- Email: [email protected]
Inter-track interference free coding and equalization
~ ELSEVIER
Journal of Magnetism and Magnetic Materials 176 (1997) 66-72
Journalof magneUsm and magnetic
, d ~ materials
Inter-track interference free coding and equalization A t s u s h i K i k a w a d a a'*, N a o k i
H o n d a a, K a z u h i r o
O u c h i a, S h u n - i c h i I w a s a k i b
"Akita Research Institute of Advanced Technology, 4-21 Sanuki Araya. Akita 010-16, Japan b Tohoku Institute of Technology, Sendai 982, Japan
Abstract A new coding technique using improved inter-track orthogonal coding (ITOC) was proposed for high track density and/or multi-track recording. The coding has, in principle, the ability to eliminate cross talk from adjacent tracks. The new coding was compared with direct NRZI by a computer simulation. The coding showed superior characteristics to the NRZI in terms of signal-to-noise ratio (S/N) and bit error rate (BER) for additive and jitter noise. These simulation results were confirmed by experiments. Furthermore, to improve the performance of ITOC, PR4 and integral equalization for wave form equalization were also studied. It was shown that the new coding technique has a high ability to establish high track density recording with neither guard bands nor azimuth, and to realize a collective reading system of multi-track channel signals by a single head or simultaneous reading by array heads. Keywords: Inter-track interference; Orthogonal code; Magnetic recording; Equalization; Collective reading; Multi-track
I. Introduction Submicron-order narrow track recording was examined, claiming that over 10 Gbits/in 2 areal density will be possible [1]. Such narrowed track recording may generate severe problems of intertrack interference [2]. In order to reduce the interference, some methods were proposed based on simultaneous reading of multi-tracks by array heads as shown in Fig. 1 [3-5]. However, proposed methods so far were effective only for small cross talk cases and cannot be applied to a collective
*Corresponding author. Tel.: + 81 188 66 5800; fax: + 81 188 66 5803; e-mail: [email protected].
reading system as shown in Fig. 2 [-6]. We proposed a principal scheme of inter-track orthogonal coding (ITOC) which can effectively reduce the cross talk interference I-7]. However, the coding exhibited a missing error problem caused by the cancellation of opposite sign pulses between the adjacent tracks that was inherent in the use of second-order H a d a m a r d matrix elements. In this paper, an improved I T O C using fourth-order H a d a m a r d matrix elements, which can solve the problem, is described. The performances of the new I T O C are compared with a conventional N R Z I method by computer simulations and experiments. Elimination ability of this I T O C for cross talk from the adjacent tracks is described along with the improvement of the I T O C by wave form equalization.
0304-8853/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S0304-88 53(97)00578-7
A. Kikawada et al. / Journal of Magnetism and Magnetic Materiah" 176 (1997) 66- 72 DATA1 '''11''" I 0 1 0 1 0 1 0 [ ~ ~ I I II | • L--i
67
ex.
write/read heads 1010"~
1
0
""..
,,7,L.j,
"===0
.'/
0
ex..DIAoTA2TRACK2 1 o o 1 o 1 I o
if >0 then "1" if <0 then'0" "". ."DATA1 "".:''"11"'"
p;/[;R~ACK2~]: "~x']'-
I - - "I " "V~lk~.. r"-======~ ^~A._ ~MDD.~'dI~'~',
DATA2 "I 1001 --...a~ 0110
10-1@10-1o ~ ~ [-.'...d~
°, •
,1,
!
:( )-( )-(- ) ( )= from TRACK1 I:0)-(0)+(-I)-(o)=0
.
~
I~£=LL2=L~L~
.,"!DATAZ
if >0 then "I ~ if <0 then °0=
Fig. I. Example configurationof array head system.
Fig. 3. Principal scheme of ITOC using fourth-order Hadamard matrix elements.
write heads read h e a d
Fig. 2. Example configuration of collectivereading system.
gonal relation between signals of adjacent tracks, indicating complete elimination of any cross talk from the adjacent tracks, when the two code sets are used alternately on recording tracks. It is also possible to discriminate the data of each channel even from collectively read signals. If the number of channels is larger than 2, the ITOC could be extended using higher-order Hadamard matrix elements. The extension is simpler than so far proposed coding and signal processing methods. However, in that case, the coding will suffer from further decrease in the code rate.
