Disk drive having built-in self-test system for characterizing performance of the drive

Information

  • Patent Grant
  • 6292912
  • Patent Number
    6,292,912
  • Date Filed
    Friday, February 27, 1998
    26 years ago
  • Date Issued
    Tuesday, September 18, 2001
    23 years ago
Abstract
A disk drive has a normal mode of operation and a built-in self-test (BIST) mode of operation for producing a sequence of channel metrics {Γn}. The disk drive includes a recording surface having a plurality of bit cells and a transducer for reading the plurality of bit cells to produce a noise-corrupted read signal. The disk drive further includes means responsive to the noise-corrupted read signal for generating a sequence of observed samples {yn}, the sequence of observed samples {yn} forming a sequence of observed-sample subsequences {Yn}. An expected sample generator operates during the BIST mode of operation to provide a sequence of expected samples {wn}, the sequence of expected samples forming a sequence of expected-sample subsequences {Wn}. A channel metrics Γn computation system computes a sequence of channel metrics {Γn}. Each channel metric Γn is a function of a distance determined from one of the observed-sample subsequences Yn to the corresponding expected-sample subsequence Wn. Each channel metric Γn is independent of the earliest observed sample in every prior observed-sample subsequence Yn and the earliest expected sample in every prior expected-sample subsequence Wn.
Description




BACKGROUND OF THE INVENTION




1. Field of the Invention




The present invention relates to a disk drive such as a magnetic hard disk drive. More particularly, the present invention relates to such a drive having a built-in self-test system for characterizing performance of the drive.




2. Description of the Prior Art




A huge market exists for bard disk drives for mass-market host computer systems such as servers, desktop computers, and laptop computers. To be competitive in this market, a hard disk drive must be relatively inexpensive, and must accordingly embody a design that is adapted for low-cost mass production In addition, it must provide substantial capacity, rapid access to data, and reliable performance. Numerous manufacturers compete in this huge market and collectively conduct substantial research and development, at great annual cost, to design and develop innovative hard disk drives to meet increasingly demanding customer requirements.




An appreciable portion of such research and development has been, and continues to be, directed to developing effective and efficient ways to conduct, as part of the manufacturing process, unit-by-unit testing of drives. One aspect of such testing relates to determining the effect random noise has on drive performance. Data produced from such testing are useful in tuning processes directed to improving drive performance. Another aspect of such testing relates to determining the existence and location of defects such as defects in the media.




Random noise presents difficulties particularly in circumstances in which its magnitude is material in relation to the magnitude of a signal. In other words, a low signal-to-noise ratio (“S/N”) presents problems. In a drive, a low S/N presents problems in attempting to achieve high areal density. Areal storage density relates to the amount of data storage capacity per unit of area on the recording surfaces of the disks. The available areal density may be determined from the product of the track density measured radially and the linear bit density measured along the tracks.




The available linear bit density depends on numerous factors including the performance capability of certain circuitry that is commonly referred to as a “read channel.” One type of read channel is referred to as a peak-detecting channel; another type is referred to as a sampled-data channel. The type referred to as a sampled-data channel is a category including a partial response, maximum likelihood (“PRML”) channel, a EPR4 channel, and a E


2


PR4 channel.




In a hard disk drive having any of these read channels, the read channel receives an analog read signal from a transducer during a read operation. The analog read signal is characterized by a “channel frequency.” As used in this art, “channel frequency” is the reciprocal of a time period “T,” where the “T” is the time period consumed while an elemental-length magnet passes under the transducer during a read operation with the disk spinning at a constant angular velocity. In this regard, the length of each magnet recorded along a track as a result of a write operation is, to a first order of approximation, either an elemental length or an integer multiple of the elemental length. Each elemental length magnet can be referred to as a “bit cell” that is defined during a write operation.




The analog read signal always contains some random noise. The analog read signal, and certain other signals produced by processing the analog read signal and that also contain noise, are referred to herein as noise-corrupted signals. One such other noise-corrupted signal is a signal produced by filtering the analog read signal by means of a low-pass filter. Such filtering may reduce but not eliminate noise, and the filtered signal is also noise corrupted. Further signal processing in the read channel provides for producing a digital signal comprising detected symbols, any of which can be in error in representing recovered data. Such a digital signal is referred to herein as an error-prone signal.




In a hard disk drive employing a peak detecting channel, digital data are represented in the media by transitions between oppositely magnetized bit cells. Provided that the transitions between oppositely magnetized bit cells do not unduly interfere with each other, each such transition causes a peak in the analog read signal, and a peak-detecting channel employs a peak detector that detects such peaks, and produces digital signal in the form of a serial, binary-valued signal that is an error-prone signal for numerous reasons. One reason why the peak detector produces an error-prone signal is random noise; this source of error presents a problem for any type of channel. Another reason relates to interference between adjacent transitions. Interference between such transitions is referred to as intersymbol interference and adversely affects performance of a peak detecting channel increasingly as a function of channel rate.




A sampled-data channel employs sampling circuitry that samples a noise-corrupted analog read signal to produce a sequence of noise-corrupted samples. The samples so produced are provided in sequence to a detector. Such a detector may be organized such that its detection decisions are based on a sequence of the samples. Such a detector is sometimes called a “maximum likelihood sequence detector.” A so-called “Viterbi detector” is an example of a maximum likelihood sequence detector. In a sampled-data channel employing a Viterbi detector, circuitry responds to the noise-corrupted samples to produce error-prone symbols and the produced error-prone symbols are mapped to binary-valued error-prone symbols. In a PRML channel, such internally-produced error-prone symbols are often referred to as: “−1”; “0”; and “+1”; and the binary-valued error-prone symbols are supplied to a deserializer to produce a parallel-by-bit digital signal.




Prior art methods for characterizing the performance of a disk drive are time consuming, costly, and inefficient. Prior art methods include various ways to perform test operations to produce either a bit error rate (“BER”) or a histogram of noise magnitudes.




A BER of 10


−x


means that, on the average, there is no more than one error per 10


−x


bits. A raw BER for a disk drive is typically in the range of 10


−6


BER to 10


−10


BER. The raw BER is estimated without using an ECC correction system to correct errors in a data sequence. A user BER is usually lower than the raw BER and is improved using the ECC correction system.




The BER can be used for fine tuning electronic components in the disk drive. The BER test is commonly repeated after tuning the electronic components.




Prior art methods for estimating the BER require a protracted read operation that involves reading a large number of samples and counting the number of bit errors that occur during the read operation. Prior art methods commonly require reading 10


8


samples to produce a reasonably precise estimate of BER when BER is in the neighborhood of 10


−6


BER This is time consuming and inefficient. Other prior art methods require using large and expensive test equipment to produce an estimate of the BER. This is costly as well as inefficient for use in the manufacturing environment.




U.S. Pat. No. 4,578,721 discloses a “window margin” method for estimating the bit error rate for disk drives employing peak detection read channels. The “window margin” method is not suitable for disk drives employing sampled data detection channels.




U.S. Pat. No. 5,355,261 discloses a method for estimating a BER for disk drives having a partial response maximum likelihood data detection channel. This method requires comparing read back data bits and known data bits to count read back errors.




A publication titled “A WINDOW-MARGIN LIKE PROCEDURE FOR EVALUATING PRML CHANNEL PERFORMANCE”, IEEE Transactions on Magnetics, Vol. 31, No.2, March 1995, discloses a method for estimating the BER that requires counting read back errors during the read operation.




As for a test for measuring the performance of a disk drive by generating a histogram, U.S. Pat. No.5,121,263 discloses such a method. This patent teaches generating a histogram using the following procedures:




1. writing a pattern of binary data bits on the disk of the drive being tested;




2. reading the data bits from the disk;




3. sampling the amplitude of the analog signal at recurring clock intervals;




4. comparing the sampled amplitude to reference amplitude values that are expected to be received for each binary data bit that was recorded on the disk;




5. calculating a difference value for each binary bit that was stored on the disk;




6. storing like magnitude difference values in one of a plurality of registers.




