JP2572487B2 - Magnetic recording method of data - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates generally to magnetic recording. Specifically, the present invention relates to linear magnetic recording of digital data on essentially parallel recording tracks.

[Background Art] Magnetic recording devices such as magnetic disk devices are digital
Widely used for data recording. In such devices, data is typically stored on the surface of mobile magnetic media, such as hard disks, floppy disks, magnetic tapes, magnetic drums, and the like. Data is generally recorded on the media in magnetic recording tracks that extend generally linearly along the surface of the media.

The track width of the magnetic recording system that maximizes the storage capacity is estimated. <1> T. Howell and E. Fei
g), IEEE International Symposium of Information T
heory, Ann-Arbor, Mich., October 6-9, 1986. <2> Marison (JCMallison), IEEE Trans.Magn., V
ol. MAG-10, pp. 368-373, (June 1974). <3> DFEldridge, IEEE Trans.Aud
io., vol. AU-11, pp. 3-6, (January to February 1963).

This approach applied Shannon's formula to the information capacity of a communication channel. <4> Shannon (CEShannon), Bell Syst.Tech.J.2
7, pp. 623-656, (October 1958).

The theory of information theory concludes that "excessive low performance channels have greater capacity than a single high performance channel." In these early studies, it was assumed that the noise power of the channel was linearly dependent on the track width. This is a characteristic of the medium noise, and it was considered that this was a fundamental restriction at the time of recording. On the other hand,
The signal power increases with the square as the track width increases. Earlier studies concluded that storage capacity was essentially a monotonically increasing function of track density.

In subsequent studies, electronic noise was added to the analysis (see above).
<1> ). Electronic noise is characterized by being essentially constant and substantially independent of track width. It is no longer possible to achieve asymptotically optimality by arbitrarily increasing the track density. Instead, the capacity once peaks as the number of tracks increases and then asymptotically drops to zero. The problem of interference from adjacent tracks was not considered.

What greatly contributes to signal degradation in conventional magnetic recording devices is interference from adjacent tracks due to imperfect servo mechanisms. Adjacent track interference becomes more significant as the track width decreases. This is because the ratio between the interference signal and the desired signal increases. further,
The output of the interference signal increases by the square of the width of the portion that slides on the adjacent track of the head. Marison
"Principally, the purely mechanical constraints associated with the difficulty of holding the readhead on the track during the playback mode are more crucial and more critical than those associated with purely electrical or magnetic phenomena. We can conclude that there will be significant restrictions. "<5> Marison (JCMallison), Proceedings IEEE,
(February 1976). <6> Wildman, IEEE Trans.Mag
n., vol. MAG-10, pp. 509-514, (September 1974).

The analysis published by Howell and Fague in <1> above can be extended to incorporate servo issues into this model. The resulting analysis characterizes the nature of the effect of various contributing noise sources on channel capacity. The servo mechanism has a deviation from its center track,
It is assumed to be a random, Gaussian distribution with mean 0 and variance σ ₂ . The magnetic recording head width may be smaller than the track width. When using the normal read / write method, as far as the channel capacity is concerned, "broad write,
It seems that the principle of "read narrowly" is justified. When narrow tracks are used, the channel capacity increases. However, to achieve the maximum capacity, the ratio of the head width to the track decreases as the value of the track width decreases until the optimum head width / track width combination is obtained, after which the ratio becomes asymptotic. Increase to 1. This ratio is initially partially reduced because as the track becomes narrower, interfering signals from adjacent tracks become increasingly important.

Writing to a narrow track results in a "dead area" that produces false signals over a significant period of time. If a wide track is used, the obstruction spot on the medium is only a small point with respect to the rest of the medium that defines the track width. This is increasingly problematic as tracks become narrower. DISCLOSURE OF THE INVENTION The present invention relates to magnetic recording devices and means for storing and retrieving digital information. This magnetic recording device includes a magnetic recording medium optimized for AC bias type recording and a magnetic transducing head applied for AC bias magnetic exchange.

The invention will now be described with reference to a magnetic disk, but it should be understood that the invention can be used with other magnetic recording media as well.

In the method of the present invention, data to be recorded on a magnetic disk is encoded in any desired binary format. This binary encoding preferably includes standard error control redundancy and encoding. The coded data is divided into contiguous blocks and mapped into a complex sequence according to a predetermined set of coding rules. This complex number may be a component of various conventional coding scheme constellations known in the art as QAM, PSK, CROSS and other trellis coded modulation designs. The specific form of the mapping from the sequence of binary data to the sequence of complex numbers is not important to the invention. Methods for implementing the mapping of complex numbers to sequences are found in the following publications, incorporated herein by reference: <7> Pele and A. Ruiz, IEEE I
nternational Conference on Acoustics, Speech, and Si
gnal Processing, Denver Colo, pp. 964-967 (April 1980
Month). <8> Minzer and T. Howe
ll), IBM-RC 9429 (# 41644) (June 16, 1982). <9> E. Feig and F. Mintze
r), IBM-RC 13701 (# 60788) (March 14, 1988). <10> Weinstein and Evert (SBWeinstein
and PMEbert), IEEE Trans.Commun., vol.COM-19, p
628-634 (October 1971).

The generic name for these techniques is digital frequency division multiplexing, also referred to in the literature as Fourier Transform Division Multiplexing (FTDM).

The data is preferably mapped into a sequence of length N (N is a power of 2) which is particularly suitable for fast Fourier transform (FFT) calculations. More preferably, N is in the range of 256 to 4096. The choice of N depends in part on the speed of the hardware used to perform the fast Fourier transform and the peak power handling capability of the magnetic transducing head.