2. Principle The principal scheme of the present ITOC system for the case of two tracks is shown in Fig. 3. Two orthogonal codes (code 1: 1010, code 2: 1001) from the fourth-order Hadamard matrix elements are used. They are designed in such a way that the occurrence of reproduced pulses with opposite polarities is avoided for adjacent tracks, for which the ambiguity problem caused by the cancellation of the pulses in reproducing [7] is solved. In this ITOC, one data bit contains four code bits and the code ratio is reduced to ¼. Each coded data sequence was modulated as NRZI to form the recording signals. The reproduced signals were processed by the decoding rules (for code 1: D 3 - - D 2 - - D + 1, for code 2 : 0 3 - - D 2 + D -- 1) given by the code and the polarity of the signal. The cross talk from the adjacent tracks always becomes zero in the decoding process because of the ortho-
3. Recording and reproducing model We performed a computer simulation in order to investigate effectiveness of the ITOC. The parameters and conditions were chosen to be almost the same as those of the experiment which will be described later. The reproduced wave form of the magnetic recording and reproducing processes were simulated using a sequence of Lorentzian pulses. We assumed only inter-symbol interference caused by the linear superposition of pulses for the simulation. The number of tracks was limited to two for simplicity, and the cross talk signal was generated using a reproduced signal of the adjacent track. Here, we define the amount of cross talk as the amplitude of the signal induced from the adjacent track. The M-sequence that has the characteristics of pseudo-random-data sequences (PRDS}
68
A. Kikawada et al. / Journal of Magnetism and Magnetic Materials 176 H997) 66 72
was used as the data sequences. The same code sets as those shown in the explanation of the principle were used for the present ITOC. The resulting error rates were compared with those from a conventional direct NRZI modulation process. A data sequence shifted by one bit from the object track was used for the adjacent track data. For the conventional direct NRZI process, an amplitude detection was used and the threshold value was set at half of the peak value of a reproduced isolated pulse. The data rate for ITOC was reduced to ¼ in order to equal the minimum magnetization reversal separation to that of the NRZI. The clock rate was the same in both the recording and the reproducing processes. Here, Tdock is the bit time interval, Tewso is the half-width time of an isolated pulse and Kc ( = Tpw5o/Tclock) represents the normalized linear density. The Sop shows the peak amplitude of an isolated pulse and N r m s shows the rootmean-square value of additive noise. The bandwidth of Nrms was 10/Tpws0. The number of data for measurement of bit error rate was about 30000 bits which was restricted by our computer processing ability and memory capacity. Linear density was chosen to be a low value so that little inter-symbol interference could be expected to investigate the influence of cross talk over a wide range. A longitudinal medium of a hard-disk drive and a ring-type head with 5 gm track width were used for the experiment. The measurement parameters and conditions were almost the same as computer simulations, but self-bit clock synchronization and block synchronization were used in the experiments.
4. Basic characteristics of ITOC The new ITOC process resulted in a three order of magnitude reduction of the bit error rate compared with direct NRZI on the s a m e Sop/Nrm s of 11.5 dB, or provided higher S/N by 6 dB for the additive white Gaussian noise at the same bit error rate as NRZI as shown in Fig. 4. This is because the I T O C uses 4 bits to decode the original data and two-level detection. In general, coding techniques like spread spectrum [8] or trellis
i Exk
..,
I ITOC : , o " ........... !-
,,,~,~___~'~-~ ~,NRZI . .i;,..
~ 10 .6 ........:I:::2: .S:~:
............i::
characterlstlc~ 1 O I12
"
'
0
10 Sop/Nrms[dB]
20
Fig. 4. Comparison of additive noise dependence of bit error rate for I T O C and NRZI. Results of simulation and experiment are plotted along with theoretical curves. (K¢ = Tewso/Tdo¢k = 0.625, no cross talk.)
coding result in the S/N gain [9] at the expense of the linear density. The results of the computer simulation were also in good agreement with the results obtained from a theoretical calculation using error function for the error occurrence probability, which are represented as follows for additive white Gaussian noise: BERNRz, = ~ [ 1 -
err( S ~l, ~\2x~Nrms//J
BER,Toc = ~ [ 1 -
erd-S
\
"~l,
s,JJ
eft(x): error function, where the equation of BER for NRZI is given by a three-level amplitude detection [2], and the equation for ITOC is by a two-level amplitude detection in each decoding process. Experimental results supported the results obtained by the theoretical calculation and the simulation analysis. The difference from the simulation must be caused by lack of preciseness in the bit timing clock in the actual recording channel. Although the present ITOC method reduces the linear density down to ¼ compared to direct NRZI, the ITOC has the possibility to reduce the track width to ¼ at the same bit error rate through
A. Kikawada et al. /Journal of Magnetism and Magnetic Materials 176 (1997) 66 72
aforementioned 6 dB S/N gain. Thus, the loss in the linear density resulting from the orthogonal coding method should be compensated by the increase in the track density. Furthermore, it should be noted that in the I T O C method, no guard bands are necessary because of the sufficient ability to remove the cross talk. The bit error rate increased with increasing the density, Kc, due to the increased inter-symbol interference for the I T O C as well as for the N R Z I as shown in Fig. 5. In the experiment, the results were worse for both the cases in comparison with the simulation results. The increased bit timing clock error due to the decreased S/N in the experiment would be the cause of the performances. The bit error rate remained unchanged for the I T O C for cross talk interference from no cross talk ( ~ ( d B ) ) to the level of cross talk equal to the objective signal (0 dB) as shown in Fig. 6. This was caused by the no cross-correlation property of the signals between adjacent tracks by the orthogonalization in the ITOC. The bit error rate for the I T O C remained unchanged up to 4 ~tm (80%) of off-track in the experiment, which is shown in Fig. 7. It shows the relationship between off-track length and bit error rate. It should be noted that the bit error rate with an adjacent track was lower than that without the adjacent track. This is caused by
i.. i,. ¢1
I
=,,,.,N R Z I i
1 0 "I
,
1 0 .2 I...