The count content of the plurality of registers provides a histogram depicting the distribution of the like magnitude difference values. The shape of the histogram characterizes the performance of the disk drive and provides a criterion for deciding whether the disk drive being tested meets specifications.




There is a need for an efficient, accurate, and cost effective method for characterizing the performance of a disk drive in a manufacturing environment.




SUMMARY OF THE INVENTION




The invention can be regarded as a disk drive having a normal mode of operation and a built-in self-test mode of operation for producing a sequence of channel metrics {Γ


n


}. The disk drive includes a recording surface having a plurality of bit cells; a transducer for reading the plurality of bit cells to produce a noise-corrupted read signal; and a means responsive to the noise-corrupted read signal for generating a sequence of observed samples {y


n


}. The sequence of observed samples {yn} forms a sequence of observed-sample subsequences {Y


n


}. Each observed-sample subsequence Y


n


has an earliest observed sample and a latest observed sample. The disk drive includes means operative during the built-in self-test mode of operation for providing a sequence of expected samples {w


n


}. The sequence of expected samples forms a sequence of expected-sample subsequences {W


n


}. Each expected-sample subsequence W


n


has an earliest expected sample and a latest expected sample. The disk drive includes computation means for computing a sequence of channel metrics {Γ


n


}. Each channel metric Γ


n


is a function of a distance determined from one of the observed-sample subsequences Y


n


to the corresponding expected-sample subsequence W


n


. Each channel metric Γ


n


is independent of the earliest observed sample in every prior observed-sample subsequence Y


n


and the earliest expected sample in every prior expected-sample subsequence W


n


.




In accordance with a feature of the invention, the disk drive further includes means for computing a mean μ


Γ


of the channel metrics Γ


n


; means for computing a standard deviation σ


Γ


of the channel metrics Γ


n


; and means for computing a ratio of the mean μ


Γ


to the standard deviation σ


Γ


. The ratio corresponds to a signal to noise ratio. According to another feature of the invention, the disk drive includes means for estimating a BER from the ratio μ


Γ





Γ


.




This invention can also be regarded as a method for computing a sequence of channel metrics {Γ


n


} for characterizing the performance of a disk drive. This method include the steps of reading a plurality of bit cells stored on a recording surface in the disk drive to produce a noise-corrupted read signal and generating a sequence of observed samples {y


n


} responsive to the noise-corrupted read signal. The sequence of observed samples {y


n


} forms a sequence of observed-sample subsequences {Y


n


}. Each observed-sample subsequence Y


n


has an earliest observed sample and a latest observed sample. The method includes the step of providing a sequence of expected samples {w


n


}. The sequence of expected samples forms a sequence of expected-sample subsequences {W


n


}. Each expected-sample subsequence W


n


has an earliest expected sample and a latest expected sample. The method includes computing a sequence of channel metrics {Γ


n


}. Each channel metric Γ


n


is a function of a distance determined from one of the observed-sample subsequences Y


n


to the corresponding expected-sample subsequence W


n


. Each channel metric Γ


n


is independent of the earliest observed sample in every prior observed-sample subsequence Y


n


and the earliest expected sample in every prior expected-sample subsequence W


n


.




In accordance with another feature of the invention, the method further includes the steps of computing a mean μ


Γ


of the channel metrics Γ


n


; computing a standard deviation σ


Γ


of the channel metrics Γ


n


; and computing a ratio of the mean μ


Γ


to the standard deviation σ


Γ


. The ratio corresponds to a signal to noise ratio. According to another feature of the invention, the method further includes estimating the BER from the ratio μ


Γ





Γ


.




The foregoing and other features of the invention are described in detail below and set forth in the appended claims.











BRIEF DESCRIPTION OF THE DRAWINGS





FIG. 1

is a block diagram of a disk drive embodying the invention.





FIG. 2

is a block diagram of the HDA and channel components in the disk drive of

FIG. 1

; the channel includes a built-in self-test system for computing a sequence of channel metrics {Γ


n


}, and for accumulating a sum of the channel metrics Γ


n


(ΣΓ


n


) and a sum of the squares of the channel metrics Γ


n


(ΣΓ


n




2


).





FIG. 3

is a trellis diagram showing a trellis path route corresponding to an expected-sample subsequence W


n


, the expected-sample subsequence W


n


being defined by an expected correct-sample subsequence R


n


and an expected error-sample subsequence R′


n


.





FIG. 4A

is a sequence diagram for a sampled signal produced by sampling and shows a sequence of noise corrupted unequalized samples u


0


, . . . u


6


.





FIG. 4B

is a sequence diagram for a sampled signal that defines a sequence of noise corrupted observed samples y


0


, . . . y


6


.





FIG. 4C

is a sequence diagram for a sampled signal that defines a noiseless sequence of expected correct samples r


0


, . . . ,r


6


.





FIG. 5A

is a trellis diagram showing an expected correct trellis path corresponding to the sequence of expected correct samples r


0


, . . . ,r


6


in FIG.


4


C.





FIG. 5B

is a set of six overlapping trellis diagrams that show a sequence of trellis path routes corresponding to a sequence of expected-sample subsequences W


1


, W


2


, W


3


, W


4


, W


5


, and W


6


.





FIG. 6

is a signal space diagram illustrating two space distances Γ


R′1


and Γ


R1


used in computing channel metric Γ


1


.





FIG. 7

is a table that, for a set of conditions defined by a set of expected correct sample subsequences R


n


and associated state information s


n


, relates the conditions to a set of simplified channel metric Γ


n


equations that each is used for computing the channel metric for the corresponding condition.





FIG. 8

is a block diagram of a channel metric Γ


n


computation system, the channel metric Γ


n


computation system including the set of conditions defined by table 700 of

FIG. 7

for selecting a channel metric Γ


n


equation.





FIG. 9

is a flow chart showing the steps for estimating the BER for the disk drive of FIG.


1


.











DESCRIPTION OF THE PREFERRED EMBODIMENTS




Referring to

FIG. 1

, a disk drive


1


in accordance with a preferred embodiment of the invention includes a head disk assembly (“HDA


10


”) and a printed circuit board assembly (“PCBA


12


”). HDA


10


includes a disk


14


having a recording surface


14




a


for storing a plurality of bit cells, a transducer


20


, and a preamp


22


coupled between transducer


20


and PCBA


12


. HDA


10


also includes a spindle motor


16


and a voice coil motor (“VCM


18


”). PCBA


12


includes a host interface and disk controller (“HIDC


32


”) and a channel


26


. Channel


26


participates in the transfer of data bits between HIDC


32


and HDA


10


. PCBA


12


also includes a microprocessor


34


, a data buffer


42


, a read only memory (“ROM


54


”), a writeable random access memory (“RAM


60


”), a spindle motor driver


56


, and a VCM driver


58


.




The disclosure of commonly owned co-pending U.S. patent application Ser. No. 08/815,352, filed Mar. 11, 1997, entitled DISK DRIVE EMPLOYING READ ERROR TOLERANT SYNC MARK DETECTION, is incorporated herein by reference (the “


352


application”). A description of the elements shown in

FIG. 1

is set forth in the '


352


application.




Disk drive


1


has a normal mode of operation and a built-in self-test (BIST) mode of operation. The BIST mode of operation has (a) a test write mode of operation and (b) a test read mode of operation. Alternatively, the BIST mode of operation may include the test read mode of operation only.




The BIST mode of operation can be used for estimating the BER of disk drive


1


and locating defective sites on recording surface


14




a


of disk


14


. The BIST mode of operation can also be used for tuning electronic components in disk drive


1


to improve the BER.




During the BIST mode of operation, channel


26


computes a sequence of channel metrics {Γ


n


} and accumulates a sum of the channel metrics Γ


n


(ΣΓ


n


) and a sum of the squares of the channel metrics Γ


n


(ΣΓ


n




2


). Channel


26


compares each channel metric Γ


n


to a channel metric Γ


n


defect threshold. If the channel metric Γ


n


is below the channel metric Γ


n


defect threshold, channel


26


generates a defect discovery signal indicating a defective site. The defect discovery signal can be transmitted from channel


26


to HIDC


32


using a channel data bus


38


. The sequence of channel metrics {Γ


n


} can be used for performing a bit-by-bit defect discovery.




