JPH1166755A - Vertical magnetic recording and reproducing system and magnetic recording and reproducing device adopting it - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain excellent SN ratio and a large normalized line density by using (1, 7) RLL encoded system and positive coefficient PRML method as a recording and reproducing system in a vertical magnetic recording using an MR head for a double layer medium for perpendicular recording and for reproducing. SOLUTION: ak '} is a binary input data system of '1' and '0' inputted at each bit interval Tb , bk } is (1, 7) RLL or 8/9 encoding system, and ck } is a precoder output system. In the case of (1, 7) RLL code, the precoder is inserted for NRZI-recording, and there is a relation of Ck =bk +Ck-1 (mod 2) between bk } and ck }. When an estimate value of the precoder output system ck } is assumed to be ck }, the output system bk } of a post coder by an inverse- precoding operation has a relation of bk =ck +ck-1 (mod 2) for (1, 7) RLL code.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a perpendicular magnetic recording / reproducing system and a magnetic recording / reproducing apparatus using the same. More specifically, in a perpendicular magnetic recording using a dual-layer medium for perpendicular recording and an MR head for reproduction, a perpendicular magnetic recording / reproducing method capable of obtaining an excellent SN ratio and a large normalized linear density, and a magnetic recording using the same. It relates to a playback device.

[0002]

2. Description of the Related Art Recently, studies on high-density recording using a combination of a high-sensitivity MR head and a perpendicular medium having a high recording resolution have been actively conducted ("Journal of the Japan Society of Applied Magnetics 19, supple").
ment, S2, pp. 117-121, 1995 "," Journal of the Japan Society of Applied Magnetics 19, supplement, S2, pp. 122-125, 1995 ",
"5th Perpendicular Magnetic Recording Symposium Material, pp.115-11
9 Oct. 1996 ”,“ 5th Perpendicular Magnetic Recording Symposium Material, pp. 124-128 Oct. 1996 ”). P in longitudinal record
Although the study of the RML (Partial Response Maximum-Likelihood) method has been widely performed, the study of the PRML method with respect to the combination with the MR head in perpendicular recording is only for a single-layer film medium. Has not been done yet ("Journal of the Japan Society of Applied Magnetics 19, S2,
pp. 28-33, 1995 ”).

Therefore, as a method for high-density recording using an MR head and a two-layer perpendicular recording medium, a recording / reproducing method having excellent S / N characteristics and a large standardized linear density has not been found at present. .

[0004]

SUMMARY OF THE INVENTION The present invention provides an excellent SN
It is an object of the present invention to provide a recording / reproducing method for a high-density recording medium having a high ratio and a high standardized linear density.

[0005]

SUMMARY OF THE INVENTION The gist of the present invention is to provide a (1,7) RLL encoding method and a positive coefficient as a recording / reproducing method in perpendicular magnetic recording using a dual-layer medium for perpendicular recording and an MR head for reproducing. There is a perpendicular magnetic recording / reproducing method characterized by using the PRML method.

[0006]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The embodiments of the present invention will be described below together with the knowledge obtained when making the present invention, the operation thereof, and the like.

It is known that the readout waveform at the read point in the case of a combination of a perpendicular double-layered film medium and an MR head is a rectangular waveform corresponding to the recording magnetization distribution ("Journal of the Japan Society of Applied Magnetics 19, supplement, S2, pp. 117-121, 199
5 "," Journal of the Japan Society of Applied Magnetics 19, supplement, S2, pp.
122-125, 1995 ").

[0008] In the case of longitudinal recording having a dipulse reproduction waveform, the recording / reproduction system has differential characteristics.
(1, 0, -1) ML (commonly known as PR4ML), PR (1,
1, -1, -1) ML (commonly known as EPR4ML), PR
(1, 2, 0, -2, -1) ML (commonly known as E ² PR4 M
L), PR (1,1,0, -1, -1) ML (commonly known as ME
² PRML) and other polynomials with negative coefficients
The ML method shows good characteristics.