In the present invention, the tracks on the disk are numbered such that adjacent tracks have numbers with different parities. In other words, for each pair of adjacent tracks, one has an even track number and the other has an odd track number. Further, in the present invention, data recorded on odd tracks and data recorded on even tracks of the disk are mapped substantially orthogonally. Data recorded on an even track is mapped only to an entry having an even index in a certain sequence, and a value 0 is assigned to an entry having an odd index. The data recorded on the odd track is mapped only to the entry having the odd index in the sequence, and the value 0 is assigned to the entry having the even index.

After the mapping of the binary data to the complex sequence, preferably before the sequence, the inverse conjugate sequence is added to form a sequence of length 2N. The added sequence has the property that the j-th entry from the beginning is equal to the conjugate number of the j-th entry from the end. The new added sequence is subjected to a fast Fourier transform calculation to obtain a real sequence of length 2N.

A real number sequence of length 2N may have a small portion of the beginning of the sequence, preferably at the end. This length L buffer segment corresponds to the length of the channel's memory, for example due to head response. This procedure, called cyclic extension, has been proposed to compensate for the problem of intersymbol interference inherent in the communication and storage channels.

The resulting cyclically extended, appended length
The 2N + L real sequence passes through a digital-to-analog converter and low-pass filter to produce an analog signal that is recorded on the disk. This analog signal is passed to a magnetic recording head for writing to the disk in a substantially linear manner and is recorded on the disk.

During the reading process, data is collected in contiguous blocks. Each block is sampled at the same frequency as at the time of writing, and real 2N + L samples are obtained. These are, above <7> Pele and Lewis of the announcement and the above-mentioned
<8> Passed to the equalizer described in Minzer and Howell's announcement. The first 2N values of the output of the equalizer are subjected to a fast inverse Fourier transform algorithm to obtain a sequence of 2N complex numbers. The second half of the output of the fast inverse Fourier transformer (a total of N complex numbers) is sent to the predecoder.

If this data is from an even track, the predecoder sends only the even entries of the sequence to the decoder. The predecoder also checks the magnitude of the number of odd entries in the sequence. If this exceeds a predetermined limit, it is an indication that the magnetic head has penetrated an adjacent track, and the predecoder generates a signal for a corrective action.

On the other hand, if the data comes from an odd track, the predecoder sends only the odd entries of this sequence to the decoder. The predecoder also checks the magnitude of the number of even entries in the sequence. If this exceeds a predetermined limit, it is an indication that the magnetic head has penetrated an adjacent track, and the predecoder generates a signal for a corrective action.

After receiving the data, the decoder starts decoding the data according to a method reverse to the method of encoding the data.

Using the orthogonalization method of the preferred embodiment of the present invention, off-track interference can be reduced, if not completely avoided. Suppose that data is to be read from an even track, but the head has penetrated an odd track adjacent thereto. In that case, the head reads a slightly weaker signal from the desired even track, since it is not entirely above that track. The head also reads weak signals from adjacent odd tracks.
If these signals are not orthogonal, weak signals superimposed on the weakened desired signal can cause errors during decoding. The probability of this error increases as the displacement between the head and the track increases. Using the orthogonalization procedure of the present invention, the head reads a slightly weaker signal from the desired even track, on which a weaker signal from an adjacent odd track is superimposed. However, after the fast Fourier transform stage, the contribution from the desired even track to the signal is found only in the even entry of the output sequence of the fast inverse Fourier transform, while the contribution from the interfering odd track to the signal is Only found in the odd entries of the output sequence of the fast inverse Fourier transform. The amplitude of the even entries attenuates, albeit slightly, evenly since the head was not directly above the track. Such attenuation can be easily corrected and subsequent decoding is straightforward. Interference signals found in the odd entries of the fast inverse Fourier transformed sequence mean that the interference does not appear essentially as noise in the even entries of the fast inverse Fourier transformed sequence used for decoding.

A similar situation occurs when one wants to read data from an odd track, but the head has penetrated one of the adjacent even tracks, but the decoding is performed in the same manner as presented earlier, with the even number The process proceeds with the odd numbers replaced.

In the present invention, it is advantageous to utilize a linear magnetic recording technique such as the AC bias method. As a result, the track number,
Useful information such as embedded servo data and timing information can be advantageously superimposed on the data signal.
For example, during disk manufacture, low frequency servo information may be "buried" deep enough into the disk to be unaffected by the AC biased writing process. At the time of reading back, the embedded servo signal can be separated from the data signal by using a low-pass filter.

In the prior art embedded servo system, the data signal has residual power near DC even though the frequency notch in the code at DC frequency is narrow. <11> Haynes (MKHaynes), IEEE Trans.Magn.vol.
MAG-17, no. 6, pp. 2730-2734 (November 1978).

In the preferred embodiment of the present invention, in contrast, the data component signal has a fairly wide gap near DC. Therefore, servo information and data can be basically completely separated in the frequency domain. Servo information obtained by low-pass filtering is not destroyed by intrusion of data, and data is not destroyed by low-frequency servo information. Further, the servo information only needs to describe whether the track in which the head has entered is right or left of a desired position. This is because the data signal itself contains information as to whether the head is on a track in the power of either the even or odd entries of the sequence after the inverse Fourier transform. The embedded servo information may be one of three different low frequency sine waves arranged in a circular order.
The predecoder generates a signal asking it to take corrective action when it senses that the head is going off track. The low pass filter is 3
Two of the low frequency sinusoidal signals can be separated, but this is sufficient to know if the head is off the right or left.