Microprocessor


34


receives the accumulated channel metrics Γ


n


from channel


26


and computes a mean μ


Γ


and a standard deviation σ


Γ


of the channel metrics Γ


n


. Microprocessor


34


also computes a ratio of the mean μ


Γ


to the standard deviation σ


Γ


, the ratio corresponding to a signal to noise ratio.




HIDC


32


receives and transmits the ratio (μ


Γ





Γ


) from microprocessor


34


to the host computer (not shown). Alternatively, microprocessor


34


estimates a BER from the ratio (μ


Γ





Γ


) For example, the BER can be estimated from Q (μ


Γ





Γ


), where Q is the Gaussian Q function. HIDC


32


receives and transmits the BER from microprocessor


34


to the host computer (not shown). HIDC


32


receives the defect discovery signal from channel


26


and records the defective site in a defect list.




Referring to

FIG. 2

, channel


26


of

FIG. 1

includes a pattern generator


202


, a write channel


204


, a read channel


206


, and a BIST mode test system


208


. Read channel


206


includes a variable gain amplifier (“VGA


212


”), a low pass filter (“LPF


214


”), a sampler


216


, a sampled data equalizer


218


, a slicer detector


220


, a timing control


222


, a gain control


224


, a Viterbi detector


226


, and a decoder


228


. Write channel


204


includes an encoder and a precoder (not shown).




Pattern generator


202


is a data source suitable for providing a data signal


203


representing a test data sequence {b


n


} to write channel


204


. As used in herein, for a sequence of elements having a lower case letter and a subscript n, the subscript n represents the n


th


element in the sequence of elements.




For example, pattern generator


202


is a PN signal generator that provides a pseudo-random test data sequence {b


n


}. The disclosure of commonly owned co-pending U.S. patent application Ser. No. 08/870,515, now U.S. Pat. No. 6,208,477, filed Jun. 6, 1997, entitled HARD DISK DRIVE HAVING A BUILT-IN SELF-TEST FOR MEASURING READBACK SIGNAL DISTORTION, is incorporated herein by reference (the “515 application”). A description of a PN signal generator is set forth in the '515 application.




Alternatively, pattern generator


202


can be a data source that is external to channel


26


. For example, pattern generator


202


can be an external memory unit for providing a data signal


203


representing the test data sequence {b


n


}. The test data sequence {b


n


} can be a predetermined test data sequence. Pattern generator


202


can also be a host computer (user data) or a servo track writer (servo data) that provides a data signal


203


representing a non-test data sequence {b


n


}.




BIST mode test system


208


includes an expected sample generator


230


, a channel metric Γ


n


computation and defect detection system


232


(“Γ


n


computation system


232


”), and a channel metric Γ


n


accumulation system


234


. Alternatively, BIST mode system


208


includes channel metric Γ


n


accumulation system


234


only. In this alternate embodiment, Viterbi detector


226


computes and transmits the sequence of channel metrics {Γ


n


} to channel metric Γ


n


accumulation system


234


. Viterbi detector


226


can include a defect detection system for generating a defect discovery signal indicating a defective site for channel metrics Γ


n


that do not meet a channel metric Γ


n


defect threshold.




Write Mode of Operation




During the test write mode of operation, write channel


204


receives data signal


203


representing the test data sequence {b


n


} from pattern generator


202


and produces a data signal


205


representing a test data sequence {b*


n


). Alternatively, during the normal write mode of operation, write channel


204


receives a data signal


203


representing the non-test data sequence {b


n


} from pattern generator


202


and produces a data signal


205


representing a non-test data sequence {b*


n


}.




Data signal


205


has a sequence of state information {s


n


} that corresponds to the test data sequence {b*


n


}. The precoder in write channel


204


is suitable for generating data signal


205


representing the test data sequence {b*


n


}.




According to another embodiment, write channel


204


does not includes the encoder and the precoder. Write channel


204


receives data signal


203


representing the test data sequence {b


n


} from pattern generator


202


and produces a data signal


205


without encoding and precoding signal processing.




Preamp


22


receives data signal


205


from write channel


204


and generates write signal


17




a


corresponding to the test data sequence {b*


n


}. Transducer


20


receives write signal


17




a


and records the test data sequence {b*


n


} as a plurality of bit cells on recording surface


14




a.






Read Mode of Operation




During the test read mode of operation, transducer


20


reads the plurality of bit cells stored on recording surface


14




a


to produce a noise-corrupted analog read signal


17




b


. Preamp


22


receives analog read signal


17




b


and produces a noise-corrupted analog read signal


211


. VGA


212


receives analog read signal


211


and under control of gain control


224


produces an analog read signal


213


that has a substantially constant amplitude. LPF


214


receives analog read signal


213


and generates analog read signal


215


having an improved signal to noise ratio. Sampler


216


receives analog read signal


215


and in response generates sampled signal


217


. Sampled data equalizer


218


receives sampled signal


217


and generates an equalized sampled signal


219


representing a sequence of observed samples {y


n


}.




Slicer detector


220


receives equalized sampled signal


219


and in response generates a slicer sampled signal


221


representing a sequence of slicer samples {a


n


}. Slicer sampled signal


221


is a coarsely quantized estimate of equalized sampled signal


219


. For example, slicer sampled signal


221


for a PR


4


ML channel has one of three possible slicer sample values (+1,0, −1). If the equalized sample value for equalized sampled signal


219


is more positive than a first predetermined factor (e.g., ½) of the target value +1, the slicer sample value is +1. If the equalized sample value for equalized sampled signal


219


is more negative than a second predetermined factor (e.g., ½) of the target value −1, the slicer sample value is −1. If the equalized sample value for equalized sampled signal


219


is between (a) the first predetermined factor (e.g., ½) of the target value +1 and (b) the second predetermined factor (e.g., ½) of the target value −1, then the slicer sample value is 0.




Viterbi detector


226


receives equalized sampled signal


219


representing the sequence of observed samples {y


n


} and generates a data signal


227


representing a data sequence {{circumflex over (b)}


n


}. Decoder


228


receives data signal


227


and generates a decoded data signal


229


.




Expected sample generator


230


receives data signal


205


representing the test data sequence {b*


n


} that was supplied to preamp


22


during the test write mode of operation. Expected sample generator


230


generates an expected sample signal


231


representing a sequence of expected samples {w


n


}. Expected sample generator


230


includes a finite state channel model (not shown) that receives state information {s


n


} associated with the test data sequence {b*


n


} to produce expected sample signal


231


. For example, the finite state channel model for disk drive


1


having a PR


4


ML signal processing system is defined by the transfer polynomial (1-D


2


).




Alternatively, expected sample generator


230


receives signal


203


representing the test data sequence {b


n


} that was supplied to write channel


204


during the test write mode of operation. In this alternative embodiment, expected sample generator


230


includes an encoder, a precoder and a finite state channel model. The encoder and precoder generate the test data sequence {b*


n


} corresponding to data signal


205


. The finite state channel model receives state information {s


n


} associated with the test data sequence {b*


n


} and generates signal


231


representing the sequence of expected samples {w


n


}.




According to alternate embodiment, the BIST mode of operation includes the test read mode of operation only. Expected sample generator


230


receives signal


221


representing the sequence of slicer samples {a


n


} and generates signal


231


representing a sequence of expected samples {w


n


}. In this alternate embodiment, the sequence of slicer samples {a


n


} corresponds to the non-test data sequence {b*


n


}. Expected sample generator


230


includes a state machine (not shown) for defining state information {s


n


} associated with the non-test data sequence {b*


n


}




State information {s


n


} associated with the test data sequence {b*


n


} defines the sequence of expected correct samples {Γ


n


}. According to an alternate embodiment, state information {s


n


} associated with the non-test data sequence {b*


n


}defines the sequence of expected correct samples {Γ


n


}.




