewords with large DC-

contribution if we do not add SC criterion, and SC

definitely prohibits the random selection among

codewords with the same penalty.

2. The efficiency of MPRDS/SC outperforms that of

conventional criteria except for MSW, and the

efficiency difference between MPRDS and MPRDS/SC

is small. Thus, the difference of spectral performance

between them is not distinguished. The fact can be

identified through the power spectral density of Figure 4.

It infers that MPRDS itself can achieve better DC-

control unlike MTO criterion.

3. The ABSRDS criterion almost perfectly uses the chance

provided by broader selection sets. Thus, its efficiency

approaches to that of MSW. The fact implies that

ABSRDS well confine the upper bound of absolute RDS

like MSW. The efficiency difference between ABSRDS

(or MSW) and ABSRDS/SC (or MSW/SC) is much

smaller than that between MPRDS and MPRDS/SC.

Thus, the difference of spectral performance between

them is not noticeable. Here, we note that criteria with

SC clearly have the spectral gain even if its difference is

small.

Figure 4 illustrates the power spectral density (PSD) of

codewords generated by each criterion when the number

of redundancy bits is 6. Figure 4 has a horizontal axis fc

(dB) and a vertical axis H(fc) (dB), where dB is defined

by 10log fc and 10logH(fc), respectively, and fc is channel

sequence frequency. Here, the channel sequence denotes

the sequence encoded by GS algorithm. The results in

Figure 4 show that the proposed main criteria can

independently control DC-content in sequences, but the

conventional main criteria except for MSW need the

support of SC. The suggested main criteria clearly reduce

the possibility that two or more codewords in a selection

set have the same penalty value. As a result the

performance of the proposed main criteria is not

deteriorated compared to that of the proposed main

criteria with SC.

Figure 5 presents the sum variance of codewords selected

by GS scheme with the efficiency corresponding to each

point of Figure 3. The results indirectly supports why the

proposed criteria achieve larger efficiency, and MTO/SC

obtains the efficiency better than MTO, and the efficiency

difference between MTO/SC and MPRDS/SC is not

noticeable.

Table 1 shows the spectral performance of CR criteria

at regular intervals I = 5, 10, 15 and 20. From Table 1 and

Figure 4, we can identify that CR criteria have the

performance loss at critical frequency (H(10-4)) compared

to criteria without CR, but the loss is not noticeable. As a

result, the CR criteria achieve the reliable DC-suppression

at critical frequency for optical recording system. The fact

J. Lee and K. A. S. Immink: DC-free Multimode Code Design Using Novel Selection Criteria for Optical Recording Systems 557

infers the possibility that GS scheme with CR criteria can

be applied to optical recording system with less

complexity.

TABLE 1

The spectral performance of CR criteria at r=6 and H (10-4)

I CRMSW CRABSRDS CRMPRDS/SC CRMTO/SC

5 -33.42dB -34.17dB -33.53dB -33.45dB

10 -32.82dB -34.08dB -33.48dB -32.82dB

15 -32.75dB -33.99dB -32.62dB -32.75dB

20 -32.48dB -33.60dB -32.55dB -32.48dB

(a) Criteria without SC

(b) Criteria with SC

Fig. 4. The spectral performance of the proposed criteria when r=6.

(a) Criteria without SC

(b) Criteria with SC

Fig. 5. The sum variance of the proposed criteria at (1-R)=1/56.

IV. APPLICATIONS

This section introduces two applications exploiting the

proposed criteria applying to GS scheme with RLL

constraints and the 2/3 (1, 7) PP code.

A. GS scheme with Runlength-Limited (RLL) Code

The scheme can be implemented by inserting RLL code

encoder between the second scrambler and selection

criterion in Figure 1. As a result, the whole transmitted

sequence satisfies RLL constraints. In the scheme, the RLL

code is the fixed-length code because GS scheme

accomplishes the block based encoding and decoding. The

RLL code used in this work is the 2/3 (1,7) code, and its

DC-content is large.

Figure 6 presents the spectral performance of GS

scheme using conventional and proposed criteria. The

code rate of GS scheme is 330/504 (r=6), and the

redundancy is 1/56. Here, the code rate (R) of the scheme

is given by R=(m×r)/((m+1)×r×3/2). From simulation

IEEE Transactions on Consumer Electronics, Vol. 55, No. 2, MAY 2009

558

(a)

(b)

Fig. 6. Spectral performance of the GS scheme with RLL constraints

and R=330/504 using various criteria.

results, we can identify that the proposed criteria can

conduct better DC-control compared to conventional

criteria even if GS scheme satisfies given RLL constraints.