=. 10-3
I ITOC
10-4
(code
1, c o d e
2)
j , , ,
0
5
0
15
20
25
30
35
(E0p,TRACKI=I)/Eop.TRACK2 [ d B ] Fig. 6. C o m p a r i s o n of bit e r r o r (Kc = 0.625, Sov/Nrm, = 11.5 dB.)
rate
versus
cross
talk.
10 "°
_¢ 10"1
P oi
10-4 ~ 01 2 3 4 5 6 7 8 O f f t r a c k l e n g t h [ ~ m]
10 "°
.=
69
Fig. 7. Comparison of bit error rate versus off-track length of head. (Open marks: no cross talk, closed marks: with cross talk.)
10 "1 10 .2
,i
10 "a 10 .4 10 "s 0.1
1
10
Kc
Fig. 5. D e p e n d e n c e of bit e r r o r r a t e o f I T O C a n d N R Z I o n l i n e a r density. ( N o c r o s s talk, Sop/N,,~ = 11.5 d b o n s i m u l a t i o n , Sop./Nrrn~ = 21.5 d b o n e x p e r i m e n t . )
the increased number of pulses for the case with the adjacent track. The I T O C was also found to be resistant to timing jitter noise on reproducing as shown in Fig. 8 where the simulation was performed using jitter noise with a Gaussian distribution limited to a half-interval of the timing clock. This is because two-level detection using 4 bits in the I T O C has an averaging effect on the jitter noise. The ITOC, however, exhibited sensitivity to time lag between adjacent tracks on recording. If the time lag becomes large, the ability to eliminate cross talk
A. Kikawada et al. /Journal of Magnetism and Magnetic Materials 176 (1997) 66 72
70
10 "° IN R Z l ~o./N rms=R1.5[OBI 10" ~' i '
5. Improvement by wave form equalization
• i
i.
10"
" / ' ~
f
," 1 o
4 ~ I0"s
"
0
/
..........
....... -i-,.;0 C i:~........ l:;i';.ild =1 B] B]
~ o u t 3 0 0 0
0
20
"SoplNrm$ --]
0
additive noise ~
40
60
80
O IIt/Tpws0[%
I
100
]
Fig. 8. Comparison of bit error rate versus jitter noise for the two coding with and without additive noise. (Kc = 0.625, no cross talk.)
10 "°
OOO~ 10-I
~
•
R Z I e/oOO, , ...........
m I,=
~
!i
,W,o
,
10 "z,
.............. riTOi;
lcode 1
n
.... i
i
ii
i
II1 1 0 -3
10 "4 10 "s -2
i
i
-1
i
i
0
i
2
T l ~ , / (PW~o/2) Fig. 9. Influence of time lag between adjacent (Kc = 0.625, cross talk = 0 dB, Sop/Nrm~ = 11.5 dB.)
tracks.
decreases as shown in Fig. 9. This is a common problem of coding and signal-processing methods for reducing cross talk interference. Higher precision of dish drive motors in recent days could moderate the problem. Simultaneous recording of tracks by array heads would also solve the problem.
Next, we considered the use of wave form equalization in order to improve the efficiency of the ITOC, especially in the linear density. Application of partial response class 4 (PR4) and integral equalization were investigated in the present study. Orthogonal code sets (Code 1: 1010, Code 2: 1111) used for I T O C with PR4 were different from those of NRZI to keep the orthogonal relation through entire recording channel. The ITOC with PR4, however, exhibited a problem that output amplitude after decoding depended on the amount of cross talk for decoding with code 2. For example, the amplitude level after decoding is either level 0 for data '0' or 4 for data '1' without cross talk, but the level becomes 2 for '0' or 6 for '1' with the cross talk of the same amplitude of the object signal. This is because that code 2 has DC components after decoding process. The problem was solved by adjusting the threshold level depending on the amount of cross talk. For integral equalization, data sequences after orthogonal coding were recorded on each track by NRZ without modulation. The orthogonal code sets and decoding rules were the same as those without the equalization. Highpass filters were inserted before the orthogonal decoding process in order to reduce the DC component in the signal. Fig. 10 shows the relationship between S o p / N r m s and bit error rate for PR4 and integral equalizations. ITOC with integral equalization was the best in terms of S o p / N r m s characteristic, and the S/N gain was higher than 6dB due to the integral equalization. ITOC with PR4, however, may not have such a remarkable improvement as the integral equalization when the S/N is low. On the contrary, PR4 was the most effective at higher linear densities in ITOC, which are seen in Fig. 11 as the relationship between linear density and bit error rate. Though the integral equalization was less effective than the PR4 at higher linear densities, it was still better than NRZI using ITOC. Fig. 12 shows the relationship between cross talk and bit error rate. In both of the PR4 and integral equalization for ITOC, the bit error rate had no dependence on the cross talk level. This indicates that ITOC with the wave form equalization holds
A. Kikawada et al. /Journal of Magnetism and Magnetic Materials 176 (1997) 66 72
10 "°
.