The sequence of expected error samples {r′


n


} is defined by the state information {s


n


} associated with the sequence of expected correct samples {Γr


n


}. The sequence of expected samples {w


n


} is defined by the sequence of expected correct samples {Γr


n


} and the sequence of expected error samples {r′


n


}.




Channel metric Γ


n


computation system


232


receives equalized sampled signal


219


representing the sequence of observed samples {y


n


} and signal


231


representing the sequence of expected samples {w


n


}. Channel metric Γ


n


computation system


232


generates a signal


233


representing a sequence of channel metrics {Γ


n


}.




The sequence of observed samples {y


n


} forms a sequence of observed-sample subsequences {Y


n


}. Each observed-sample subsequence Y


n


has an earliest observed sample and a latest observed sample. The sequence of expected samples {w


n


} forms a sequence of expected-sample subsequences {W


n


}. Each expected-sample subsequence W


n


has an earliest expected sample and a latest expected sample. As used herein, for a sequence of subsequences having an upper case letter and a subscript n, the subscript n represents the n


th


subsequence in the sequence of subsequences.




Each channel metric Γ


n


is a function of a distance determined from one of the observed-sample subsequences Y


n


to the corresponding expected-sample subsequence W


n


. Each channel metric Γ


n


is independent of the earliest observed sample in every prior observed-sample subsequence Y


n


and the earliest expected sample in every prior expected-sample subsequence W


n


.




The distance determined from the observed-sample subsequences Y


n


to the corresponding expected-sample subsequence W


n


corresponds to a space distance, such as a Euclidean or Hamming distance. Alternatively, the distance can be an absolute value of the difference between the observed-sample subsequence Y


n


and expected-sample subsequence W


n


.




Channel metric Γ


n


computation system


232


compares signal


233


representing the channel metric Γ


n


to a channel metric Γ


n


defect threshold. If signal


233


(channel metric Γ


n


) is below the channel metric Γ


n


defect threshold, channel metric Γ


n


computation system


232


generates a defect discovery signal


238


indicating a defective site associated with the observed sample y


n


.




Channel metric Γ


n


accumulation system


234


receives signal


233


and generates a signal


235


representing a sum of the channel metrics Γ


n


(ΣΓ


n


). Channel metric Γ


n


accumulation system


234


also generates a signal


236


representing a sum of the squares of the channel metrics Γ


n


(ΣΓ


n




2


).




Microprocessor


34


receives signal 235 (representing the sum of the channel metrics Γ


n


) and signal


236


(representing the sum of the squares of the channel metrics Γ


n


) to compute the mean μ


Γ


and the standard deviation σ


Γ


. Microprocessor


34


also computes the ratio of the mean μ


Γ


to the standard deviation σ


Γ


. The ratio represents the signal to noise ratio. According to an alternate embodiment, microprocessor


34


estimates a BER from the ratio (μ


Γ/σ




Γ


)




HIDC


32


receives and transmits the ratio (μ


Γ





Γ


) from microprocessor


34


to the host computer (not shown). Alternatively, HIDC


32


receives and transmits the BER from microprocessor


34


to the host computer (not shown). HIDC


32


receives defect discovery signal


238


and records the defective site in the defect list.




Referring to

FIG. 3

, trellis diagram path route


300


corresponds to an expected-sample subsequence W


n


for disk drive


1


(

FIG. 1

) employing a sampled data signal processing system tuned to a (1-D) channel response. This illustration is suitable for each of the (1-D) interleaves in a PR


4


ML signal processing system.




The expected-sample subsequence W


n


is defined by an expected correct-sample subsequence R


n


and an expected error-sample subsequence R′


n


. As previously mentioned, the sequence of expected samples {w


n


} is defined by the sequence of expected correct samples {r


n


} and the sequence of expected error samples {r′


n


}. The sequence of expected correct samples {r


n


} forms the sequence of expected correct-sample subsequences {R


n


}. Each expected correct-sample subsequence R


n


has an earliest expected correct sample and a latest expected correct-sample. The sequence of expected error samples {r′


n


} forms the sequence of expected error-sample subsequences {R′


n


}. Each expected error-sample subsequence R′


n


has an earliest expected error sample and a latest expected error sample.




Path route


300


has a correct path


302


corresponding to the expected correct-sample subsequence R


n


and an error event path


304


corresponding to the expected error-sample subsequence R′


n


. Correct path


302


begins from a beginning state s


n−2




306


and ends at an ending state s


n




308


. Error event path


304


is a minimum distance error event path that begins from the beginning state s


n−2




306


and ends at the ending state


308


s


n


.




Path route


300


has two time steps between the beginning state s


n−2




306


and the ending state


308


s


n


. Alternatively, path route


300


has more than two times steps between the beginning state


306


and the ending state


308


. The number of time steps corresponds to the number of samples between the beginning state


306


and ending state


308


.




Example




The following is an example of disk drive


1


(

FIG. 1

) employing a sampled data signal processing system tuned to a (1-D) channel response. This example is also suitable for each of the (1-D) interleaves in a PR


4


ML signal processing system. The mean μ


Γ


of the channel metrics {Γ


n


} is computed for each interleave and then combined together. The standard deviation of the channel metrics {Γ


n


} is also computed for each interleave and then combined together.




During the test write mode of operation, write channel


204


receives a test data sequence b


0


=1, b


1


=0, b


2


=0, b


3


=0, b


4


=0, b


5


=1, and b


6


=0 and generates a test data sequence b*


initial


=0, b*


0


=1, b*


1


=1, b*


2


=1, b*


3


=1, b*


4


=1, b*


5


=0, and b*


6


=0. Transducer


20


receives state information s


initial


=−, s


0


=+, s


1


=+, s


2


=+, s


3


=+, s


4


=+, s


5


=−, and s


6


=− associated with the test data sequence {b*


n


} and records the test data sequence {b*


n


} as a plurality of bit cells on recording surface


14




a


of disk


14


.




During the test read mode of operation, transducer


20


reads the plurality of bit cells stored on recording surface 14


a


to produce a noise-corrupted read signal. Sampler


216


generates a noise corrupted sequence of unequalized samples u


0


=+0.8, u


1


=−0.1, u


2


=−0.8, u


3


=−0.3, u


4


=−0.4, u


5


=−1.7, and u


6


=−0.9 responsive to the noise-corrupted read signal. Referring to

FIG. 4A

, sequence diagram


402


shows the noise corrupted sequence of unequalized samples u


0


, u


1


, u


2


, u


3


, u


4


, u


5


, and u


6


.




Sampled data equalizer


218


generates a sequence of observed samples y


0


=+0.8, y


1


=−0.1, y


2


=−0.6, y


3


=+0.1, y


4


=+0.3, y


5


=−1.2, and y


6


=−0.2 responsive to the noise corrupted sequence of unequalized samples. Referring to

FIG. 4B

, sequence diagram


404


shows the sequence of observed samples y


0


, y


1


, y


2


, y


3


, y


4


, y


5


and y


6


. The sequence of observed samples {y


n


} includes noise which contributes to sample values deviating from their expected correct values.




The sequence of observed samples {y


n


} forms a sequence of observed-sample subsequences Y


n


: Y


1


=y


0


,y


1


; Y


2


=y


1


,y


2


; Y


3


=y


2


,y


3


; Y


4


=y


3,y




4


; Y


5


=y


4


,y


5


; and Y


6


=y


5


,y


6


. Each observed-sample subsequence Y


n


has an earliest observed sample and a latest observed sample.




Expected sample generator


230


receives the test data sequence b*


initial


=0, b*


0


=1, b*


1


=1, b*


2


=1, b*


3


=1, b*


4


=1, b*


5


=0, and b*


6


=0 and provides a corresponding sequence of expected correct samples r


0


=+1.0, r


1


=0.0, r


2


=0.0, r


3


=0.0, r


4


=0.0, r


5


=−1.0, and r


6


=0.0. State information {s


n


} associated with the test data sequence {b*


n


} defines the sequence of expected correct samples {r


n


}. Referring to

FIG. 4C

, sequence diagram


406


shows the sequence of expected correct samples r


0


, r


1


, r


2


, r


3


, r


4


, r


5


, and r


6


. The sequence of expected correct samples {r


n


} represents noiseless samples having expected values.