On the other hand, in the case of perpendicular recording (for example, a combination of a perpendicular double-layer film medium and an MR head) showing a rectangular waveform, a PR (1,1) ML, PR (1,
2,1) ML, PR (1,3,1) ML, PR (1,
It is expected that the PRML system represented by a positive coefficient polynomial such as (2, 2, 1) ML and PR (1, 3, 3, 1) will exhibit good characteristics. As the recording code, an 8/9 code and a (1,7) RLL code can be considered (see “IEICE Technical Report, MR
95-61, Dec. 1995 ”), the minimum value d of the Euclidean distance between the decoder input sequences is determined by the Viterbi decoding method using the run length constraint of the (1,7) RLL code for the PRML method of the positive coefficient. _{The min} can be made larger than in the case of the 8/9 code, and the improvement effect by this can be expected. On the other hand, as in the case of the conventional longitudinal recording, when the PRML method of the negative coefficient is adopted, it is considered that the 8/9 code having a larger coding rate is more advantageous.

Therefore, the present inventor has proposed (1, 1) in perpendicular magnetic recording using an MR head and a perpendicular double-layered medium.
7) PR (1,1) is used as the RLL-encoded PRML system.
ML, PR (1, 2, 1) ML, PR (1, 3, 1) M
L, PR (1, 2, 2, 1) ML, PR (1, 3, 3,
1) When the ML system is an 8/9 encoded PRML system,
^{R4ML, EPR4ML, E 2 PR4ML,} ME 2 PR4
Bit error rate when ML method is adopted (commonly known as BER)
Characteristics were determined and compared.

Furthermore, these Ps for the PR4ML system
The relationship between the degree of improvement in the SN ratio of the RML system and the normalized linear density was examined.

The details will be described below.

(Recording / Reproducing System Model) FIG. 1 shows a perpendicular magnetic recording using an MR head and a perpendicular double-layered medium.
(1,7) RLL coded PRML system or 8/9
1 shows a block diagram of a recording / reproducing system of an encoded PRML system. Here, {a _{k '}} is a binary input data sequence is entered for each bit interval _{T b "1", "0} ", {b k} are (1, 7) RLL or 8/9 code Series, {c _k }
Is a precoder output sequence. In the case of the (1,7) RLL code, the precoder is inserted to perform NRZI recording, and the following relationship holds between {b _k } and {c _k }. c _k = b _k + c _k-1 (mod 2) (1) The 8/9 code uses a (0, 4/4) code.
Assume that the precoder of each PRML system for the 8/9 code is as shown in Table 1.

[0014]

[Table 1]

Table 1 also shows the maximum run length of “0” in the equalizer output sequence {d _k }. This allows
Since the maximum run length in the equalizer output sequence is limited as shown in Table 1, stable clock reproduction and gain control can be performed. In the case of the 8/9 code, NRZ recording is performed using the precoder output sequence {c _k }.

It is known that the reproduction waveform at the read point in the case of the combination of the perpendicular double-layer film medium and the MR head is a rectangular waveform corresponding to the recording magnetization distribution, and the differential waveform is a dipulse shape as in the case of the longitudinal recording. Have been.

[0017] Now, differential waveform g of height 1, read point signal waveform g width for equal recording waveform to the symbol interval _{T s (t) '(t} ) = h' (t) -h '(t- T _s ) (2), let h ′ (t) be represented by a Lorentzian waveform such as h ′ (t) = B / {1+ (2t / T ₅₀ ) ² } (3) where B and T ₅₀ are the peak value and half width of the Lorentzian waveform, respectively. Equation (2), by integrating the (3), g (t) = {A / 2tan -1 (η c / K p)} · [tan -1 {2η c t / K p T s} -tan ^-1 {2η _c (t−T _s ) / K _p T _s }] (4). However, A is the peak value of g (t), when the T _b and bit _{interval, η c = T s / T} b, K p = T 50 / T
_b is a coding rate and a normalized linear density, respectively. (1,
7) the case where η _c = 2 / 3,8 / 9 code RLL code η _c = 8/9.

[0018] The noise of the read points, the average is 0, both sides power spectral density is assumed white Gaussian noise N _0/2,
It is assumed that the transfer characteristic of the equalizer is determined so that the transfer characteristic from the recording head to the output of the equalizer has a desired partial response (PR) characteristic. That is, PR (u ₀ ,
u ₁ , u ₂ ,..., u _L-1 ), the equalizer output waveform w (t) for the equation (4) is The transfer characteristic of the equalizer may be determined so that Here, r (t) is a Nyquist waveform having a roll-off rate β, an intersymbol interference amount, and a parameter η for adjusting the bandwidth of the equalizer, and r (t) = [{sin (πt / ηT _b )} / (Πt / ηT _b )] · [{cos (πβt / ηT _b )} / {1- (2βt / ηT _b ) ² }] (6) As η increases, the amount of intersymbol interference increases, but the bandwidth and the resulting noise intensity at the discrimination point decrease.