If desired, other data can be superimposed in the channel used in the basic Fourier transform division multiplexing scheme. The surface information can be encoded by a time (space) division multiplexing method as before. In the preferred embodiment of the present invention, it is possible to freely select whether to perform multiplexing by time division, frequency division, or both. Furthermore, special high frequency components can be allocated for special information for special tasks such as timing control. High-frequency signals are greatly attenuated and may produce somewhat weak signals, but a high signal-to-noise (S / N) ratio is not required for the timing control signal to be effective. A particularly preferred embodiment would be to superpose a high frequency sine wave well separated from the data frequency so that it can be easily separated using a filter. During readback, the reader can phase lock to this high frequency sine wave for accurate timing control.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a typical magnetic disk channel having a track width of 1, average signal power = 200, medium noise power _M = 150, electronic noise power _E = 50, and servo standard deviation σ = 0.15. of
5 is a graph plotting calculated values of S / N ratio and capacity as a function of head width.

FIG. 2 is four graphs showing the effect of changing the track width of the magnetic disk channel of FIG.
The horizontal axis indicates the track width. FIG. 2a is a graph of the S / N ratio of a channel having an optimum head width to track width ratio. FIG. 2b is a graph of the calculated value of the corresponding channel capacity. FIG. 2c is a graph of the calculated optimal head width plotted as a function of track width. FIG. 2d is a graph of the calculated value of the ratio between the optimum head width and the track width.

FIG. 3 is a graph of the same parameters as FIG. 1 except that σ = 0. FIG. 3a is a graph plotting the calculated optimal capacity as a function of track width. FIG. 3b is a graph of the corresponding calculated S / N ratio.

FIG. 4 is a graph of the same parameters of FIG. 3 except that _E = 0. FIG. 4a is a graph plotting the calculated optimal capacity as a function of track width. 4b
The figure is a graph of the corresponding calculated S / N ratio.

Figure 5, except that the interference signal P ₁ is removed is a graph of the same parameters as the first FIG. FIG. 5a is a graph plotting the calculated optimal capacity as a function of track width. FIG. 5b is a graph of the corresponding calculated S / N ratio.

FIG. 6 is a diagram showing scje and atoc expressions of four constellations of Fourier transform division multiplex coding.

FIG. 7 is a block diagram of a transmission channel and a reception channel of the magnetic storage device of the present invention.

FIG. 8a is a graph of the calculated value of the channel frequency response and the noise power spectrum of one embodiment. FIG. 8b is a graph showing the ratio of the corresponding channel response to the noise power spectrum.

FIG. 9a is a graph showing the allocation of the four input powers given in Table 1. FIG. 9b is a graph of the corresponding calculated output S / N ratio.

FIG. 10a is a graph showing classic water injection power allocation. FIG. 10b shows the corresponding calculated output S / N ratio,
6 is a graph of the S / N ratio required to achieve an error rate of 10 ^-7 .

FIG. 11a is a graph showing input power allocation using three constellations. FIG. 11b is a graph of the calculated output S / N ratio.

FIG. 12a is a graph showing the allocation of the four input powers given in Table 2. FIG. 12b is a graph of the corresponding calculated S / N ratio.

Preferred Embodiment of the Invention Linear Magnetic Recording of Digital Data In the present invention, the magnetic storage channel is linearized by the application of an AC bias. When using the AC bias,
Generally, a significant loss of signal-to-noise ratio can be recovered using signal processing techniques. This can be done in four ways. The first method takes advantage of the specific signal-to-noise characteristics of the channel as a function of frequency to reduce the
Design a practical coding / modulation method to obtain high reliability in S / N ratio. The coding scheme in the above frequency domain is
Recently, <7> Pele and Lewis announced and <9>
It was mentioned in the announcement by Fague and Minzer. In the second method, signals orthogonal to each other in the frequency domain are alternately written to odd-numbered and even-numbered tracks,
Reduce adjacent track interference. In the third method, the effects of berth and noise are reduced. In a fourth method, the orthogonalized signal is used during playback with extra superimposed information for continuous track servo operation. In addition, in order to assist writing, an embedded servo can be added to a frequency band in the vicinity of orthogonality sufficiently distant from a frequency band including data.

Orthogonalization can be achieved by decomposing the channel into two subchannels, an even numbered track group and an odd numbered track group. The signal to be written is such that, upon discrete Fourier transforming the values sampled at appropriately selected intervals, either the odd or even entries are all equal to zero. The actual coding / modulation technique is a variant of the Fourier Transform Coding (FTC) method described in <8> Minzer and Howell and <7> Pele and Lewis. Using the ideal example of a typical channel, the potential benefits of this method will be described.

With the orthogonalization method of the present invention, channel integrity can be maintained even for very narrow tracks.
If the head penetrates an adjacent track during the writing process, the signal which is partially overwritten thereby will not be completely erased. Usually, such partial erasure is sufficient to make the original data unreliable, since coherent interference prevents accurate retrieval of the original data. With the present invention, the spectrum of the superimposed signal is decoupled from its support of the spectrum of the pre-recorded data, so the probability of obtaining a signal sufficient to be able to read it from the old data is increased . In fact, taking this into account places restrictions on the track density. During the reading process, the off-track signal does not interfere with the desired data signal.

Influence of Track Positional Displacement of Standard Channel In the dictated computer model simulation, distance and time units are normalized for track width and bandwidth, and both are used with 1 as a reference. Let the average signal power of this reference system be under the assumption that track-to-head alignment is perfect. Let _{M be} the medium noise power of this reference system. The medium noise power does not change when the head enters an adjacent track. Let _{E be} the electronic noise power of this system. This is much more constant.