The sequence of expected correct samples {Γr


n


} forms a sequence of expected correct-sample subsequences R


n


: R


1


=r


0


r


1


; R


2


=r


1


,r


2


; R


3


=r


2


,r


3


; R


4


=r


3


,r


4


; R


5


=r


4


,r


5


; and R


6


=r


5


,r


6


. Each expected correct-sample subsequence R


n


has an earliest expected correct sample and a latest expected correct sample. The sequence of expected correct-sample subsequences R


n


defines a sequence of expected error-sample subsequences R′


n


: R′


1


,=r′


0


,r′


1


; R′


2


r′


1


,r′


2


; R′


3


=r′


2


,r′


3


; R′


4


=r′


3


,r′


4


; R′


5


=r′


4


,r′


5


; and R′


6


=r′


5


,r′


6


. Each expected error-sample subsequence R′


n


has an earliest expected error sample and a latest expected error sample.




Referring to

FIG. 5A

, trellis diagram


500


includes an expected correct trellis path


502


corresponding to the sequence of expected correct samples r


0


=+1.0, r


1


=0.0, r


2


=0.0, r


3


=0.0, r


4


=0.0, r


5


=−1.0, and r


6


=0.0. Expected correct trellis path


502


defines a sequence of six overlapping path routes


504


,


506


,


508


,


510


,


512


, and


514


. Each path route corresponds to an expected-sample subsequence W


n


.




Referring to

FIG. 5B

, trellis diagram


516


shows the sequence of overlapping path routes


504


,


506


,


508


,


510


,


512


, and


514


corresponding to a sequence of expected-sample subsequences W


n


: W


1


, W


2


, W


3


, W


4


, W


5


and W


6


. As previously mentioned, each expected-sample subsequence W


n


is defined by an expected correct-sample subsequence R


n


and an expected error-sample subsequence R′


n


. As shown in trellis diagram


516


, each path route includes a correct path (solid line) corresponding to an expected correct-sample subsequence R


n


: r


n−1


,r


n


and an error event path (dotted line) corresponding to an expected error-sample subsequence R′


n


: r′


n−1


,r′


n


.




Referring to

FIGS. 5A and 5B

, path route


504


corresponds to the expected-sample subsequence W


1


. The expected-sample subsequence W


1


is defined by expected correct-sample subsequence R


1


: r


0


=+1.0, r


1


=0.0, and expected error-sample subsequence R′


1


: r′


0


=0.0, r′


1


=+1.0. Path route


506


corresponds to expected-sample subsequence W


2


. The expected-sample subsequence W


2


is defined by expected correct-sample subsequence R


2


: r


1


=0.0, r


2


=0.0, and expected error-sample subsequence R′


2


: r′


1


=−1.0, r′


2


=+1.0. Path route 508 corresponds to expected-sample subsequence W


3


. The expected-sample subsequence W


3


is defined by expected correct-sample subsequence R


3


: r


2


0.0, r


3


=0.0, and expected error-sample subsequence R′


3


: r′


2


=−1.0, r′


3


=+1.0. Path route


510


corresponds to expected-sample subsequence W


4


. The expected-sample subsequence W


4


is defined by expected correct-sample subsequence R


4


: r


3


=0.0, r


4


=0.0, and expected error-sample subsequence R′


4


: r′


3


=−1.0, r′


4


=+1.0. Path route


512


corresponds to expected-sample subsequence W


5


. The expected-sample subsequence W


5


is defined by expected correct-sample subsequence R


5


: r


4


=0.0, r


5


=−1.0, and expected error-sample subsequence R′


5


: r′


4


=−1.0, r′


5


=0.0. Path route


514


corresponds to expected-sample subsequence W


6


. The expected-sample subsequence W


6


is defined by expected correct-sample subsequence R


6


: r


5


=−1.0, r


6


=0.0, and expected error-sample subsequence R′


6


: r′


5


=0.0, r′


6


=−1.0.




Table 1 shows sample values for the sequence of observed-sample subsequences {Y


n


: y


n−1


,y


n


} and the sequence of expected-sample subsequences {W


n


}, wherein the sequence of expected-sample subsequences {W


n


} is defined by the sequence of expected correct-sample subsequences {R


n


: r


n−1


,r


n


} and the sequence of expected error-sample subsequences (R′


n


: r′


n−1


,r′


n


}.














TABLE 1












observed-sample




expected-sample






sub-




subsequence Y


n






subsequence W


n
















sequence




Y


n


: y


n−1


,y


n






R


n


: r


n−1


,r


n






R′


n


: r′


n−1


,r′


n











n = 1




y


0


= +0.8, y


1


= −0.1




r


0


= +1.0, r


1


= 0.0




r′


0


= 0.0, r′


1


= +1.0






n = 2




y


1


= −0.1, y


2


= −0.6




r


1


= 0.0, r


2


= 0.0




r′


1


= −1.0, r′


2


= +1.0






n = 3




y


2


= −0.6, y


3


= +0.1




r


2


= 0.0, r


3


= 0.0




r′


2


= −1.0, r′


3


= +1.0






n = 4




y


3


= +0.1, y


4


= +0.3




r


3


= 0.0, r


4


= 0.0




r′


3


= −1.0, r′


4


= +1.0






n = 5




y


4


= +0.3, y


5


= −1.2




r


4


= 0.0, r


5


= −1.0




r′


4


= −1.0, r′


5


= 0.0






n = 6




y


5


= −1.2, y


6


= −0.2




r


5


= 1.0, r


6


= 0.0




r′


5


= 0.0, r′


6


= −1.0














The channel metric Γ


n


can be determined from the equation [(y


n−1


−r′


n−1


)


2


+(y


n


−r′


n


)


2


]−[(y


n−1


−r


n−1


)


2


+(y


n


−r


n


)


2


]. The channel metric equation includes a channel metric component Γ


R′n


corresponding to [(y


n−1


−r′


n−1


)


2


+(y


n


−r′


n


)


2


] and a channel metric component Γ


Rn


corresponding to [(y


n−1


−r


n−1


)


2


+(y


n


−r


n


)


2


]. Alternatively, the channel metric Γ


n


can be determined from other simplified equations derived from the channel metric Γ


n


equation [y


n−1


−r′


n−1


)


2


+(y


n


−r′


n


)


2


]−[(y


n−1


−r


n−1


)


2


+(y


n


−r


n


)


2


].














TABLE 2













sample n




















initial state




n = 0




n = 1




n = 2




n = 3




n = 4




n = 5




n = 6























test data sequence {b


n


}





1




0




0




0




0




1




0






test data sequence {b*


n


}




0




1




1




1




1




1




0




0






observed sample sequence {y


n


}





+0.8




−0.1




−0.6




+0.1




+0.3




−1.2




−0.2






expected sample sequence {r


n


}





+1.0




0.0




0.0




0.0




0.0




−1.0




0.0






expected state information {s


n


}









+




+




+




+




+
















channel metrics {Γ


n


}






1.80




3.00




.60




1.60




3.00




5.40






Viterbi state metric (+1 state)





.04




.05




.41




.42




.51




1.95




1.99






Viterbi state metric (−1 state)




0




.64




.65




.21




.22




.31




.55




.59














Channel metric Γ


n


computation system


232


receives one of the observed-sample subsequences Y


n


: y


n−1


,y


n


, the corresponding expected correct-sample subsequence R


n


: r


n−1


,r


n


, and the corresponding expected correct-sample subsequence R′


n


: r′


n−1


,r′


n


to compute the channel metric Γ


n


. Alternatively, channel metric Γ


n


computation system


232


receives one of the observed-sample subsequences Y


n


: y


n−1


,y


n


the corresponding expected correct-sample subsequence R


n


: r


n−1


,r


n


, and the corresponding state information s


n


associated with the expected correct-sample subsequence R


n


.