The transfer function E (x) of the equalizer is given by the following equation (4).
Obtained by taking the ratio of the Fourier transform of (5), It is expressed as Here, X is a frequency normalized by the bit rate f _b , R (x) is a Fourier transform of f _b r (t), and R (x) = η: | x | <(1-β) / 2η = (η / 2) {1−sin (ηπ / β) (| x | −1 / 2η)｝ = 0: given by | x | ≧ (1 + β) / 2η (8)

[0020] In the formula (7), P having a negative coefficient u _m
R system, for example, PR4ML, EPR4ML, E ² PR4
E (x) in the case of ML, ME ² PR4ML, etc. is the transfer function of these PRML systems in conventional longitudinal magnetic recording (see “Research on IEICE, J79-C-II, 7, pp.366-375, July 199”).
6 ") multiplied by a transfer function x as a differentiator. Therefore, these PRs in perpendicular magnetic recording
It is considered that equalization of the system is equivalent to performing PR equalization of longitudinal magnetic recording after performing differential equalization.

In FIG. 1, when the estimated value of the precoder output sequence {c _k } is {c _k }, the post-coder output sequence {b _k } by the inverse precoding operation is shown.
Is expressed as ＾ b _k = ＾ c _k + ＾ c _k-1 (mod 2) (9) in the case of (1,7) RLL code. Table 2 shows the postcoder of each PRML system for the 8/9 code. The Viterbi decoder can take these post-coding operations into account.
{B _k } is decoded by a (1,7) RLL or 8/9 decoder to give an output data sequence {a _{k ′} }.

[0022]

[Table 2]

(Identification Point Signal Waveform) The identification point signal waveform y (t) for the precoder output sequence {c _k } is Can be expressed as

After the input data sequence generated by the M-sequence is (1,7) RLL-coded or 8 / 9-coded, a precoder output sequence is obtained from Equation (1) and Table 1, and is obtained by using Equation (10). The calculated (1,7) RLL code and 8/9
FIGS. 2 and 3 show eye patterns of each PRML system for codes.
Are shown below.

FIG. 2 shows the P for the (1,7) RLL code.
R (1,1) ML, PR (1,2,1) ML, PR
(1,3,1) ML, PR (1,2,2,1) ML, P
R (1, 3, 3, 1) ML, PR (1, 2, 3, 2,
1) The eye pattern of each system of ML is shown in FIG. 3 as PR4ML, EPR4ML, and E ² PR4M for 8/9 code.
L, shows the eye pattern of the type of ME ² PR4ML.
Here, β = 0.5 and η _opt are set. Where η = η
_opt is an optimal value of η that minimizes the bit error rate.
Each eye pattern is obtained by multiplying e ₀ / e ₁ so that the median value e ₁ of the maximum signal level at t = kT _s matches the maximum signal level e ₀ at η = η _c. Standardized.

As shown in the figure, the inter-symbol interference of the eye pattern in the case of the (1,7) RLL code is larger than that of the eye pattern in the case of the 8/9 code. This is (1,7) RL compared to the case of the 8/9 code.
This is because the difference between η _opt and η _c is larger in the case of the L code. On the other hand, regarding the timing margin,
The (1,7) RLL code is larger than in the case of 8/9.

(Distinction point noise power) Discrimination point noise power σ
^2, N ₀ using equation (7) | obtained by integrating the ^{2/2, | E (x} ) Becomes Where N (x) is the one-sided noise power spectral density at the discrimination point, It is. Here, a = A / (N ₀ f _b ) ^1/2 is the S / N ratio at the readout point and is defined as the ratio between the peak value of g (t) and the rms value of noise in a bandwidth equal to f _b. You.

FIGS. 4 and 6 show the discrimination point noise power spectrum of each PRML system for the (1, 7) RLL code and FIGS. 5 and 7 for the 8/9 code. However, β = 0.
5, and η = η _opt. Generally, the half width of the differentiated waveform h '(t) in perpendicular recording is smaller than the half width of the isolated reproduction waveform in longitudinal recording. 4 and 5 show that K _p = 1.5
6 and FIG. 7 show the results when K _p = 2.5, respectively.