_
10 "1
1 O"°
I NO c r o s s t a l k [ Kc=0 .625 _
_
_
_
_
_
[
I
I
"--'I
TOO+P"41/ S/N=11.5dB
[10011
~
~
~
~
'\
11
Kr=0"625
10 "1
ITO 10 .2 ~
NRZ,
_
,
--
71
r
_
®
~k I I T O C + P R 4
[11111
10.=
m,.
®
® ~
10-s
1 0 .3
I
ITOC+NRZ S/N=11.5dB
m
104 I [1°°1]
1 0 .4
L i
1 O ' S / ,
,
I
h
I
0
I
*
I
,
I
,
i
,
i
i
¢
i
i
I
10
i
i
I
~
I
,
,
I
I
10 s
20
I
. . . . . . . . .
0
Sop/Nrms= 11.5dB no crosstalk
10 "°
10"1
O -m'
1 0.2
i.
o
10 .3
m
10 "4
1 0 "s
0.1
1
10
Kc
Fig. 11. Comparison of linear density dependence of bit error rate for ITOC with different equalizations.
the ability to eliminate inter-track interference. The difference in bit error rate between the equalizations came from the difference in frequency characteristics for each equalization.
~ ]
I
! .... i
. . . . . . . . .
,
Large
I
I
JIs/N=12dBI l.[L0t0 ] I
I
i
i
. . . .
10 20 (Eop'rKI=I)/EopTK2 [dB]
Sop/Nrm, [ d B ]
Fig. 10. Comparison of the effects of equalizations on S/N gain for ITOC.
I
ITOC+
Inte~rat Equalization
-,-[I i
I
I
. . . .
l
i
,
30
crosstalk
Fig. 12. Comparison of cross talk dependence of bit error rate for ITOC with different equalizations.
In addition to the above characteristics, ITOC with PR4 suffers from the limitation of code or variation of decoding signals, while integral equalization has some advantages as follows: ITOC with integral equalization allows to use second-order Hadamard matrix elements for two tracks while PR4 requires 4 bit code. Then the code ratio is increased from ¼ to ½ for integral equalization, though the equalization has a minor problem of sensitivity to the DC components. It is known that reproduced signals of double-layered perpendicular media without integral equalization have similar wave forms as of longitudinal media with integral equalization. This would allow us to use reproduced signals without integration circuit, improving the linear density and S/N gain for ITOC. Furthermore, other orthogonal or nearly orthogonal code sets that have higher code ratio are also able to be used for ITOC recording.
6. Conclusions
It is indicated that the proposed ITOC method has advantages over the conventional coding
72
A. Kikawada et a L / Journal of Magnetism and Magnetic Materials 176 (1997) 66- 72
methods for submicron narrow track width recording system where severe cross talk interference from adjacent tracks is unavoidable. Decrease in linear density by the orthogonal coding is compensated by the large S/N gain, and over compensated by the ability of guard band-less recording, suggesting overall gain in areal recording density. Further improvement in recording density is expected by adapting wave form equalization. The ITOC enables to realize not only a simultaneous reading system by array heads but also a multi-track system using collective read with a single head. Stability against jitter noise and ability to obtain position error signal from the data track [10] are also additional advantages of the ITOC.
References [1] Y. Nakamura, H. Muraoka, Y. Shimizu, T. Inaguma, J. Magn. Soc. Japan 18 (S1) (1994) 583. [2] W.J. van Gestel, Publ. Inst. Electron. Radio. Eng. 79 (1988) 35. [3] W.L. Abbott, J.M. Cioffi, H.K. Thapar, IEEE Trans. Magn. 24 (6) (1988) 2964. [4] L.C. Barbosa, IEEE Trans. Magn. 26 (5) (1990) 161. [5] Jaejin Lee, Vijay K. Madisetti, Conf. Rec. IEEE GLOBECOM, vol. 3, 1994, p. 1477. [6] Y. Nakamura, J. Magn. Soc. Japan 18 (S1) (1994) 161. [7] N. Honda, A. Kikawada, K. Ouchi, S. Iwasaki, IEEE Trans. Magn. 31 (6) (1995) 3099. [8] A.J. Viterbi, IRE Trans. Space Electron. Telemet. 7 (1961) 3. [9] K.A.S. Immink, IEEE Trans. Commun. 37 (5) (1989) 413. [10] L. He, N. Honda, K. Ouchi, S. Iwasaki, IEEE Trans. Magn. 32 (5) (1996) 3896.