The displacement between the head and the track affects both the writing process and the reading process. The effect corresponding to the write process is fundamentally more significant as the old data on the adjacent track may be destroyed and cannot be recovered again. As for the track position shift during the reading process, the track can be scanned a plurality of times, so that the influence of the track position shift is negated. In practice, such delays are rarely tolerated. To make capacity estimation easier,
Assume the same during a read operation and during a write operation. The easiest way to study this situation is
Assuming that a complete track is written, the deviation of the head position from the track center is to be doubled.
This method is used herein. Capacity estimates should not be confused with performance analysis of a particular read / write scheme. The latter should be done with worst-case considerations in mind.

Consider a system having a track of width ≤ 1 and a read head of width H ≤ W. The tracks are completely written and no guard band is used to separate adjacent tracks. The reader can easily extend this analysis to take this situation into account. Head center position at the time of reading back is assumed in the center of the expected value tracks, a standard distribution of deviation sigma ^2. In the above system, the media noise power is N _M = H _M and the electronic noise power is N _E = _E. The average power of the interfering signal is It is. However, Similarly, the average power of the desired signal is It is. However, Then, the formula Use to specify the channel capacity. Note that since the individual contributing noise powers are assumed to be completely uncorrelated, they were added to obtain the denominator of the Shannon equation signal-to-noise equation.

FIG. 1 is a graph showing calculated values of capacity and S / N ratio when the head width is changed in a typical channel. Track width is 1, average signal power = 200, medium noise power _M
= 150, electronic noise power _E = 50, servo standard deviation is σ =
0.15. For a fixed track width, the capacity is a monotonic function of the S / N ratio. As shown in FIG. 1, the maximum capacity is obtained when the head width is about 70% of the track width.

Next, what happens when the track width is reduced is examined.
The ratio between the optimum head width and the track width varies as a function of the track width. FIG. 2 shows a state when the track width is changed from 0 to the reference track width 1. FIG.
FIG. 2b is a graph plotting the S / N ratio (in dB) of the channel having the optimum head width against the track width, and FIG. 2b is a graph showing the corresponding capacity. FIG. 2c is a graph showing optimal head width as a function of track width,
FIG. 2d is a graph showing the ratio between the corresponding optimum head width and the track width. The swing seen in this last figure is due to a numerical error in the discretization, which is
The ratio is greatly expanded by taking the ratio. Note that capacity as a function of track width is optimal when the ratio of optimal head width to track width is minimized. The optimum capacity is obtained when the track width is reduced to about 1/2, and a channel having an S / N ratio lower than that of the reference channel by 8 dB or more is obtained. The actual capacity increase is 25%.

To emphasize the role of TMR in degrading channel performance, we now consider the same channel except for perfect tracking, ie, assuming σ = 0. FIG. 3a is a graph showing the capacity as a function of track width, and FIG. 3b is a graph showing the corresponding S / N ratio. Since the tracking is perfect, the ratio of the optimum head width to the track width is 1
It is. The optimum capacity is obtained when the track width is 1/10 of the reference track width, and the capacity increase is more than three times. However, to achieve this capacity, channels with very low S / N ratios, on the order of 6.7 dB, must be used. More important in practical terms, if tracking is perfect, 5.1 dB S
The track density can be doubled by lowering the / N ratio and increasing the capacity by about 65%. Similar results are shown in <1> above . From a historical perspective, a graph showing capacity as a function of track width (<3> above) is shown in Figure 4.
Shown in the figure. In this case, not only the servo deviation but also the electronic noise is removed. At this time, the capacity monotonically increases as the track density increases. Although not apparent from this figure, as the track width approaches zero, this increase reaches an asymptotic limit.

Interference signal P ₁ is beneficial Knowing how much influence the S / N ratio and capacity of the system. This is particularly important later, after orthogonalizing the signals of the adjacent tracks, this component of the noise is no longer present. FIG. 5 shows a graph of the optimum capacity and the corresponding S / N ratio when P ₁ = 0. The capacity is optimized at a track width of 1/5 of the original size, and the capacity increase more than doubles. When the track width is 0.3 times the original size, the capacity is just about twice and the S / N ratio is 9dB
descend. When the track width is 1/2 of the original size, the capacity is about 5
Although it increases by 0%, the corresponding decrease in S / N ratio is less than 5 dB. More importantly, when comparing a non-interfering half track width channel to an interfering reference channel (see FIG. 2), the capacity is increased by 75% and the SNR is reduced by less than 3 dB. .

As a result of improving the servo, the standard deviation of tracking is σ
Assume that it has decreased to = 0.05. When reading and writing are performed by the standard method under the influence of the interference signal from the adjacent track, when the track width is 1, the S / N ratio is 2
2.45dB, capacity becomes 7.4. Therefore, the S / N ratio is increased by 2.2 dB over the reference channel, but the capacity increase is negligible. The optimum capacity when the track width is 0.5 is 11.9 for a head width of 0.45, and the corresponding S / N ratio is 17.86 dB
It is. Optimum capacity is track width 0.175, head width 0.156
The capacitance is 16.9 and the S / N ratio is 8.9 dB.

Finally, assuming that interference signals from adjacent tracks are also removed, when the track width is 1, the S / N ratio is 22.7 dB and the capacity is 7.56. When the track width is 0.5, the capacity is 12.3 (the head width is also 0.5), and the corresponding S / N ratio is 18.47 dB. The optimum capacity is obtained when the track width is 0.125, the capacity is 21.
3. The S / N ratio is 7.25dB. This last track width 0.5
In comparison with the reference channel having a track width of 1, a capacity increase of 83% can be obtained with an S / N ratio reduction of less than 1.8 dB.