Each spectrum is normalized by multiplying by (e ₀ / e ₁ ) ² in accordance with the specification of the eye pattern level in FIGS. 2 and 3 by e ₀ / e ₁ .

FIGS. 4 and 5 show that the noise spectrum of the discrimination point is smaller in the case of the (1,7) RLL code than in the case of the 8/9 code as a whole. It was found that the noise component was also small. This is because the former η _opt is larger than the latter. Of the (1,7) RLL codes shown in FIG. 4, PR (1,1) ML
The noise power spectrum of the scheme is minimized and then PR
(1, 2, 1) ML, PR (1, 2, 2, 1) ML, P
The R (1, 3, 1) ML and PR (1, 3, 3, 1) ML systems are in order. Further, among the 8/9 codes shown in FIG. 5, the noise power spectrum of ME ² PR4ML is minimized, and then PR4 ML, EPR4ML, and E ² PR
The order is the 4ML system.

FIGS. 6 and 7 show that (1,7) RL
The discrimination point noise power spectrum and the high frequency noise component for the L code are generally smaller than those for the 8/9 code, and the value of η _opt for the (1,7) RLL code is smaller for the 8/9 code. Because it is bigger than the one,
Equalizer bandwidth for (1,7) RLL code is 8/9
It turned out to be narrower than that for the sign.

(PRML system) A Viterbi decoder input signal sequence {d _k } is obtained by sampling equation (10) for each T _s , and d _k = y (kT _s ) = _{ (2c _i − 1) w {(ki) T _s } (13) ⁱ

On the other hand, the Viterbi decoder input noise sequence {n _k }
Is colored noise determined by the transfer function of the equalizer, and can be obtained by superimposing the white noise sequence at the readout point and the impulse response of the equalizer.

Here, P for the (1,7) RLL code
The PR (1, 2, 2, 1) ML system will be described as an example of the RML system. In the case of the (1,7) RLL code, the run length of “0” or “1” in the precoder output sequence {c _k } is limited to 2 to 8. Therefore,
The sequence “010”, “101” does not appear in {c _k }. Considering this, PR (1,2,2,1)
For ML method, the state at time t = kT _s can be determined as shown in Table 3.

[0035]

[Table 3]

From the equations (5), (6), and (13), the input signal sequence {d _k } of Viterbi decoder when η = η _c is d _k = c _k + 2c _k−1 + 2c _k−2 + c _k−3 −3 (14) Using this, and further considering the above-mentioned run length constraint, the state transition table of the Viterbi decoder is as shown in Table 4.
PR (1, 2, 2, 1) for (1,7) RLL code
The ML Viterbi decoder can be configured based on Table 4.

[0037]

[Table 4]

As described above, by using the run length constraint in the case of the (1,7) RLL code, the number of states can be reduced from eight to six, and the Viterbi decoder can be simplified. In the case of the (1,7) RLL code, the run length constraint is P
R (1,2,2,1) ML ACS (Add Compare
Select) also has the effect of reducing the number from eight to four. Therefore, in Table 4, the number of ACS (Add Compare Select) of the PR (1, 2, 2, 1) ML system is described as 4. Other P
Similarly, the RML method can be simplified.
(1,3,3,1) ML, PR (1,2,1) ML, P
The number of states in the R (1,3,1) ML and PR (1,1) ML systems is 6, 4, 4, and 2, respectively.

Furthermore, another important effect of the run length constraint in the case of (1,7) RLL codes is that the minimum value d of the Euclidean distance d between all possible series of {d _k } sequences
Increasing _min results in improved BER performance. For other PRML systems, (1,7) RL
Similar to the run length constraint of the L code, a Viterbi decoder can be formed.

The ACS numbers are 4, 2, 2,
It becomes 2. FIG. 8 shows the PR (1, 2, 2) obtained from Table 4.
2, 1) A trellis diagram of the ML Viterbi decoder is shown. Incidentally, the value assigned to the branches in the figure represents a c _k / d _k. A metric is obtained by expressing the length of a branch on the trellis diagram by a negative log likelihood function.