Journal of Magnetism and Magnetic Materials 176 (1997) 66-72
Journalof magneUsm and magnetic
, d ~ materials
Inter-track interference free coding and equalization A t s u s h i K i k a w a d a a'*, N a o k i
H o n d a a, K a z u h i r o
O u c h i a, S h u n - i c h i I w a s a k i b
"Akita Research Institute of Advanced Technology, 4-21 Sanuki Araya. Akita 010-16, Japan b Tohoku Institute of Technology, Sendai 982, Japan
Abstract A new coding technique using improved inter-track orthogonal coding (ITOC) was proposed for high track density and/or multi-track recording. The coding has, in principle, the ability to eliminate cross talk from adjacent tracks. The new coding was compared with direct NRZI by a computer simulation. The coding showed superior characteristics to the NRZI in terms of signal-to-noise ratio (S/N) and bit error rate (BER) for additive and jitter noise. These simulation results were confirmed by experiments. Furthermore, to improve the performance of ITOC, PR4 and integral equalization for wave form equalization were also studied. It was shown that the new coding technique has a high ability to establish high track density recording with neither guard bands nor azimuth, and to realize a collective reading system of multi-track channel signals by a single head or simultaneous reading by array heads. Keywords: Inter-track interference; Orthogonal code; Magnetic recording; Equalization; Collective reading; Multi-track
I. Introduction Submicron-order narrow track recording was examined, claiming that over 10 Gbits/in 2 areal density will be possible [1]. Such narrowed track recording may generate severe problems of intertrack interference [2]. In order to reduce the interference, some methods were proposed based on simultaneous reading of multi-tracks by array heads as shown in Fig. 1 [3-5]. However, proposed methods so far were effective only for small cross talk cases and cannot be applied to a collective
*Corresponding author. Tel.: + 81 188 66 5800; fax: + 81 188 66 5803; e-mail: [email protected].
reading system as shown in Fig. 2 [-6]. We proposed a principal scheme of inter-track orthogonal coding (ITOC) which can effectively reduce the cross talk interference I-7]. However, the coding exhibited a missing error problem caused by the cancellation of opposite sign pulses between the adjacent tracks that was inherent in the use of second-order H a d a m a r d matrix elements. In this paper, an improved I T O C using fourth-order H a d a m a r d matrix elements, which can solve the problem, is described. The performances of the new I T O C are compared with a conventional N R Z I method by computer simulations and experiments. Elimination ability of this I T O C for cross talk from the adjacent tracks is described along with the improvement of the I T O C by wave form equalization.
0304-8853/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S0304-88 53(97)00578-7
A. Kikawada et al. / Journal of Magnetism and Magnetic Materiah" 176 (1997) 66- 72 DATA1 '''11''" I 0 1 0 1 0 1 0 [ ~ ~ I I II | • L--i
67
ex.
write/read heads 1010"~
1
0
""..
,,7,L.j,
"===0
.'/
0
ex..DIAoTA2TRACK2 1 o o 1 o 1 I o
if >0 then "1" if <0 then'0" "". ."DATA1 "".:''"11"'"
p;/[;R~ACK2~]: "~x']'-
I - - "I " "V~lk~.. r"-======~ ^~A._ ~MDD.~'dI~'~',
DATA2 "I 1001 --...a~ 0110
10-1@10-1o ~ ~ [-.'...d~
°, •
,1,
!
:( )-( )-(- ) ( )= from TRACK1 I:0)-(0)+(-I)-(o)=0
.
~
I~£=LL2=L~L~
.,"!DATAZ
if >0 then "I ~ if <0 then °0=
Fig. I. Example configurationof array head system.
Fig. 3. Principal scheme of ITOC using fourth-order Hadamard matrix elements.
write heads read h e a d
Fig. 2. Example configuration of collectivereading system.
gonal relation between signals of adjacent tracks, indicating complete elimination of any cross talk from the adjacent tracks, when the two code sets are used alternately on recording tracks. It is also possible to discriminate the data of each channel even from collectively read signals. If the number of channels is larger than 2, the ITOC could be extended using higher-order Hadamard matrix elements. The extension is simpler than so far proposed coding and signal processing methods. However, in that case, the coding will suffer from further decrease in the code rate.