Basics of FTC This section describes the basics of Fourier Transform Coding (FTC) and examples of its implementation. Standard based on water injection theory
The FCT method is described in <8>, <8>, and <12> below . <12> Green (B. Greene), September 1984 .

The mixed method of FTC and trellis coding is described in <9> above.
And <13> below . <13> Lewis, Sioffy and Kasturia (A. Ruiz, J.
M. Cioffi, and S. Kasturia), IBM-RC (March 10, 1988)
Days) .

A more elaborate method is described in <14> below . <14> Fague (E. Feig), IEEE Trans. Commun. Basically, a channel is divided into discrete narrow-band sub-channels, and information is stored in sub-channels with a high S / N ratio. The same reliability (error pre-correction rate) is required from each of these utilization sub-channels, which is referred to as the "utilization" sub-channel. The amount of energy allocated to each of the utilized subchannels is exactly the same as that required to obtain the desired error probability. The number of sub-channels used depends on the average power constraint.

Information is stored in successive blocks. Each subchannel stores its information as one of a plurality of allowed complex numbers for each block. These allowed sets of complex numbers are called constellations and have 2 ^B elements. Here, B is an integer. These elements are selected such that their root mean square is one. The minimum distance between two elements of a conformation is
It is called d _free . 4 corresponding to B = 1, 2, 3, 4
The two conformations are shown in FIG. In Figure 6a, the square root of 1 is 2
In FIG. 6b, four 4th roots of 1 are included.
Figure 6c shows the origin and the radius around the origin. 7 points equally spaced along the circumference of the circle. This eight-point conformation is often chosen as the standard 8-PSK conformation, whose elements are all eight roots of one. The 16-point conformation in FIG. 6d includes complex numbers ± ba ± cai. However, And the values of b and c are 1 or 3. In these conformations, Or It is. Each constellation element is used to encode a different sequence of B bits.

The basic idea of FTC is that after applying a discrete Fourier transform (DFT) to a block of values sampled from an analog signal at the Nyquist frequency and equalizing by simple complex division, the resulting sequence In this case, the analog signal is stored so that it becomes 0 in the sub-channel) and becomes an encoded constellation element accurately in the used frequency. Since this channel is contaminated by noise, the actual DFT output will not be a coding constellation element.
The decoder then determines the constellation element closest to the calculated value,
Select as representation of the stored bit sequence (if using encoding in the frequency domain (see <9> above and
<13>) , the decoder becomes considerably complicated). If the signal and the channel response are real values, it means that the output frequency response is conjugate symmetric about the origin. In practice, this contrast serves to average the signal before decoding.

Let the channel frequency response be denoted by H (f), and assume that the contamination noise is an additive Gaussian distribution with a spectral density N (f). This channel is band limited and | f |> W
Assume that H (f) = 0 in the case of The signal leaving this channel is uniquely determined by the value sampled at the Nyquist frequency. Continuous time interval T
Encodes a continuous block of data. This signal has a spectral density of N = 2WT + 1 in each of the above time intervals. Sampling this output at N equally spaced points in each time interval yields the equally spaced points in the channel bandwidth.
The N values of the output spectrum sampled at f _j are
The approximation can be made sufficiently using DFT. Aliasing issues will be discussed shortly. Each channel has a bandwidth of W / N and a flat frequency response H _j = H
Consider the union of independent narrowband sub-channels C _j with (f _j ). Each sub-channel C _j has a deviation σ _j ² = N
Contaminated by additive white noise with (f _j ), denoted by N _j .

Assume that it is desired to compensate that the probability that an error occurs in an arbitrary sub-channel _Cj during an arbitrary block section is less than a certain ε. To obtain this reliability, we want to know the amount of energy E _j ² that must be injected into this subchannel. The S / N ratio of this subchannel is And the reliability criterion is become. However, Is the complement cumulative probability function, and c is the maximum number of nearest neighbors of a given conformational element. In the configuration shown in FIG. 6, c = 1, 2, 7, 4 respectively. In 8 = P SK conformation alternative, a c = 2. Denominator in parentheses (instead of the usual 2) Appears because the signals have been averaged.

Required energy input from reliability criteria Is obtained. The complex number used to encode information on the j-th subchannel is a value obtained by multiplying the _{constellation} element by E _j .
Also, the following equation is applied as a constraint on the total energy.

However, this addition is performed for all the used sub-channels {C _j : _j }. The utilized subchannel is the subchannel with the highest S / N ratio and is used as needed until the total energy constraint is satisfied. The concentration of Θ is represented by M. Normally, as is the case with AC biased magnetic recording channels (<8> and <15> above) , for an integer a, the first a frequency bands (counting upward from 0) are not used. , And the next M bands are included in Θ. <15> Haynes (MKHaynes), IEEE Trans.Magn., Vo
l.MAG-13, no. 5, pp. 1284-1285 (September 1977) .

The set of utilized subchannels 関 数 is a function of the type of conformation selected. Different constellations may be used for different sub-channels. Due to cost constraints, a constellation that maximizes the total number of bits that can be stored in the time interval T is selected. The bit sequence is sequentially M complex numbers (constellation elements)
are mapped to _{ca + 1} , ..., ca _{+ M.} These are amplitude modulated according to our input power allocation scheme and sequenced
E _{a + 1} c _{a + 1} ,..., E _{a + M} c _{a + M} are obtained. Next, a sequence of WT complex numbers is formed by substituting the value 0 into an index that does not correspond to the used channel of the positive frequency.
A zero is connected to this column and then its own inverse conjugate column. A sequence of length 2WT + 1 is obtained, whose DFT is a real value. The value sampled at the Nyquist frequency of the analog write signal is a calculated value of a real number. This is a unique signal of the bandwidth W. The formation of this analog signal
A sequence of real calculated values must be passed through a D / A converter and a low-pass filter.