The minimum value is determined based on this metric, and the maximum likelihood sequence {c _k } is obtained by tracing the surviving path back. Further, the (1,7) RLL decoder input sequence {b _k } is obtained by the operation of Expression (9).

On the other hand, in the case of the 8/9 code, (1,7) RL
There is no reduction in the number of states of the Viterbi decoder due to the run length constraint such as the L code, and the length of the response constrained by the PR scheme, ie, PR (u ₀ , u ₁ , u ₂ ,..., U _{N -1)} ) Using the number N of u _k in the description ML requires 2 ^{N -1} states. Therefore, ME ² PR4ML, E ² PR4ML,
The number of states in the EPR4ML and PR4ML systems is 1 each.
6, 16, 8, and 4. Also, the number of ACSs is required to be the same as the number of states.

Therefore, P for the (1,7) RLL code
R (1,2,1) ML, PR (1,2,2,1) ML,
PR (1,3,3,1) ML method, as the number of states as compared to the PRML method and the number of ACS is reduced for 8/9 code, a large (d _{mi n)} ² is obtained.

(Comparison of Performance) FIGS. 9 and 10 show (1,7) RLL obtained by computer simulation.
The bit error rate (BER) characteristics of each PRML system for the code and the 8/9 code are shown. However, FIG. 9 shows K _p = 1.5,
If β = 0.5 and η = η _opt , FIG. 10 shows K _p = 2.
5, β = 0.5 and η = η _opt respectively.

In FIG. 9, .largecircle., .DELTA., .Quadrature., .DELTA.
ML, PR (1, 2, 1) ML, PR (1, 3, 1) M
L, PR (1, 2, 2, 1) ML, PR (1, 3, 3,
1) In the case of the ML system, ●, ▲, Δ, and Δ indicate PR4ML, EPR4ML, E for 8/9 code, respectively.
² PR4ML, ME ² The case of the PR4ML system is shown.

In FIG. 10, the symbols △, Δ, □, and Δ indicate PR (1, 2, 2, 3) for the (1, 7) RLL code, respectively.
1) ML, PR (1, 2, 2, 1) ML, PR (1,
3, 3, 1) ML, PR (1, 2, 3, 2, 1) ML system
PR4ML, EPR4ML, E ² PR4M for codes
The case of the L, ME ² PR4ML system is shown.

As can be seen from FIG. 9, the bit error rate (BER) characteristic of the (1,7) RLL code is better than that of the 8/9 code. PR (1,2,
The 2,1) ML and PR (1,3,3,1) ML systems show almost the same best bit error rate characteristics. Next, PR (1,2,1) ML and PR (1,3,1) M
L, PR (1,1) ML, ME 2 PR4ML, E 2 PR4
The order is ML, EPR4ML, PR4ML.

Also in FIG. 10 as in FIG.
Bit error rate (BER) for (1,7) RLL code
The characteristics are better than those of the 8/9 code,
(1,2,3,2,1) ML method is the best
I understood. Then, PR (1,2,2,1) ML, P
R (1,3,3,1) ML, PR (1,2,1) ML,
ME ^TwoPR4ML, E^TwoPR4ML, EPR4ML, PR
The order is the 4ML system.

Assuming that the opening ratio of the eyes is almost the same in any of the PRML systems, the smaller the noise spectrum of the discrimination point, the smaller the SN ratio deterioration due to equalization. Also, assuming that the minimum value of the Euclidean distance between the input sequences of the Viterbi decoder is d _min , the gain of the SN ratio (SNR _G ) with respect to the threshold detection by Viterbi decoding is approximately, and the input noise of the Viterbi decoder is white noise. In this case, SNR _G ≒ ₁₀ log ₁₀ (d _min ) ² [dB] (15). In practice, the input noise sequence is a colored noise sequence and is characterized by the transform function of the equalizer. Therefore,
The SNR gain (SNR _G ) may be degraded by the influence of the correlation. However, the SNR gain (SN
R _G ) can be used to roughly evaluate the characteristics of each PRML system. The gain of the SN ratio (SNR _G ) in each PRML system is obtained by calculating (d _min ) ² given in Table 5 by the equation (1).
It is determined by substituting into 5).