2. Principle The principal scheme of the present ITOC system for the case of two tracks is shown in Fig. 3. Two orthogonal codes (code 1: 1010, code 2: 1001) from the fourth-order Hadamard matrix elements are used. They are designed in such a way that the occurrence of reproduced pulses with opposite polarities is avoided for adjacent tracks, for which the ambiguity problem caused by the cancellation of the pulses in reproducing [7] is solved. In this ITOC, one data bit contains four code bits and the code ratio is reduced to ¼. Each coded data sequence was modulated as NRZI to form the recording signals. The reproduced signals were processed by the decoding rules (for code 1: D 3 - - D 2 - - D + 1, for code 2 : 0 3 - - D 2 + D -- 1) given by the code and the polarity of the signal. The cross talk from the adjacent tracks always becomes zero in the decoding process because of the ortho-
3. Recording and reproducing model We performed a computer simulation in order to investigate effectiveness of the ITOC. The parameters and conditions were chosen to be almost the same as those of the experiment which will be described later. The reproduced wave form of the magnetic recording and reproducing processes were simulated using a sequence of Lorentzian pulses. We assumed only inter-symbol interference caused by the linear superposition of pulses for the simulation. The number of tracks was limited to two for simplicity, and the cross talk signal was generated using a reproduced signal of the adjacent track. Here, we define the amount of cross talk as the amplitude of the signal induced from the adjacent track. The M-sequence that has the characteristics of pseudo-random-data sequences (PRDS}
68
A. Kikawada et al. / Journal of Magnetism and Magnetic Materials 176 H997) 66 72
was used as the data sequences. The same code sets as those shown in the explanation of the principle were used for the present ITOC. The resulting error rates were compared with those from a conventional direct NRZI modulation process. A data sequence shifted by one bit from the object track was used for the adjacent track data. For the conventional direct NRZI process, an amplitude detection was used and the threshold value was set at half of the peak value of a reproduced isolated pulse. The data rate for ITOC was reduced to ¼ in order to equal the minimum magnetization reversal separation to that of the NRZI. The clock rate was the same in both the recording and the reproducing processes. Here, Tdock is the bit time interval, Tewso is the half-width time of an isolated pulse and Kc ( = Tpw5o/Tclock) represents the normalized linear density. The Sop shows the peak amplitude of an isolated pulse and N r m s shows the rootmean-square value of additive noise. The bandwidth of Nrms was 10/Tpws0. The number of data for measurement of bit error rate was about 30000 bits which was restricted by our computer processing ability and memory capacity. Linear density was chosen to be a low value so that little inter-symbol interference could be expected to investigate the influence of cross talk over a wide range. A longitudinal medium of a hard-disk drive and a ring-type head with 5 gm track width were used for the experiment. The measurement parameters and conditions were almost the same as computer simulations, but self-bit clock synchronization and block synchronization were used in the experiments.
4. Basic characteristics of ITOC The new ITOC process resulted in a three order of magnitude reduction of the bit error rate compared with direct NRZI on the s a m e Sop/Nrm s of 11.5 dB, or provided higher S/N by 6 dB for the additive white Gaussian noise at the same bit error rate as NRZI as shown in Fig. 4. This is because the I T O C uses 4 bits to decode the original data and two-level detection. In general, coding techniques like spread spectrum [8] or trellis
i Exk
..,
I ITOC : , o " ........... !-
,,,~,~___~'~-~ ~,NRZI . .i;,..
~ 10 .6 ........:I:::2: .S:~:
............i::
characterlstlc~ 1 O I12
"
'
0
10 Sop/Nrms[dB]
20
Fig. 4. Comparison of additive noise dependence of bit error rate for I T O C and NRZI. Results of simulation and experiment are plotted along with theoretical curves. (K¢ = Tewso/Tdo¢k = 0.625, no cross talk.)
coding result in the S/N gain [9] at the expense of the linear density. The results of the computer simulation were also in good agreement with the results obtained from a theoretical calculation using error function for the error occurrence probability, which are represented as follows for additive white Gaussian noise: BERNRz, = ~ [ 1 -
err( S ~l, ~\2x~Nrms//J
BER,Toc = ~ [ 1 -
erd-S
\
"~l,
s,JJ
eft(x): error function, where the equation of BER for NRZI is given by a three-level amplitude detection [2], and the equation for ITOC is by a two-level amplitude detection in each decoding process. Experimental results supported the results obtained by the theoretical calculation and the simulation analysis. The difference from the simulation must be caused by lack of preciseness in the bit timing clock in the actual recording channel. Although the present ITOC method reduces the linear density down to ¼ compared to direct NRZI, the ITOC has the possibility to reduce the track width to ¼ at the same bit error rate through
A. Kikawada et al. /Journal of Magnetism and Magnetic Materials 176 (1997) 66 72
aforementioned 6 dB S/N gain. Thus, the loss in the linear density resulting from the orthogonal coding method should be compensated by the increase in the track density. Furthermore, it should be noted that in the I T O C method, no guard bands are necessary because of the sufficient ability to remove the cross talk. The bit error rate increased with increasing the density, Kc, due to the increased inter-symbol interference for the I T O C as well as for the N R Z I as shown in Fig. 5. In the experiment, the results were worse for both the cases in comparison with the simulation results. The increased bit timing clock error due to the decreased S/N in the experiment would be the cause of the performances. The bit error rate remained unchanged for the I T O C for cross talk interference from no cross talk ( ~ ( d B ) ) to the level of cross talk equal to the objective signal (0 dB) as shown in Fig. 6. This was caused by the no cross-correlation property of the signals between adjacent tracks by the orthogonalization in the ITOC. The bit error rate for the I T O C remained unchanged up to 4 ~tm (80%) of off-track in the experiment, which is shown in Fig. 7. It shows the relationship between off-track length and bit error rate. It should be noted that the bit error rate with an adjacent track was lower than that without the adjacent track. This is caused by
i.. i,. ¢1
I
=,,,.,N R Z I i
1 0 "I
,
1 0 .2 I...
