Patent Application
20090168620
1. Field of Invention
The present invention relates to modulation of data transfer signals, for instance in reading from, and writing to a magnetic medium, such as a hard disk drive. The invention more specifically relates to modulation intended to make the signal properties meet specific criteria, for instance enforcing run-length limited conditions, making signals more distinguishable (increasing “distance”), and providing clock recovery information.
2. Relevant Background
x
i
=c
i
+x
i−2.
Such an operation needs two initial conditions x−1 and x0 to be set for x, for instance (0, 0).
Codeword x passes in a channel 16 through one or more channel filters 18. The channel, which is where the data is written to the hard-disk and read back from the hard-disk, is typically corrupted by additive noise n, such that the received sequence r is defined by r=z+n, where z is the output of filters 18.
Based on the received sequence r, a Viterbi detector 20, for example, generates a detected sequence x̂, which is a reproduction of the input x to the channel filters 18. Next, bits x̂ are filtered by a filter 22 which performs the function (1+D2) that is an inverse of the function performed by precoder 14, and generates g. The output g of the filter 22 is decoded by a decoder 24 to produce a decoded sequence d, which is a reproduction of the ECC output sequence b. An ECC decoder 26 receives the output sequence d and reestablishes the user input to ECC coder 10.
As mentioned above, the codewords used in the system have k+r bits, whereas the corresponding user data blocks have a lower number of bits k, whereby there is an efficiency loss. The efficiency of the encoder is called “rate” and it is defined as k/(k+r).
Known modulation techniques implemented by the encoder 12 strive to increase the rate and impose desired properties on the codeword. Often this makes each bit of a codeword depend on every bit of the incoming data block. Such techniques have the drawback of increasing “error propagation”—often one corrupted bit in a codeword would cause the loss of most of the bits in the resulting data block.
US published application 20040059980, incorporated herein by reference, discloses a modulation method for use in encoder 12, which has short error propagation while imposing desirable properties on the codewords.
The modulation has the following generic transform:
where D is a one-bit delay and f=(f0, f1, f2 . . . fr) is a set of constant binary values, with f0=fr=1, characterizing the modulation scheme. In other words, given an i-th bit bi of a user data block, the i-th bit as of the resulting codeword a is defined as:
a
i
=b
i
+f
1
a
i−1
+f
2
a
i−2
+ . . . +f
r
a
i−r,
where i varies from 1 to k.
This operation requires r initial conditions, one for each of bits a1−r to a0. Since each initial condition is one bit, there are 2r possible choices for a set of initial conditions.
In a first part of the modulation scheme, an intermediate codeword a is calculated as above from b with a set of initial conditions set to zero. Thus:
a
1−r=0,
a
2−r=0,
. . .
a0=0,
a1=b1,
a
2
=b
2
+f
1
a
1,
a
3
=b
3
+f
1
a
2
+f
2
a
1,
. . .
a
r
=b
r
+f
1
a
r−1
+f
2
a
r−2
+ . . . +f
r−1
a
1,
a
r+1
=b
r+1
+f
1
a
r
+f
2
a
r−1
+ . . . +f
r
a
1
. . .
a
k
=b
k
+f
1
a
k−1
+f
2
a
k−2
+ . . . +f
r
a
k−r,
In a second part of the modulation scheme, a set of initial conditions is selected for each codeword c to be generated, depending on a predefined map relating the initial conditions to a predefined set of values for the intermediate codeword a. For instance, if a is all 1s, all 01s or all 10s, use “initial conditions No. 1”, otherwise use “initial conditions No. 2”.
Once the set of initial conditions is selected, rather than recalculating the final codeword c by applying the above transform with the selected initial condition set, the effect t (t1−r, t2−r, . . . t0, t1, t2, . . . tk) of the initial condition set is simply added to the intermediate codeword a, i.e. c=a+t. The effect t is calculated by inserting the selected initial condition set in the above transform, and applying the transform to all variables b set to zero.
Of course, the zero initial conditions may also be selected, in which case the intermediate codeword a becomes the final codeword c.
An interesting property of this modulation technique is that these initial conditions may thus be changed from one codeword to the next without requiring the decoder to be reconfigured. This allows real-time setting of the initial conditions for each codeword so that each codeword may be made to have desired properties.