Table 5 shows (d _min ) ² , the number of states (the number of ACS), and the number of signal levels for each PRML system. In addition, the table shows a state-reduced PRML (FS (folding) that can reduce the number of states by half using the symmetry of the trellis diagram.
State) -PRML) method is PR (1,2,2,1) M
FS- applied to L and PR (1,3,3,1) ML system
PR (1, 2, 2, 1) ML and FS-PR (1, 3,
3, 1) The case of the ML system is also shown.

[0051]

[Table 5]

The PR (1, 7) for the (1, 7) RLL code
The 2,3,2,1) ML and PR (1,2,2,1) ML systems have a relatively small noise power spectrum and (d)
_min ) ² is large, so that it exhibits excellent characteristics that the gain of the SN ratio (SNR _G ) is large. PR (1,3,3,1)
The ML system shows relatively good characteristics except for its large noise power spectrum, because the gain of the SN ratio (SNR _G ) is the largest among the PRML systems studied here. Also, the PR (1, 2, 1) ML system having the minimum noise power spectrum shows good characteristics. Except for the PR (1, 2, 3, 2, 1) ML system, these three systems have a smaller number of states (the number of ACS) than the EPR4ML system for 8/9 codes, but have a larger number of signal levels. . PR (1,2,3,2,1) ML method is 8
Number of states (ACS
Number) is somewhat larger, but has twice the number of signal levels.
FS-PR (1, 2, 2, 1) ML and FS-PR (1,
The (3,3,1) ML method can be expected because (d _min ) ² is large and the number of states (the number of ACSs) and the number of signal levels are small and the Viterbi decoding method can be simplified.

Note that (d _min ) ² shown in Table 5 is given by η = η
It is a value obtained from the signal level when _c is set, and η = η
_In the case of _opt , as shown in FIGS. 2 and 3, the gain of the S / N ratio due to deviation from these signal levels (SNR
_G ). In addition, since the decoder input noise is actually colored noise, the characteristics are also deteriorated by the influence of the correlation. For these reasons, the final error rate (BE
FIG. 9 (when K = 1.5) and FIG.
(When K = 2.5).

Table 6 shows the 8/9 encoded P obtained from FIG.
R4ML method (K = 1.5, β = 0.5, η = η _opt ,
This is the degree of improvement (SNR _I ) of the SN ratio of each PRML system with respect to BER = 10 ⁻⁴ ). Table 7 shows the 8/9 coded PR4ML system (K = 2.5, β = 0.
5, each PRML for η = η _opt , BER = 10 ^-4 )
This is the degree of improvement (SNR _I ) of the SN ratio of the system.

[0055]

[Table 6]

[0056]

[Table 7]

From Tables 6 and 7, it can be seen that the PRML method for the (1, 7) RLL code is better than the PRM method for the 8/9 code.
It was found that the degree of improvement of the SN ratio (SNR _I ) was larger than that of the L method. This is because, in the case of the (1,7) RLL code, (d _min ) ² is generally increased by using the run length constraint, and the noise power spectrum is smaller than the 8/9 code. In particular, the (1,7) RLL coded PR
It became clear that the (1,2,3,2,1) ML system can provide the most excellent SNR improvement (SNR _I ) of about 13.8 dB.

[0058] The relationship between the degree of improvement and the normalized linear density of the SN ratio of the PRML method for PR4ML scheme, FIG. 11 (K _p
= 1.5) and FIG. 12 ( _Kp = 2.5)
Shown in

[0059] From FIG. 11, when K _p is larger than 1.5, improvement of PR (1, 2, 2, 1) ML method is maximum, then, PR (1,3,3,1) ML, PR
It was found that the (1, 2, 1) ML and PR (1, 3, 1) ML systems were in order.

FIG. 12 shows that the highest S in FIG.
The PR (1,2,3,2,1) ML system has a better SN ratio improvement than the PR (1,2,2,1) ML system showing the N ratio improvement. It became clear. Do you get it. That is, PR (1, 2, 3, 2, 1)
In the ML method, the degree of improvement in the SN ratio is maximized for all linear densities in the range of 1.5 ≦ K _p ≦ 3.

Further, from FIG. 11 and FIG. 12, it was confirmed that the degree of improvement of the SN ratio was increased with an increase in the linear density K in any of the PRML systems.

In the above embodiment, the coefficients of the PRML system are (1, 3, 3, 1), (1, 3, 1), (1, 2, 2, 3).
Although all positive integers such as (3, 2, 1) are shown,
(1, p, p, 1), (1, q, 1), (1, r, s,
r, 1) (however, the coefficients p, q, r, and s are positive real numbers), and can be easily applied to the positive coefficient PRML method.

