Error detection/correction and fault detection/recovery – Pulse or data error handling – Error/fault detection technique
Reexamination Certificate
1998-12-18
2001-06-05
Chung, Phung M. (Department: 2133)
Error detection/correction and fault detection/recovery
Pulse or data error handling
Error/fault detection technique
C714S801000, C714S799000
Reexamination Certificate
active
06243847
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates generally to write precoders for use in magnetic storage disk drives and more particularly to a method and apparatus for detecting and controlling errors within a data stream through a write precoder.
BACKGROUND OF THE INVENTION
Conventional magnetic storage devices include a magnetic transducer or “head” suspended in close proximity to a recording medium, for example, a magnetic disk having a plurality of concentric tracks. The transducer is supported by an air-bearing slider mounted to a flexible suspension. The suspension in turn is attached to a positioning actuator. During normal operation, relative motion is provided between the head and the recording medium as the positioning actuator dynamically positions the head over the desired track. The information recorded on the magnetic disk is transmitted to a preamplifier which is in turn transmitted to a read channel. One example of read channels in use in todays technology is a PRML read channel.
The magnetic recording channel can be characterized as a channel with significant intersymbol interference, particularly at high recording densities. Partial response maximum likelihood (PRML) detection systems based on shaping the channel response to a suitable partial response have become a popular detection method for such channels. Partial responses such as class IV partial response (PR4) and enhanced PR4 (EPR4) are common due to their good performance on moderate density and high density channels. At higher densities, higher order polynomials such as EEPR4 have been proposed. These partial responses are of the form (1−D)(1+D)
n
, with n determining the order of the polynomial. As n increases, the high frequency response is attenuated, hence better matching the high frequency attenuation of the magnetic recording channel at high recording densities.
As recording densities increase, the use of trellis-based coding schemes have also been proposed. These include matched spectral null coding schemes based on the matched spectral null theorem. These have been used to increase the minimum distance on the PR4 based target from 2{square root over (2)} to 4 and have achieved efficient implementations with practical code rates of 8/10 through the use of time varying trellises.
At higher recording densities with higher order partial responses, run length constrained codes demonstrate improved distance properties. For example, the use of an EEPR4 target with a ⅔ (1,7) code increases the minimum distance from 2{square root over (6)} to 2{square root over (10)} . Codes achieving the same increase in minimum distance but without the “d=1” constraint such as maximum transition run length (MTR) codes have been proposed for the EEPR4 partial response and finite delay tree search type detectors. These run length constrained codes help simplify the target trellis by eliminating states. Even higher rate codes to achieve the same increase in minimum distance have also been proposed. These include a family of codes and the rate 8/9 code based on a time varying MTR (TMTR) constraint.
Coding to detect and eliminate certain error events on the PR4 channel was considered. The eliminated error events were the ones most likely due to noise correlation from the equalization to the PR4 response. This achieved an increase in detection SNR of ≈1.25 dB with a rate 8/9 code at recording densities around 2 bits per PW
50
.
A single bit parity code is utilized to detect the presence of the identified dominant error events. This coding constraint can achieve a moderate coding gain but with a high code rate which is desirable for high density magnetic recording. For the detection of the coded data, a postprocessor is possible based on correlating the received signal to identify the likely locations of the error events. The most likely event is then corrected.
The basic recording and detection system model is shown in
FIG. 5
with the channel response based on the Lorentzian step response. The channel frequency response is
H
chan
(ƒ)=j&pgr;PW
50
sin(&pgr;ƒT)e
−|&pgr;PW
50
ƒ|
where PW
50
is the half amplitude pulse width and T is the recorded bit period.
The recording channel is often shaped to the required target frequency response G(ƒ) through the use of a continuous time and discrete time filter. For the purpose of analysis, the continuous time filter is assumed to band limit the signal and equalize it to the desired response before sampling at the baud rate 1/T. The equalizer is assumed to minimize the mean square error between the equalizer output and the desired target. This requires an equalizer response of
E
(
f
)
=
S
x
(
f
)
G
(
f
)
H
chan
(
f
)
*
N
(
f
)
+
&LeftBracketingBar;
H
chan
(
f
)
&RightBracketingBar;
2
S
x
(
f
)
where S
X
(ƒ) is the power spectral density of the input data and N(ƒ) is the noise power spectral density at the channel output. At the detector input, the signal consists of the input signal shaped to the desired partial response plus correlated noise with a power spectral density of
N
d
(ƒ)=
{fraction (1/+L T)}(S
X
(ƒ)|G(ƒ)−H
chan(ƒ)
E(ƒ)|
2
+N(ƒ)|E(ƒ)|
2
).
While this includes distortion, it is considered as Gaussian noise for the purpose of analysis and the noise autocorrelation is assumed to be
R
(
k
)
=
T
∫
-
1
/
2
T
1
/
2
T
N
d
(
f
)
ⅇ
j2π
fkT
ⅆ
f
.
WIth maximum likelihood detection, the error rate performance is determined by the distance between any two allowable data sequences and the noise correlation. The probability of an error event occurring in the presence of correlated noise can be calculated as
P
(
Error
Event
)
=
Q
(
∑
k
=
0
J
e
k
2
2
∑
k
=
0
J
e
k
2
R
n
(
0
)
+
∑
i
=
0
J
∑
j
=
0
,
j
≠
i
J
e
i
e
j
R
n
(
i
-
j
)
)
where the error event {e
0
, e
1
, . . . ,ej} is the difference between any two possible noiseless sequences at the detector input and R(k) is the noise autocorrelation at the detector input. The corresponding error event in terms of channel input symbols will be denoted a
k
with
e
k
=a
k
*g
k
where * denotes convolution and the sequence g
k
is the inverse D transform of the desired target response G(D).
The optimum target response is the one which whitens the noise at the detector input. While the exact response to achieve this is impractical to implement, a reasonable compromise is to shape the response to a suitable polynomial. While polynomials of the form (1−D)(1+D)
n
have been used, it is proposed here to use a polynomial of the form (1−D
2
)(h
0
+h
1
D+h
2
D
2
). The (1−D
2
) term provides a null at DC and at the Nyquist frequency which correspond with the DC null and high frequency attenuation in the magnetic recording channel. The h
0
+h
1
D+h
2
D
2
filter allows further high frequency attenuation to be introduced to match the channel response. In order to avoid requirements for multipliers in the detector, the target response should contain simple integer ratios. In particular, the response (1−D
2
)(2+2D+D
2
) has been determined to perform better at higher recording densities.
FIG. 6
shows the magnitude of the proposed target response compared to the EPR4 and the EEPR4 target responses and the Lorentzian channel response at a density of 3.0 bits per PW
50
. It can be seen that the proposed target provides additional attenuation at high frequencies and hence should be a better match to the recording channel. The event error rate performance of the proposed target (labeled 6221), the EPR4 target, and the EEPR4 target are plotted in FIG.
7
. The plot shows the calculated required channel SNR for an event error rate of 10
−6
based on the probability of th
Fu Leo
Jeon Tae-hyun
Leung Michael
McClellan Brett
Brady W. James
Chung Phung M.
Swayze, Jr. W. Daniel
Telecky , Jr. Frederick J.
Texas Instruments Incorporated
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