Referring to tables 1 and 2, channel metric Γ


1


(table 2, at column n=1) is 1.80 and represents a distance determined from the expected-observed sample subsequence Y


1


: y


0


=+0.8,y


1


=−0.1 to the corresponding expected correct-sample subsequence W


1


. Channel metric Γ


2


(at column n=2) is 3.00 and represents a distance determined from the expected-observed sample subsequence Y


2


: y


1


=−0.1,y


2


=−0.6 to the corresponding expected correct-sample subsequence W


2


. Channel metric Γ


3


(at column n=3) is 0.60 and represents a distance determined from the expected-observed sample subsequence Y


3


: y


2


=−0.6,y


3


=+0.1 to the corresponding expected correct-sample subsequence W


3


. Channel metric Γ


4


(at column n=4) is 1.60 and represents a distance determined from the expected-observed sample subsequence Y


4


: y


3


=+0.1, y


4


=+0.3 to the corresponding expected correct-sample subsequence W


4


. Channel metric Γ


5


(at column n=5) is 3.00 and represents a distance determined from the expected-observed sample subsequence Y


5


: y


4


=+0.3,y


5


=−1.2 to the corresponding expected correct-sample subsequence W


5


. Channel metric Γ


6


(at column n=6) is 5.40 and represents a distance determined from the expected-observed sample subsequence Y


6


: y


5


=−1.2,y


6


=−0.2 to the corresponding expected correct-sample subsequence W


6


.




Referring to

FIG. 6

, signal space


600


illustrates the space distance corresponding to channel metric Γ


1


. Signal space


600


includes possible expected sample points


602


(0.0,+1.0),


604


(−1.0,+1.0),


606


(−1.0,0.0),


608


(0.0,0.0),


610


(+1.0,0.0),


612


(0.0,−1.0), and


614


(+1.0,−1.0). Each possible expected sample point corresponds to a possible expected correct-sample subsequence R


n


: r


n−1


,r


n


or a possible expected-error sample subsequence R′


n


: r′


n−1


,r′


n


.




For example, sample point


616


corresponds to the observed-sample subsequence Y


1


: y


0


=+0.8,y


1


=−0.1. The channel metric Γ


1


(table 2, at column n=1) is 1.80 and represent a distance determined from the expected-observed sample subsequence Y


1


to the corresponding expected correct-sample subsequence W


1


. The expected correct-sample subsequence W


1


is defined by the expected correct-sample subsequence R


1


: r


0


=+1.0,r


1


=0.0 associated with the correct path in path route


504


, and the expected error-sample subsequence R′


1


: r′


0


=0.0,r′


1


=+1.0 associated with the error event path in path route


504


.




Sample point


602


corresponds to the expected error-sample subsequence R′


1


: r′


0


=0.0,r′


1


=+1.0. Sample point


610


corresponds to the expected correct-sample subsequence R


1


: r


0


=+1.0,r=0.0. Space distance


618


represents the channel metric component Γ


R′1


(1.85). Space distance


620


represents the channel metric component Γ


R1


(0.05). The channel metric Γ


1


(1.8) represents a distance determined from space distance


618





R′1


=1.85) minus space distance


620





R1


=0.05).




Table 2 shows a Viterbi state metric at a +1 state and a −1 state. The Viterbi state metric is computed for each state beginning from an initial state and continuing to a state at n=6. The initiate state s


initial


is—and the Viterbi state metric for the −1 state is 0.




Viterbi detector


220


has a structure defining a Viterbi engine for computing the +1 Viterbi state metric and the −1 Viterbi state metric. The Viterbi detector also has a path memory for retaining and generating a trellis path having the least accumulated state metrics. The Viterbi engine operates in a repeated cycle. During each cycle, it computes two Viterbi state metrics for each of the two respective states (+1 state and −1 state). The Viterbi engine computes a branch metric for each possible path entering each state, adds the branch metric to a previous Viterbi state metric to produce a candidate Viterbi state metric, and selects the candidate Viterbi state metric having the lowest value.




During each cycle, the path memory is updated so that it selects a path having the lowest accumulated Viterbi state metric. The Viterbi engine computes each branch metric by computing the square of the difference between the value of an observed sample y


n


and the value of a possible target sample t


n


. The branch metric equation is (y


n


−t


n


)


2


. Viterbi detector


220


includes branch metric registers for holding computed branch metrics and state metric registers for holding accumulated Viterbi state metrics.




The selected Viterbi state metric is a sum of a branch metric and a previous state metric having the least accumulated Viterbi state metric. The selected Viterbi state metric depends on the earliest observed sample in the observed sequence and the earliest target sample in the possible sample sequence.




Table 3 differs from table 1 in that the earliest observed sample y


0


is changed from +0.8 to +0.3. Channel metric Γ


1


(at column n=1) decreased from 1.8 to 0.8. The remaining channel metrics Γ


2


through Γ


6


are not affected by this change in the earliest observed sample y


0


. Channel metrics Γ


2


through Γ


6


are independent of the earliest observed sample y


0


. Each channel metric Γ


n


is independent of the earliest observed sample in every prior observed-sample subsequence Y


n


and the earliest expected sample subsequence in every prior expected sample-subsequence W


n


.




Each Viterbi state metric (columns n=0 through n=6) is affected by changing the earliest observed sample y


0


. Each Viterbi state metric (+1 state and −1 state) shown in columns n=1 through n=6 depends on the earliest observed sample y


0


.














TABLE 3













sample n




















initial state




n = 0




n = 1




n = 2




n = 3




n = 4




n = 5




n = 6























test data sequence {b


n


}





1




0




0




0




0




1




0






test data sequence {b*


n


}




0




1




1




1




1




1




0




0






observed sample value {y


n


}





+0.3




−0.1




−0.6




+0.1




+0.3




−1.2




−0.2






expected sample value {r


n


}





+1.0




0.0




0.0




0.0




0.0




−1.0




0.0






expected state information {s


n


}









+




+




+




+




+
















channel metrics {Γ


n


}






.80




3.00




.60




1.60




3.00




5.40






Viterbi state metric (+1 state)





.49




.50




.86




.87




.96




2.4




2.44






Viterbi state metric (−1 state)




0




.09




.10




.46




.47




.56




1.00




1.04














Channel metric Γ


n


computation system


232


compares each channel metric Γ


n


to a channel metric Γ


n


defect threshold. For example, if the channel metric Γ


n


defect threshold is 1, channel metric Γ


n


computation system


232


will generate a defect discovery signal for channel metric Γ


3


. The defect discovery signal indicates a defective site associated with observed samples Y2 and y


3


.




Channel metric Γ


n


accumulation system


234


receives and accumulates a sequence of the channel metrics {Γ


n


} to produce a sum of the channel metrics ΣΓ


n


and a sum of the squares of the metrics ΣΓ


n




2


.




Microprocessor


34


receives the sum of the channel metrics Γ


n


and the sum of the squares of the channel metrics Γ


n


to compute the mean μ


Γ


and the standard deviation σ


Γ


. Microprocessor


34


also computes the ratio of the mean μ


Γ


to the standard deviation σ


Γ


. The ratio represents the signal to noise ratio. According to an alternate embodiment, microprocessor


34


estimates a BER from the ratio (μ


Γ





Γ


).




HIDC


32


receives and transmits the ratio (μ


Γ





Γ


) from microprocessor


34


to the host computer (not shown). Alternatively, HIDC


32


receives and transmits the BER from microprocessor


34


to the host computer (not shown). HIDC


32


receives the defect discovery signal and records the defective site in the defect list.




Referring to

FIG. 7

, table 700 shows eight simplified channel metric Γ


n


equations


706


corresponding to eight possible trellis path routes


708


. Each channel metric Γ


n


equation


706


includes a constant C having a value equal to +2, 0 or −2; a y


n−1


coefficient having a value equal to +2 or −2; and a y


n


coefficient having a value equal to +2 or −2. Channel metric Γ


n


equations


706


are derived from the equation [(y


n−1


−r′


n−1


)


2


+(y


n


−r′


n


)


2


]−[(Y


n−1


−r


n−1


)


2


+(y


n


−r


n


)


2


].