In practice, to avoid aliasing at the decoder,
Add some redundancy. It simply retransmits the beginning of the signal after the end of the block. The persistence of the retransmission portion is an essential support for the impulse response of the channel (persistence of channel memory). This has the effect of converting the linear convolution of the channel into a circular convolution. The idea was Winograd
( <8> above ) proposed. At the receiver, after low-pass filtering the output and sampling at the Nyquist frequency,
Inverse Fourier transform. Then, in the decoder, for j∈Θ, among the elements of the constellation corresponding to sub-channel C _j , H _j
When multiplied by E _j , it is determined which is closest to the calculated value of the inverse Fourier transform output in the j-th subchannel, and a bit string corresponding to this number is returned as information in the subchannel. FIG. 7 shows the lay-down of the entire transmitter / receiver.
In the figure, an update routine and a rotation routine that compensate for timing drift and adaptively adjust the equalizer parameters are also incorporated into the receiver. See <7> above for details.
And <8> above . Later, when discussing the superposition of other information on the linearized channel, more efficient timing control will be presented.

This procedure is best illustrated by example.
Consider a channel divided into 128 sub-channels in FIG. The frequency response H (f) satisfies | H (f) | ² = e ^{−4 | f | / π} | sin f | | f | <π, and is 0 otherwise. Also, the frequency response H
(F) is contaminated by additive Gaussian noise whose power spectrum is N (f) =. 003 + .01 | sin f |. This channel is divided into 128 narrowband sub-channels. The square value of the channel correspondence and noise power spectrum is
It is shown in Figure 8a. The horizontal axis is the sub-channel index,
Not a frequency value. The function of the ratio | H (f) | ² / N (f)
It is shown in Figure 8b. Block length is 256 (at Nyquist frequency)
Samples. Ignore any additional redundancy for anti-aliasing. Error pre-correction rate of 10
^-7 is required.

A first embodiment of the FTC allocates the same amount of information to each subchannel. FIG. 9 is a graph plotting the input power allocation for the four constellations of FIG. 6 and the corresponding output S / N ratio as a function of frequency. In Table 1 below,
The number of sub-channels, the corresponding number of used bits per block, and the output S / N ratio corresponding to each of the four allocations are shown. The output signal-to-noise ratio is a value required to accurately achieve the output reliability criterion.

From Table 1, it may be better to use an allocation of 74 subchannels. However, as can be seen from the discussion in the "Peak Limiting" section, allocation of 48 subchannels is more desirable for protection against clipping errors.

Trellis coding proposed in <9> above ( <<
16> ), use B =
Two bits each of the 96 subchannels corresponding to 2 can be encoded, giving 192 bits per block. <16> Ungerbook (G. Ungerboeck), IEEE Trans.I
nformat.Theory, vol.IT-28, pp.56-57 (1982/1
Month)

At the price, four Viterbi decoders add complexity. Also, in this case, the variance of the power allocation of the 96 sub-channels is larger than the variance of the allocation of the 48 sub-channels, so that errors due to clipping at the peak amplitude value are more likely to occur.

Allocate these to water injection theory (<17> below and
<18>) , the above <7>, the above <8>,
It would be beneficial to compare with the allocation performed in <10> and <12> above . <17> Lucky, Salts and Weldon (RWLucky,
J. Saltz, and EJ Weldon), Principles of Data Commun
ication.New York, NY: McGraw-Hill, p.28 (1968
Year) . <18> Gallager, Information Theory
and Reliable Communication, New York, NY: Wiley, pp.
383-389 (1968) .

The latter is based on an optimal strategy, but in practice often gives values significantly worse than those obtained using the heuristic method we use. This is particularly evident in this example. FIG. 10 shows the above <8> and <12
Fig. 6 is a graph showing the allocation of input power using the prescription shown in &gt; and the corresponding output S / N ratio. The stepped straight line in FIG. 10b represents the output S / N ratio required for the above-mentioned reliability. For most of the channels, the output reliability is much higher than required, indicating the amount of energy wasted. In this allocation, 1 bit for each of the 26 subchannels, 2 bits for each of the 32 subchannels,
A total of 90 bits are provided per block.

Additional benefits can be obtained if one seeks to utilize different conformations simultaneously. Such an allocation is shown in FIG.
In this case, 1, 2, and 3 bits are respectively stored in 21, 3
7, 19 subchannels are obtained, for a total of 152 bits per block. More importantly, as described in the section "Peak Limiting", the real benefit in this case is that the input power is much more evenly allocated to the sub-channels utilized. This reduces the effect of clipping at the peak amplitude level.

The simplest two trellis codes from <16> above , d
4-state 8-state with _free = 2 and 8-state with d _free = 1
If a 16-CROSS code is also to be incorporated, 48 subchannels and 33 bits storing 2 and 3 bits respectively.
An allocation with a reasonably uniform input power allocation of sub-channels, totaling 195 bits per block, is obtained.

Alternate Fourier Transform Coding for High Track Density Quadrature signals can be efficiently written to alternating tracks. In this procedure, the track of the even numbered using only sub-channel C _j of the even number, the track of the odd numbered it is necessary to use only the sub-channel odd number. The even numbered tracks are separate sets of utilized subchannels Θ _e , and the odd numbered tracks are also Θ _o.
Having. Each track is subject to the same total energy constraint, which significantly changes the energy allocation. The union Θ _e ∪Θ _o is not always equal to Θ.
In addition, the sum of the concentration of Θ _e and Θ _o is not necessarily equal to the concentration of Θ. New energy allocations need to be recalculated anew. Again, we will show how to allocate the same amount of information to each used sub-channel, and then implement this scheme on the model channels introduced in the previous section. FIG. 12 shows the input assignment and the output S / N ratio of the even channels. 1 to 6 on the X axis
Although numbered up to four, it should be understood that these correspond to the even-numbered subchannels of the previous example.