However, compared to GS scheme without RLL code, it

shows the performance loss even if it has the acceptable

performance at critical frequency for optical recording.

We can conclude that GS scheme satisfying RLL

constraints can clearly construct the DC-free code with

small rate loss even if it uses RLL code with large DC-

content, and thus it is a promising candidate for optical

recording.

B. 2/3 (1, 7) PP Code Using Look-Ahead Algorithm

Parity preserving (PP) means that the modulo-2 addition

of a source word (the “parity”) is always equal to that of

the corresponding channel word. The mapping rule of 2/3

(1, 7) PP code used in this paper is based on the second

Table of [7]. This paper uses look ahead (LA) algorithm for

better DC-control of (1, 7) PP code.

(a) n =0

(b) n=3

Fig. 7. Spectral performance of (1,7) PP code using n LA algorithm.

Encoding step of (1, 7) PP code using n LA algorithm is

processed as follows. The scheme primarily inserts n+1

DC-control bits in the bitstream of the n+1 source words at

regular interval. Then, it generates the two tree structure

consisting of 2n possible candidate codewords. Finally, the

2n+1 possible codewords is evaluated by selection criterion,

and the root codeword of the tree with the least DC-

contribution is transmitted. Here, the encoding method with

n = 0 is the normal encoding method of (1, 7) PP code.

Figure 7 represents the spectral performance of (1,7) PP

code using new and conventional criteria when n = 0 and n

= 3, respectively. Here, the redundancy is 1/56. From

results, we can identify that the spectral performance of (1,

7) PP code using LA algorithm is more reliable, and the

proposed criteria contribute to the phenomenon.

V. CONCLUSION

This paper has proposed two new criteria for evaluating

candidate codewords for the multimode coding scheme. Two

main criteria are MPRDS and ABSRDS. The MPRDS

J. Lee and K. A. S. Immink: DC-free Multimode Code Design Using Novel Selection Criteria for Optical Recording Systems 559

criterion is very efficient for minimizing long-term low

frequency content, and it has a very simple complexity, while

the performance of ABSRDS is less than that of MSW,

ABSRDS requires less complexity than MSW. The SC

criterion complements the random selection among codewords

with the same penalty. Thus, the criterion contributes to their

efficiency improvement by supporting the main criteria. CR

criteria can be realized by computing penalty at regular

intervals instead of every bit position. Certainly, CR criteria

reduce the computation time for investigating the quality of

codewords, and the performance difference between CR

criteria and criteria without CR is not noticeable.

We have discussed the performance of the proposed criteria

in terms of efficiency, sum variance and spectral performance.

From our simulation results, we have identified that the

proposed criteria achieve a higher efficiency than the

conventional criteria, leading to a smaller sum variance and

improved spectral performance. In two applications, DC-

control using the proposed criteria is compatible with MSW

even if they have much less complexity. Thus, we conclude

that the proposed criteria are promising candidates for the

reliable DC suppression method of multimode codes in the

next generation of optical recording.

REFERENCES

[1] K. A. S. Immink, Codes for Mass Data Storage Systems,

Shannon Foundation Publishers, 1990.

[2] K. A. S. Immink, “A survey of codes for optical disk

recording,” IEEE Journal on Selected Areas in

Communications, vol. 19, no. 4, pp. 756-764, April 2001.

[3] K. A. S. Immink and W. Y. H. Wilson, “A comparison of two

schemes for generating DC-free RLL sequences,” IEEE

International Symposium on Information Theory, pp. 352,

June 2000.

[4] K. A. S. Immink and L. Patrovics, “Performance assessment

of DC-free multimode codes,” IEEE Trans. on

Communications, vol. 45, no. 3, pp. 293-299, March 1997.

[5] K. A. S. Immink, “Weakly constrained codes,” IEE

Electronics Letters, vol. 33, pp. 1943-1944, no. 23, Nov.

1997.

[6] I. J. Fair, Q. Wang and V. K. Bhargava, “Polynomial for

guided scrambling line codes,” IEEE Journal on Selected

Areas in Communications, vol. 13, no.3, pp. 449-509, April

1995.

[7] J. A. H. Kahlman and K. A. S. Immink, “Device for

encoding/decoding N-bit source words into

corresponding M-bit channel words, and vice versa,”

US Patent 5,477,222, Dec. 1995.

[8] G. L. Pierobon, “Codes for zero spectral density at zero

frequency,” IEEE Trans. on Inform. Theory, vol. 30,

no. 2, pp. 435-439, March 1984.

[9] S. K. Ahn, S. W, Suh and K. A. S. Immink, “Method for

modulation digital data and apparatus therefor,”

US patent 6,603,411, Aug. 2002.

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 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.