=. 10-3
I ITOC
10-4
(code
1, c o d e
2)
j , , ,
0
5
0
15
20
25
30
35
(E0p,TRACKI=I)/Eop.TRACK2 [ d B ] Fig. 6. C o m p a r i s o n of bit e r r o r (Kc = 0.625, Sov/Nrm, = 11.5 dB.)
rate
versus
cross
talk.
10 "°
_¢ 10"1
P oi
10-4 ~ 01 2 3 4 5 6 7 8 O f f t r a c k l e n g t h [ ~ m]
10 "°
.=
69
Fig. 7. Comparison of bit error rate versus off-track length of head. (Open marks: no cross talk, closed marks: with cross talk.)
10 "1 10 .2
,i
10 "a 10 .4 10 "s 0.1
1
10
Kc
Fig. 5. D e p e n d e n c e of bit e r r o r r a t e o f I T O C a n d N R Z I o n l i n e a r density. ( N o c r o s s talk, Sop/N,,~ = 11.5 d b o n s i m u l a t i o n , Sop./Nrrn~ = 21.5 d b o n e x p e r i m e n t . )
the increased number of pulses for the case with the adjacent track. The I T O C was also found to be resistant to timing jitter noise on reproducing as shown in Fig. 8 where the simulation was performed using jitter noise with a Gaussian distribution limited to a half-interval of the timing clock. This is because two-level detection using 4 bits in the I T O C has an averaging effect on the jitter noise. The ITOC, however, exhibited sensitivity to time lag between adjacent tracks on recording. If the time lag becomes large, the ability to eliminate cross talk
A. Kikawada et al. /Journal of Magnetism and Magnetic Materials 176 (1997) 66 72
70
10 "° IN R Z l ~o./N rms=R1.5[OBI 10" ~' i '
5. Improvement by wave form equalization
• i
i.
10"
" / ' ~
f
," 1 o
4 ~ I0"s
"
0
/
..........
....... -i-,.;0 C i:~........ l:;i';.ild =1 B] B]
~ o u t 3 0 0 0
0
20
"SoplNrm$ --]
0
additive noise ~
40
60
80
O IIt/Tpws0[%
I
100
]
Fig. 8. Comparison of bit error rate versus jitter noise for the two coding with and without additive noise. (Kc = 0.625, no cross talk.)
10 "°
OOO~ 10-I
~
•
R Z I e/oOO, , ...........
m I,=
~
!i
,W,o
,
10 "z,
.............. riTOi;
lcode 1
n
.... i
i
ii
i
II1 1 0 -3
10 "4 10 "s -2
i
i
-1
i
i
0
i
2
T l ~ , / (PW~o/2) Fig. 9. Influence of time lag between adjacent (Kc = 0.625, cross talk = 0 dB, Sop/Nrm~ = 11.5 dB.)
tracks.
decreases as shown in Fig. 9. This is a common problem of coding and signal-processing methods for reducing cross talk interference. Higher precision of dish drive motors in recent days could moderate the problem. Simultaneous recording of tracks by array heads would also solve the problem.
Next, we considered the use of wave form equalization in order to improve the efficiency of the ITOC, especially in the linear density. Application of partial response class 4 (PR4) and integral equalization were investigated in the present study. Orthogonal code sets (Code 1: 1010, Code 2: 1111) used for I T O C with PR4 were different from those of NRZI to keep the orthogonal relation through entire recording channel. The ITOC with PR4, however, exhibited a problem that output amplitude after decoding depended on the amount of cross talk for decoding with code 2. For example, the amplitude level after decoding is either level 0 for data '0' or 4 for data '1' without cross talk, but the level becomes 2 for '0' or 6 for '1' with the cross talk of the same amplitude of the object signal. This is because that code 2 has DC components after decoding process. The problem was solved by adjusting the threshold level depending on the amount of cross talk. For integral equalization, data sequences after orthogonal coding were recorded on each track by NRZ without modulation. The orthogonal code sets and decoding rules were the same as those without the equalization. Highpass filters were inserted before the orthogonal decoding process in order to reduce the DC component in the signal. Fig. 10 shows the relationship between S o p / N r m s and bit error rate for PR4 and integral equalizations. ITOC with integral equalization was the best in terms of S o p / N r m s characteristic, and the S/N gain was higher than 6dB due to the integral equalization. ITOC with PR4, however, may not have such a remarkable improvement as the integral equalization when the S/N is low. On the contrary, PR4 was the most effective at higher linear densities in ITOC, which are seen in Fig. 11 as the relationship between linear density and bit error rate. Though the integral equalization was less effective than the PR4 at higher linear densities, it was still better than NRZI using ITOC. Fig. 12 shows the relationship between cross talk and bit error rate. In both of the PR4 and integral equalization for ITOC, the bit error rate had no dependence on the cross talk level. This indicates that ITOC with the wave form equalization holds
A. Kikawada et al. /Journal of Magnetism and Magnetic Materials 176 (1997) 66 72
10 "°
.