Table 2 below shows the number of sub-channels for the various allocation strategies and the corresponding number of bits per block.

In this example, it can be seen that a good strategy is to use fewer subchannels with a large amount of information per subchannel. This is because this alternating scheme only uses half of the best part of the channel and therefore has to use up to the low SNR part of the channel during energy allocation. Therefore, the high S /
By allocating more information to the N-ratio part, it is advantageous to make better use of that part.

If the signals are alternately orthogonalized, the control method of the error due to the track position shift can be fundamentally changed. Except during the settle-down period, the deviation from the track center is a phenomenon that changes slowly compared to the actual data flow. By observing the energy of the subchannels that should not be used when processing a block of data, it is possible to determine when the magnetic recording device will begin to penetrate adjacent tracks. This opens up many possibilities for error control. Most importantly, if the head is slightly off track, there may be sufficient signal to maintain reliability without coherent interference. Second, it is possible to treat this channel as a "gross erase channel". That is, if too much energy is observed in the wrong sub-channel, the entire block can be declared unreliable and re-read. By doing this, the waiting time increases according to the probability of track misalignment. Third, the track information can be encoded and stored in one of the sub-channels of each block. For example, when scanning a track,
Can be cyclically encoded, so that by observing the calculated output of this particular sub-channel, the head is going right off this track, It is possible to determine whether the vehicle is going to the left. The amount of deviation can be obtained directly by observing the total energy of the unused subchannel. This allows the generation of a strong continuous servo signal, which facilitates much better tracking.

Table 2 shows bit allocation of only data before encoding. When using the 4-state 8-PSK trellis code of B = 2 of the Ungerbook of the above <6> , 5
Encode 114 bits using 7 subchannels. When using the Ungerbook B = 3 8-state trellis code, 111 bits are encoded using 37 subchannels. If both conformations are used simultaneously,
Two bits can be encoded using 19 sub-channels and three bits can be encoded using 30 sub-channels, for a total of 128 bits per block.

Peak Limiting The above arrangement produces an energy-constrained signal. Peak-limited signals are required to ensure that the AC biased recording channel closely approximates the linear channel. That is, the time signal s (t) is, for a given positive value P, an absolute value inequality | s (t) | ≦
P must be satisfied. Therefore, before passing the FTC signal to the write head, it must pass through a hardware limiter that clips this signal at a level of ± P.

If the average energy per sub-channel is E ² / N, the error in the j-th sub-channel due to clipping at the threshold ± P will have a mean 0, variance | H _j | ² V (E,
P) is "almost" equal to the Gaussian distribution. However, The reason this result is an approximation is that it is the result of a large number law. The statistics of these errors approach a Gaussian distribution as the input power allocation of the utilized sub-channels becomes more uniform and as the number of utilized sub-channels increases. When the input power allocation is dominated by a relatively small number of subchannels,
The base of the error distribution spreads. This is why the 48 subchannel allocation is preferred, even though the 74 subchannel allocation in Table 1 has slightly more bits per block. The above equation regarding dispersion holds for all sub-channels except the sub-channel corresponding to DC. In the case of a subchannel corresponding to DC, the variance is doubled. In any case, no direct current is used in the AC bias recording.

A good design rule for implementing FTC on peak-limited channels is to incorporate this variance as part of the noise and rewrite the above reliability criterion as

However In the above equation, an error due to clipping being added to the noise component was added. Next, the total energy constraint Becomes another design parameter. This is because the clipping error is a function of the total energy.
In this case, the optimization problem is very complicated,
It cannot be solved using the standard variational method used in classical water injection theory. This problem can be solved numerically.

Burst Error When using narrow tracks, the process of additive white noise is no longer effective. One must also consider the possibility of error bursts caused by media defects that are large compared to the track width. One of the fundamental advantages of averaging inherent to the Fourier transform coding method is that the burst error spreads over all subchannels, including unused subchannels, so that this burst The expected value of the contribution due to the error is reduced. For example, a very large standard deviation σ _b occurs in a burst sequence at samples A or A + B.
When modeled as a sample from an additive white noise source, the probability that the real part of the counting error due to this noise will be greater than some R is given by:

Similarly, the probability that the imaginary part of the calculation error due to this noise becomes larger than a certain R is given by the following equation.

By increasing the block length N, such a burst
It is easy to see how the problem of errors is reduced. In practice, the amplitude of the output must be limited in order to limit the amplitude of the burst noise and thereby ensure that σ _b does not become too large. Care must be taken that the level of restriction is not too low to affect good parts of the signal.

The noise may be a large coherent signal over an interval. In this case, its effect after the Fourier transform is almost DC. If a linearized magnetic recording channel is used, this area is not used for the code. Therefore, if a large value is observed in this region after decoding using FTC, the presence of this type of noise can be detected. However, it is not clear whether separating this portion of the signal provides an approximation of the burst error that is useful for further processing.

In environments where the signal-to-noise ratio is very low and cannot be encoded as a real number ± a with one bit per subchannel, additional information is provided to help protect against burst errors. The calculated value of the Fourier transform should ideally be a symmetric real number. The imaginary component of the output should be due to noise. Therefore, if these phase terms are subjected to inverse Fourier transform and the result is subtracted from the signal, then the Fourier transform is performed, the variance of noise is reduced by half.