Column


702


provides a list of four possible expected-correct sample subsequences R


n


(r


n−1


, r


n


) for each state (s


n


=+, s


n


=−) Column


704


provides state information s


n


associated with each of the possible expected-correct sample subsequences R


n


(r


n−1


, r


n


). The expected-correct sample subsequences R


n


(r


n−1


, r


n


)


702


and state information s


n


(−or+)


704


define a set of eight conditions, each condition being associated with a corresponding channel metric equation Γ


n




706


.




Referring to

FIG. 8

, channel metric Γ


n


computation system


232


computes a channel metric Γ


n


in accordance with the set of conditions defined in table 700 of FIG.


7


. Channel metric Γ


n


computation system


232


includes a selection matrix


250


, a first selector


252


for selecting a constant C having a value equal to +2,0,or 2, a second selector


254


for selecting a y


n−1


coefficient having a value equal to +2 or −2, a third selector


256


for selecting a y


n


coefficient having a value equal to +2 or −2, a first multiplier


258


, a second multiplier


260


, and a summer


262


.




Equation selection matrix


250


receives an expected correct-sample subsequence R


n


(r


n−1


,r


n


) and state information s


n


. Equation selection matrix


250


generates a first signal


264


representing the constant C, a second signal


266


representing the y


n−1


coefficient, and a third signal


268


representing the y


n


coefficient.




First selector


252


receives first signal


264


from equation selection matrix


250


and produces a signal


270


representing the selected constant C (+2,0,or −2). Second selector


254


receives second signal


266


from equation selection matrix


250


and produces a signal


272


representing the y


n−1


coefficient (+2 or −2). Third selector


256


receives third signal


268


from equation selection matrix


252


and produces a signal


274


representing the y


n


coefficient (+2 or −2).




First multiplier


258


receives an observed sample Y


n−1


and signal


272


representing the y


n−1


coefficient (+2 or −2) to produce a signal


276


representing a product of the observed sample y


n−1


and the y


n−1


coefficient (+2 or −2). Second multiplier


260


receives an observed sample y


n


and signal


274


representing the y


n


coefficient (+2 or −2) to produce a signal


278


representing a product of the observed sample y


n


and the y


n


coefficient (+2 or −2).




Summer


262


receives signal


270


representing the selected constant C (+2,0,or −2), signal


276


representing the product of the observed sample y


n−1


and the Y


n−1


coefficient (+2 or −2), and signal


278


representing the product of the observed sample y


n


and the y


n


coefficient (+2 or −2) to produce a signal


280


representing the channel metric Γ


n


.




Continuing the above example, channel metric Γ


n


computation system


232


receives the observed-sample subsequence Y


1


(y


0


=+0.8, y


1


=−0.1), the expected correct-sample subsequence R


1


(r


0


=+1,r


1


=0), and state information s


1


=+ associated with the expected-correct sample r


1


=0. The R


n


and s


n


conditions corresponds to the channel metric Γ


n


equation


2


(y


n−1


−y


n


) in row


6


of table 700.




Equation selection matrix


250


receives the expected correct-sample subsequence R


1


(r


0


=+1,r


1


=0) and state information s


1


=+. Equation selection matrix


250


generates first signal


264


representing the constant C having a value equal to 0, a second signal


266


representing the Y


n−1


coefficient having a value equal to +2, and a third signal


266


representing the y


n


coefficient having a value equal to −2.




First selector


252


receives first signal


264


from equation selection matrix


250


and produces a signal


270


representing the selected constant C (0). Second selector


254


receives second signal


266


from equation selection matrix


250


and produces a signal


272


representing the y


n−1


coefficient (+2). Third selector


256


receives third signal


268


from equation selection matrix


250


and produces a signal


274


representing the y


n


coefficient (−2).




First multiplier


258


receives the observed sample y


0


=+0.8 and signal


272


representing the y


n−1


coefficient (+2) to produce a signal


276


representing a value equal to +1.6. Second multiplier


260


receives the observed sample −0.1 and signal


274


representing the y


n


coefficient (−2) to produce a signal


278


representing a value equal to +0.2.




Summer


262


receives signal


270


representing the selected constant having a value equal to 0, signal


276


representing the value equal to +1.6, and signal


278


representing the value equal to +0.2 to produce a signal


280


representing the channel metric Γ


1


having a value equal to 1.8.




According to another embodiment, computation circuitry in Viterbi detector


226


can be used for computing each channel metric Γ


n


. Viterbi detector


226


receives the sequence of observed samples {y


n


} and state information {s


n


} associated with the sequence of expected samples {w


n


} to produce the sequence of channel metrics {Γ


n


}. In this embodiment, BIST mode test system


208


includes the channel metric Γ


n


accumulation system


234


only. Channel metric Γ


n


accumulation system


234


receives the sequence of channel metrics {Γ


n


} from Viterbi detector


226


and accumulates a sum of the channel metrics Γ


n


(ΣΓ


n


) and a sum of the squares of the channel metrics Γ


n


(ΣΓ


n




2


).




Referring to

FIG. 9

, flow chart


900


describes a method for computing a sequence of channel metrics {Γ


n


} for characterizing the performance of a disk drive (such as disk drive


1


of FIG.


1


). At step


902


, a transducer (such as


20


of

FIG. 1

) reads a plurality of bit cells stored on a recording surface in the disk drive to produce a noise-corrupted read signal. At step


904


, a sampled data equalizer (such as


218


of

FIG. 2

) generates a sequence of observed samples {y


n


} responsive to the noise-corrupted read signal. The sequence of observed samples {y


n


}forms a sequence of observed-sample subsequences {Y


n


}. Each observed-sample subsequence Y


n


has an earliest observed sample and a latest observed sample.




At step


906


, an expected sample generator (such as


230


of

FIG. 2

) provides a sequence of expected samples {w


n


}. The sequence of expected samples forms a sequence of expected-sample subsequences {W


n


}. Each expected-sample subsequence W


n


has an earliest expected sample and a latest expected sample. At steps


908


and


910


, a channel metric Γ


n


computation system (such as


232


of

FIG. 2

) computes a sequence of channel metrics {Γ


n


}, and a channel metric Γ


n


accumulation system (such as


234


of

FIG. 2

) accumulates a sum of the channel metrics Γ


n


(ΣΓ


n


) and a sum of the squares of the channel metrics Γ


n


(ΣΓ


n


). Each channel metric Γ


n


is a function of a distance determined from one of the observed-sample subsequences Y


n


to the corresponding expected-sample subsequence W


n


. Each channel metric Γ


n


is independent of the earliest observed sample in every prior observed-sample subsequence Y


n


and the earliest expected sample in every prior expected-sample subsequence W


n


.




At step


912


, a processor (such as


34


of

FIG. 1

) computes a mean μ


Γ


of the accumulated channel metrics {Γ


n


}. At step


914


, the processor computes a standard deviation σ


Γ


of the accumulated channel metrics {Γ


n


}. At step


916


, the processor computes a ratio of the mean μ


Γ


to the standard deviation σ


Γ


. The ratio corresponds to a signal to noise ratio. Alternatively, at step


918


, the processor estimates the BER from the ratio (μ


Γ





Γ


) For example, the BER can be estimated from Q (μ


Γ





Γ


), where Q is the Gaussian Q function.




The ratio (μ


Γ





Γ


) constitutes a very precise basis for characterizing the performance of disk drive


1


because the ratio is based on computing multiple channel metrics Γ


n


for a sequence of observed sample {y


n


}. The ratio (μ


Γ





Γ


) provides for rapidly characterizing the performance of disk drive


1


. The ratio (μ


Γ





Γ


) can be used for rapidly and precisely estimating the BER for disk drive


1


. For example, about 10


3


observed samples can produce a precise estimate of BER when the BER is in the neighborhood of 10


−6


BER. The sequence of channel metrics {Γ


n


} can be used for discovering defective sites on recording surface


14




a


of disk drive


1


.