As an example with r=1 and f1=1, there is one initial condition having two possible values: 0 or 1. For a same data block, switching the initial condition between 0 and 1 switches the resulting codeword to its complement. Therefore, it is certain that one choice of the initial condition will yield a majority of 1s in the resulting codeword. If this is a desired property, the map is such that if the 0 initial condition yields more 0s than 1s in the codeword, the 1 initial condition is selected, otherwise the 0 initial condition is selected. Producing a large number of 1s is often a desired property, because each 1 causes a transition in the signal when it passes through the precoder 14, which transition helps in recovering clock information at the other end of the channel.
Since each bit c; of a codeword c is calculated from r previous bits, corruption of one bit will corrupt r further bits, i.e. the error propagation length is r+1. Therefore, in practical applications, r will be chosen small, often equal to 1 or 2. Choosing r small also increases the rate of the encoder, equal to k/(k+r).
The above disclosed modulation technique provides satisfactory results for enhancing signal properties obeying linear laws, which is the case in the specifications for hard-disks with “longitudinal recording”, i.e. having magnetic polarization that changes along the tracks of the disk.
Currently, some hard-disks tend to be of the “perpendicular recording” type, i.e. having magnetic polarization changes perpendicular to the disk. The signal specifications for such disks require the “charge” to tend to zero, and this preferably over small sequences of consecutive bits. The charge is defined as the sum of 1s and 0s written on the disk, where each 1 is summed as +1 and each 0 is summed as −1. In other words, the data recorded on the disk should tend to have as many 1s as 0s.
The zero charge requirement becomes an additional parameter to be taken into account in the modulation scheme. The known modulation schemes do not offer enough flexibility to address this problem.
What is needed, therefore, is a signal modulation scheme with enhanced flexibility, that can in particular make the charge tend to zero while satisfying other requirements in the properties of the signal.
According to the invention, this need is satisfied by a data modulation method comprising the steps of: grouping a stream of input data and a corresponding stream of output data into elements of a finite field; applying to input elements of the input data a transform generating output elements of the output data, such that a current output element is a linear combination of a current input element and at least one previous output element, wherein a multiplier applied to at least one previous output element is a non-zero and non-unity element of the finite field; and selecting a set of initial conditions inherent to the transform, such that the output elements resulting from the transform tend to have a desired property.
According to an embodiment of the invention, the method comprises the further the steps of: calculating intermediate elements by applying the transform to the input elements with a set of initial conditions of value zero; calculating the effect of the selected set of initial conditions by applying said transform to input elements having value zero and the selected set of initial conditions; and adding the effect to the intermediate elements to obtain the output elements.
According to an embodiment of the invention, the step of selecting the initial conditions comprises the steps of: defining distinct sets of initial conditions, each set having a single non-zero element at a distinct position; and selecting each non-zero element of the sets of initial conditions such that the output elements tend to have a respective property.
The invention also provides for a decoder or inverse data modulation method comprising the steps of: grouping a stream of input data and a corresponding stream of output data into elements of a finite field; and applying to the input elements of the input data a transform generating output elements of the output data, such that a current output element is a linear combination of a current input element and at least one previous input element, wherein a multiplier applied to a previous output element is a non-zero and non-unity element of the finite field.
The invention is illustrated in the accompanying drawing, wherein:
In an embodiment of the invention, each user data block B=(b1, b2, . . . bk) fed to the encoder 12 of the processing chain of
where Dm is a one m-tuple delay and (α0, α1, α2, . . . are constant elements of GF(2m), at least one of which is non-zero and non-unity. In other words, given an i-th m-tuple Bi of a user data block B, the i-th m-tuple Ai of the resulting codeword A is defined as:
A
i=α0Bi+α1Ai−1+α2Ai−2+ . . . +αrAi−r,
where i varies from 1 to p. Of course, all arithmetic is performed over finite field GF(2m).
Addition in a finite field is a bitwise exclusive OR operation. Multiplication is more complex: the two operands are multiplied under their polynomial representation, and the resulting polynomial, modulo the “generator polynomial” of the finite field, is the final result. Such multiplication introduces pseudo-random properties in the results, which contributes to enhanced flexibility of the modulation scheme according to embodiments of the invention.
The above transform requires r initial conditions in finite field GF(2m) for A1−r to A0. Since each initial condition is an element of finite field GF(2m), there are 2mr possible choices for a set of initial conditions.
In a generic use of the modulation scheme according to embodiments of the invention, a set of constants α=(α0, α1, α2, . . . αr) is predefined. The corresponding decoder also uses this same set of constants. In operation, a set of initial conditions is found for each codeword being generated in order to make that codeword best match a set of required properties. The choice of the initial conditions does not affect the operation of the decoder, which is one of the interesting features of this type of modulation scheme.
The error propagation length of this modulation scheme is rm+1 bits, since one corrupted bit will affect r m-tuples.