Recall how we used orthogonality to generate what we referred to as the "gloss cancellation channel" in the "Alternate Fourier Transform Coding for High Track Density" section. In this case, the same idea can be used. If the unused sub-channels have too much energy, it is only necessary to declare the particular block unreliable. However, unlike the previous case, the block can no longer be asked to be re-read, since in this case permanent damage has been caused by a media defect or inadvertent overwriting. However, if you have the ability to detect such faults, you can design read / write protocols to handle them.

Superposition of other information A certain subchannel can be dedicated to information other than data. As already mentioned in the section "Alternate Fourier Transform Coding for High Track Density", one subchannel can be dedicated to information to aid tracking. The bandwidth required for this information is very low. This is because the critical information that signals that it is going off-track is sufficiently abundant, that is, the entire contents of the adjacent track. Only by encoding one subchannel, it is possible to know whether it is going to the right or to the left.

An embedded servo can be incorporated in this method.
In this method, very low frequency servo information is embedded in the deep part of the medium. This information is kept there for the life of the channel. This is used to create a more complete track during the writing procedure and to get better tracking during the reading procedure.

Timing information is also superimposed. The signals generated via the FTC are Gaussian in nature, and it is not possible to recover the timing of such signals using standard phase locked loop techniques. A method of correcting such a drift using the data itself when the timing deviation is slowly changing is described in the above <7> and the above <
8> . Basically, a slow drift causes a time shift of the signal, corresponding to a linear phase shift during the Fourier transform. This becomes encoded data.
This data contains enough information to estimate the rotation introduced by this phase shift. To handle finer timing variations, timing concessions must be superimposed at frequencies far away from the frequencies used for the data. This information can be high-pass filtered, allowing for timing recovery during operation.

In addition, there are many types of information to be superimposed, such as the identification of a track. Basically, any information that would normally be stored in a particular sector of the disk can be spread over specially allocated sub-channels throughout the disk.

Claims (2)

(57) [Claims] 1. A magnetic recording medium having a plurality of recording tracks extending generally linearly and arranged side by side,
A method for magnetically recording data, wherein (a) recording tracks are numbered in the form of serial numbers so that track numbers having different parities are assigned to adjacent tracks, and even-numbered recording tracks are even-numbered tracks. (B) encoding a sequence of digital data elements as a sequence of N complex numbers, wherein the numbered recording tracks are associated with an odd set of track numbers. c) selecting a complex number having an index value of a first parity from the sequence of N complex numbers in order, and assigning 0 between the complex numbers having an index value of the first parity, thereby forming a first parity of the N complex numbers; And (d) adding the conjugate sequence to the N complex first parity sequences. (E) performing a discrete Fourier transform on the 2N complex first parity sequence by adding the cans in reverse order to form a 2N complex first parity sequence; Obtaining a real number of first parity amplitude sequences; and (f) digitally converting the first parity amplitude sequences.
Pass through an analog converter and the resulting signal is
(G) magnetically recording in linear fashion on the recording track associated with the even track number; (g) encoding the sequence of digital data elements as a sequence of N complex numbers; By sequentially selecting a complex number having an index value of a second parity opposite to the first parity from the sequence of N complex numbers formed by and assigning 0 between the complex numbers having an index value of the second parity, N (I) adding a conjugate sequence to the N complex second parity sequence in reverse order to form a 2N complex second parity sequence; Forming a sequence of parities; and (j) performing a discrete Fourier transform on the 2N complex second parity sequences to obtain 2N real numbers. Obtaining a second parity amplitude sequence; and (k) digitally converting the second parity amplitude sequence.
Pass through an analog converter and the resulting signal is
Magnetically recording in a linear fashion on a recording track associated with an odd track number. 2. A magnetic recording medium having a plurality of recording tracks extending generally linearly and arranged side by side.
A method for magnetically recording data, wherein (a) recording tracks are numbered in the form of serial numbers so that track numbers having different parities are assigned to adjacent tracks, and even-numbered recording tracks are even-numbered tracks. (B) encoding a sequence of digital data elements as a sequence of N complex numbers, wherein the numbered recording tracks are associated with an odd set of track numbers. c) each complex number in the sequence has an integer index value;
Adding a sequence of conjugate numbers to the sequence of N complex numbers in reverse order to obtain a sequence of 2N complex numbers; and (d) calculating an index value of a first parity from the 2N complex sequences. Forming a sequence of 2N complex first parities by sequentially selecting N complex numbers and assigning N 0s between the N complex numbers having the first parity index value; (E) performing a discrete Fourier transform on the first parity sequence to obtain 2N real first parity amplitude sequences; and (f) digitally converting the first parity amplitude sequence.
Pass through an analog converter and the resulting signal is
(G) encoding the sequence of digital data elements as a sequence of N complex numbers on the recording track associated with the even track number in a linear manner; and (h) encoding each sequence in the sequence. The complex number has an integer index value,
Adding a sequence of conjugate numbers to the sequence of N complex numbers in reverse order to obtain a sequence of 2N complex numbers; and (i) from the 2N complex number sequence formed in (h) above. By sequentially selecting N complex numbers having an index value of a second parity opposite to the first parity and allocating N 0s between the N complex numbers having an index value of the second parity, 2N (J) performing a discrete Fourier transform on the second parity sequence to obtain 2N real second parity amplitude sequences; (k) The amplitude sequence of the second parity is digitally
Pass through an analog converter and the resulting signal is
Magnetically recording in a linear fashion on a recording track associated with an odd track number.