It is needless to say that a magnetic recording / reproducing apparatus having a large storage capacity can be obtained by adopting the above-described recording / reproducing method for a perpendicular magnetic recording using a two-layer medium for perpendicular recording and an MR head for reproduction. .

[0064]

According to the present invention, an excellent SN ratio is exhibited,
It is possible to provide a recording / reproducing method for a high-density recording medium excellent in normalized linear density and a magnetic recording / reproducing apparatus using the same.

[Brief description of the drawings]

FIG. 1 is a block diagram of a recording / reproducing system.

FIG. 2 is an eye pattern of each PRML for (1,7) RLL code (β = 0.5, η = η _opt ).

[Figure 3] 8/9 is an eye pattern of each PRML for the code (β = 0.5, η = η op t).

FIG. 4 is a discrimination noise power spectrum of each PRML for (1, 7) RLL code (K _p = 1.5, β = 0.
5, η = η _opt ).

FIG. 5 is a discriminant point noise power spectrum of each PRML for an 8/9 code (K _p = 1.5, β = 0.5, η =
η _opt ).

FIG. 6 is an identification noise power spectrum of each PRML with respect to a (1, 7) RLL code (K _p = 2.5, β = 0.
5, η = η _opt ).

FIG. 7 is a discriminant point noise power spectrum of each PRML for an 8/9 code (K _p = 2.5, β = 0.5, η =
η _opt ).

FIG. 8 shows (1,7) RLL encoded PR (1, 2, 2, 2).
1) Trellis diagram of ML system.

FIG. 9 shows an error rate (BER) characteristic (when K _p = 1.5)
FIG.

FIG. 10 is a graph showing an error rate (BER) characteristic (when K _p = 2.5).

FIG. 11 shows an 8/9 encoded PR4ML system (K _p = 1.5
3 is a graph showing the relationship between the degree of improvement in the SN ratio of each PRML method and the normalized linear density for the case of (1).

FIG. 12: 8/9 encoded PR4ML system (K _p = 2.5
3 is a graph showing the relationship between the degree of improvement in the SN ratio of each PRML method and the normalized linear density for the case of (1).

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Hiroaki Muraoka 6-7-502 Koriyama, Taishiro-ku, Sendai-shi, Miyagi 502 (72) Inventor Yoshihisa Nakamura 1-2-1-2 Inspector Izumi-ku, Sendai-shi, Miyagi

Claims (10)

[Claims] 1. A recording / reproducing method for perpendicular magnetic recording using a two-layer medium for perpendicular recording and an MR head for reproduction.
(1,7) A recording / reproducing method using an RLL encoding method and a positive coefficient PRML method. 2. A magnetic recording / reproducing apparatus using the recording / reproducing method according to claim 1. 3. The method according to claim 1, wherein the PRML method is PR (1, p, p,
2. The recording / reproducing method according to claim 1, wherein the (1) (p is a positive real number) ML method. 4. The method according to claim 1, wherein the PRML system is PR (1,2,2,2).
4. The recording / reproducing method according to claim 3, wherein the recording / reproducing method is a (1) ML method. 5. The method according to claim 1, wherein the PRML method is PR (1,3,3,3).
4. The recording / reproducing method according to claim 3, wherein the recording / reproducing method is a (1) ML method. 6. The method according to claim 1, wherein the PRML method is PR (1, q, 1).
2. The recording / reproducing method according to claim 1, wherein (q is a positive real number) ML method. 7. The method according to claim 1, wherein the PRML method is PR (1,2,1).
The recording / reproducing method according to claim 6, wherein the recording / reproducing method is an ML method. 8. The method according to claim 1, wherein the PRML scheme is PR (1, r, s,
2. The recording / reproducing method according to claim 1, wherein the recording / reproducing method is an r, 1,) (r, s is a positive real number) ML method. 9. The method according to claim 1, wherein the PRML system is PR (1,2,3,
9. The recording and reproducing method according to claim 8, wherein the recording and reproducing method is a 2,1,) ML method. 10. The method according to claim 1, wherein the PRML scheme is a state-reduction type PR.
2. The recording and reproducing method according to claim 1, wherein the recording and reproducing method is an ML method.