Claims
  • 1. A disk drive having a normal mode of operation and a built-in self-test mode of operation for producing a sequence of channel metrics {Γn}, the disk drive comprising:a recording surface having a plurality of bit cells; a transducer for reading the plurality of bit cells to produce a noise-corrupted read signal; means responsive to the noise-corrupted read signal for generating a sequence of observed samples {yn}, the sequence of observed-samples {yn} forming a sequence of observed-sample sequences {Yn}, each observed sample sequence Yn having an earliest observed sample and a latest observed sample; means operative during the built-in self-test mode of operation for providing a sequence of expected samples {wn}, the sequence of expected samples forming a sequence of expected-sample subsequences {Wn}, each expected-sample subsequence Wn having an earliest expected sample and a latest expected sample; computation means for computing a sequence of channel metrics {Γn}, each channel metric Γn being a function of a distance determined from one of the observed-sample subsequences Yn to the corresponding expected-sample sequence Wn, each channel metric Γn being independent of the earliest observed sample in every prior observed-sample subsequence Yn and the earliest expected sample in every prior expected-sample subsequence Wn; means for computing a mean μΓ of the channel metrics Γn; means for computing a standard deviation σΓ of the channel metrics Γn; and means for computing a ratio of the mean μΓ to the standard deviation σΓ, the ratio (μΓ/σΓ) corresponding to a signal to noise ratio.
  • 2. The disk drive of claim 1 further comprising means for estimating a bit error rate of the disk drive from the ratio (μΓ/σΓ).
  • 3. The disk drive of claim 2, wherein the means for estimating the bit error rate comprises a means for computing Q(μΓ/σΓ) where Q is a Gaussian Q function.
  • 4. A method for computing a sequence of channel metrics {Γn} for characterizing the performance of a disk drive, the method comprising the steps of:reading a plurality of bit cells stored on a recording surface in the disk drive to produce a noise-corrupted read signal; generating a sequence of observed samples {yn}, the sequence of observed-samples {yn} forming a sequence of observed-sample sequences {Yn}, each observed sample sequence Yn having an earliest observed sample and a latest observed sample; providing a sequence of expected samples {wn}, the sequence of expected samples forming a sequence of expected-sample subsequences {Wn}, each expected-sample subsequence Wn having an earliest expected sample and a latest expected sample; computing a sequence of channel metrics {Γn}, each channel metric Γn being a function of a distance determined from one of the observed-sample subsequences Yn to the corresponding expected-sample sequence Wn, each channel metric Γn being independent of the earliest observed sample in every prior observed-sample subsequence Yn and the earliest expected sample in every prior expected-sample subsequence Wn; and computing a mean μΓ of the channel metrics Γn; computing a standard deviation σΓ of the channel metrics Γn; computing a ratio of the mean μΓ to the standard deviation σΓ, the ratio (μΓ/σΓ) corresponding to a signal to noise ratio.
  • 5. The method of claim 4 further comprising the step of estimating a bit error rate of the disk drive from the ratio (μΓ/σΓ).
  • 6. The disk drive of claim 5, wherein the step of estimating the bit error rate comprises the step of computing Q(μΓ/σΓ) where Q is a Gaussian Q function.
  • 7. A method for estimating a bit error rate for a disk drive, the method comprising the steps of:reading a plurality of bit cells stored on a recording surface in the disk drive to produce a noise-corrupted read signal; generating a sequence of observed samples {yn} responsive to the noise-corrupted read signal, the sequence of observed samples {yn} forming a sequence of observed-sample subsequences {Yn}, each observed-sample subsequence Yn having an earliest observed sample and a latest observed sample; providing a sequence of expected samples {wn}, the sequence of expected samples forming a sequence of expected-sample subsequences {Wn}, each expected-sample subsequence Wn having an earliest expected sample and a latest expected sample; computing a sequence of channel metrics {Γn}, each channel metric Γn being a function of a distance determined from one of the observed-sample subsequences Yn to the corresponding expected-sample subsequence Wn, each channel metric Γn being independent of the earliest observed sample in every prior observed-sample subsequence Yn and the earliest expected sample in every prior expected-sample subsequence Wn; computing a mean μΓ of the channel metrics {Γn}; computing a standard deviation σΓ of the channel metrics {Γn}; computing a ratio of the mean μΓ to the standard deviation σΓ, the ratio (μΓ/σΓ) corresponding to a signal to noise ratio; and estimating the bit error rate from the ratio (μΓ/σΓ).
  • 8. The disk drive of claim 7, wherein the step of estimating the bit error rate comprises the step of computing Q(μΓ/σΓ) where Q is a Gaussian Q function.
  • 9. A disk drive having a normal mode of operation and a built-in self-test mode of operation for producing a sequence of channel metrics {Γn}, the disk drive comprising:a recording surface having a plurality of bit cells; a transducer for reading the plurality of bit cells to produce a noise-corrupted read signal; a sampler responsive to the noise-corrupted read signal for generating a sequence of observed samples {yn}, the sequence of observed-samples {yn} forming a sequence of observed-sample sequences {Yn}; an expected sample generator operative during the built-in self-test mode of operation for providing a sequence of expected samples {wn}, the sequence of expected samples forming a sequence of expected-sample subsequences {Wn}; channel metrics computer for computing a sequence of channel metrics {Γn}, each channel metric Γn being a function of a distance determined from one of the observed-sample subsequences Yn to the corresponding expected-sample sequence Wn; and a ratio computer for computing a mean μΓ of the channel metrics Γn, a standard deviation σΓ of the channel metrics Γn, and a ratio of the mean μΓ to the standard deviation σΓ, the ratio (μΓ/σΓ) corresponding to a signal to noise ratio.
  • 10. The disk drive of claim 9, furthers comprising a bit error rate estimator for estimating a bit error rate of the disk drive by computing Q(μΓ/σΓ) where Q is a Gaussian Q function.
  • 11. A disk drive having a normal mode of operation and a built-in self-test mode of operation for producing a sequence of channel metrics {Γn}, the disk drive comprising:a recording surface having a plurality of bit cells; a transducer for reading the plurality of bit cells to produce a noise-corrupted read signal; a sampler responsive to the noise-corrupted read signal for generating a sequence of observed samples {yn}, the sequence of observed-samples {Yn} forming a sequence of observed-sample sequences {Yn}; an expected sample generator operative during the built-in self-test mode of operation for providing a sequence of expected samples { wn}, the sequence of expected samples forming a sequence of expected-sample subsequences {Wn}; channel metrics computer for computing a sequence of channel metrics {Γn}, each channel metric Γn being a function of a distance determined from one of the observed-sample subsequences Yn to the corresponding expected-sample sequence Wn, the channel metrics computer comprising: equation circuitry for implementing a plurality of equations to compute a plurality of different channel metrics Γn; and an equation selection matrix for selecting between the different channel metrics Γn computed by the equation circuitry, the selection based on a selected number of the expected samples {wn}, the equation matrix generating a selected channel metric Γn; and an accumulator for accumulating the selected channel metric Γn.
  • 12. A method for computing a sequence of channel metrics {Γn} for characterizing the performance of a disk drive comprising a recording surface having a plurality of bit cells and a transducer for reading the plurality of bit cells to produce a noise-corrupted read signal, the method comprising the steps of:sampling the noise-corrupted read signal to generate a sequence of observed samples {yn}, the sequence of observed-samples {yn} forming a sequence of observed-sample sequences {Yn}; generating, during the built-in self-test mode of operation, a sequence of expected samples {wn}, the sequence of expected samples forming a sequence of expected-sample subsequences {Wn}; computing a sequence of channel metrics {Γn}, each channel metric Γn being a function of a distance determined from one of the observed-sample subsequences Yn to the corresponding expected-sample sequence Wn, the step of computing the channel metrics comprising the steps of: computing a plurality of different channel metrics Γn; and selecting between the different channel metrics Γn based on a selected number of the expected samples {wn} to generate a selected channel metric Γn ; and accumulating the selected channel metric Γn.
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