_
10 "1
1 O"°
I NO c r o s s t a l k [ Kc=0 .625 _
_
_
_
_
_
[
I
I
"--'I
TOO+P"41/ S/N=11.5dB
[10011
~
~
~
~
'\
11
Kr=0"625
10 "1
ITO 10 .2 ~
NRZ,
_
,
--
71
r
_
®
~k I I T O C + P R 4
[11111
10.=
m,.
®
® ~
10-s
1 0 .3
I
ITOC+NRZ S/N=11.5dB
m
104 I [1°°1]
1 0 .4
L i
1 O ' S / ,
,
I
h
I
0
I
*
I
,
I
,
i
,
i
i
¢
i
i
I
10
i
i
I
~
I
,
,
I
I
10 s
20
I
. . . . . . . . .
0
Sop/Nrms= 11.5dB no crosstalk
10 "°
10"1
O -m'
1 0.2
i.
o
10 .3
m
10 "4
1 0 "s
0.1
1
10
Kc
Fig. 11. Comparison of linear density dependence of bit error rate for ITOC with different equalizations.
the ability to eliminate inter-track interference. The difference in bit error rate between the equalizations came from the difference in frequency characteristics for each equalization.
~ ]
I
! .... i
. . . . . . . . .
,
Large
I
I
JIs/N=12dBI l.[L0t0 ] I
I
i
i
. . . .
10 20 (Eop'rKI=I)/EopTK2 [dB]
Sop/Nrm, [ d B ]
Fig. 10. Comparison of the effects of equalizations on S/N gain for ITOC.
I
ITOC+
Inte~rat Equalization
-,-[I i
I
I
. . . .
l
i
,
30
crosstalk
Fig. 12. Comparison of cross talk dependence of bit error rate for ITOC with different equalizations.
In addition to the above characteristics, ITOC with PR4 suffers from the limitation of code or variation of decoding signals, while integral equalization has some advantages as follows: ITOC with integral equalization allows to use second-order Hadamard matrix elements for two tracks while PR4 requires 4 bit code. Then the code ratio is increased from ¼ to ½ for integral equalization, though the equalization has a minor problem of sensitivity to the DC components. It is known that reproduced signals of double-layered perpendicular media without integral equalization have similar wave forms as of longitudinal media with integral equalization. This would allow us to use reproduced signals without integration circuit, improving the linear density and S/N gain for ITOC. Furthermore, other orthogonal or nearly orthogonal code sets that have higher code ratio are also able to be used for ITOC recording.
6. Conclusions
It is indicated that the proposed ITOC method has advantages over the conventional coding
72
A. Kikawada et a L / Journal of Magnetism and Magnetic Materials 176 (1997) 66- 72
methods for submicron narrow track width recording system where severe cross talk interference from adjacent tracks is unavoidable. Decrease in linear density by the orthogonal coding is compensated by the large S/N gain, and over compensated by the ability of guard band-less recording, suggesting overall gain in areal recording density. Further improvement in recording density is expected by adapting wave form equalization. The ITOC enables to realize not only a simultaneous reading system by array heads but also a multi-track system using collective read with a single head. Stability against jitter noise and ability to obtain position error signal from the data track [10] are also additional advantages of the ITOC.
References [1] Y. Nakamura, H. Muraoka, Y. Shimizu, T. Inaguma, J. Magn. Soc. Japan 18 (S1) (1994) 583. [2] W.J. van Gestel, Publ. Inst. Electron. Radio. Eng. 79 (1988) 35. [3] W.L. Abbott, J.M. Cioffi, H.K. Thapar, IEEE Trans. Magn. 24 (6) (1988) 2964. [4] L.C. Barbosa, IEEE Trans. Magn. 26 (5) (1990) 161. [5] Jaejin Lee, Vijay K. Madisetti, Conf. Rec. IEEE GLOBECOM, vol. 3, 1994, p. 1477. [6] Y. Nakamura, J. Magn. Soc. Japan 18 (S1) (1994) 161. [7] N. Honda, A. Kikawada, K. Ouchi, S. Iwasaki, IEEE Trans. Magn. 31 (6) (1995) 3099. [8] A.J. Viterbi, IRE Trans. Space Electron. Telemet. 7 (1961) 3. [9] K.A.S. Immink, IEEE Trans. Commun. 37 (5) (1989) 413. [10] L. He, N. Honda, K. Ouchi, S. Iwasaki, IEEE Trans. Magn. 32 (5) (1996) 3896.