In a preferred embodiment, the modulation scheme is used in two parts.
In a first part, an intermediate codeword A is calculated with the above transform from B with initial conditions set to zero. Thus:
A
1−r=0,
A
2−r=0,
. . .
A0=0,
A1=α0B1,
A
2=α0B2+α1A1,
A
3=α0B3+α1A2+α2A1,
. . .
A
r=α0Br+α1Ar−1+α2Ar−2+ . . . +αr−1A1,
A
r+1=α0Br+1+α1A1+α2Ar−1+ . . . +αrA1
. . .
A
p=α0Bp+α1Ap−1+α2Ap−2+ . . . +αrAp−r.
In a second part of the modulation scheme, a map M is defined that relates specific initial condition sets to specific criteria satisfied by the intermediate codeword A. Once the set of initial conditions is selected, rather than recalculating the final codeword C by applying the above transform with the selected initial condition set, the effect T (T1−r, T2−r, . . . T0, T1, T2, . . . Tp) of the initial condition set is simply added to the intermediate codeword A, i.e. C=A+T. This is possible, because the transform is linear. The effect T is calculated by inserting the selected initial condition set in the above transform, and applying the transform with input B set to zero.
The modulation scheme may be noted ENC(α, M)(X), where α represents the set of constants (α0, α1, α2, . . . αr) used in the transform, X is the set of p m-tuples to which the transform is applied, and M designates the map that defines initial conditions used in calculating the current codeword. The result of ENC(α, M)(X) is a set of k+rm bits, or r+p m-tuples or elements of GF(2m).
In one embodiment of the invention, instead of exploring all possible initial conditions, only r+1 predefined initial condition sets are used. Map M is thus characterized by r+1 submaps M0, M1, . . . Mr, each associated to a respective one of the r+1 predefined initial condition sets. M0 is associated to initial conditions set to zero, and each of maps Mi, i>0, is associated to an initial condition set where all elements are zero, except the i-th, which is equal to unity, i.e. (0, 0, . . . 0, 1, 0, . . . 0), where 1 is at the i-th position.
Thus, the transform, applied to a user data block B will be expressed as:
ENC(α, M0)(B) designates the intermediate codeword A, and all of the other terms represent the effect T of the initial conditions, wherein β=(β1, β2, . . . βr) designates a set of scaling factors in GF(2m) that will generally change for each codeword A. In fact, map M is such that β=M(X), whatever the value of X. The scaling factors β could form part of their respective submaps, but the above notation allows to better visualize which parameters are adjustable and causes submaps M0, M1, . . . Mr to be constant.
The inverse transform, i.e. the decoding operation performed by decoder 24, can be designated DEC(α)(Y). As previously mentioned, the map M does not intervene in the decoding operation. The decoder is such that:
B
i=α0−1(Ci+α1Ci−1+α2+ . . . αrCi−r),
where Bi is an m-tuple output by the decoder and Ci is an m-tuple currently input to the decoder.
The modulation scheme will be better understood through various examples illustrated below.
In this example, intermediate codeword A=ENC(α, M0)(B), is expressed as:
A0=0,
A1=B1,
A
2
=B
2
+μB
1,
A
3
=B
3
+μB
2+μ2B1,
. . .
A
14
=B
14
+μB
13+ . . . μ13B1,
The additive effect T of the initial conditions is β1ENC(α, M1)(0)=β1(1, μ, μ2, μ3, . . . μ14). β1 is chosen such that T+A has all 4-tuples non-zero, i.e. β1≠0, μβ1≠A1, μ2β1≠A2, . . . μ14β1≠A14. Hence the choice defined above in item 6.
With this choice, each 4-tuple of the final codeword C contains at least one bit at 1, which ensures that there is at least one transition in the signal every 4 bits at the output of precoder 14. This property promotes clock recovery.
The search for the desired value of β1 requires at most 14 trials out of the 15 non-zero possible values. Each trial requires a comparison with each of the 14 last values of set S. If the 14th trial is unsuccessful, it is certain that the value searched for is the 15th non-zero value.
The decoder in this example is such that:
B
i
=C
i
+μC
i−1,
where Bi is an m-tuple output by the decoder and Ci is an m-tuple currently input to the decoder.
The search for the required value of β1 is particularly simple in this example, since there are only four values to try.
This exemplary modulation does not require a precoder 14 (nor the inverse precoder 22), since the codewords are short (12 bits) and the modulation inherently inserts transitions. Indeed, transitions are necessary to make the charge tend to zero.
In using this example in a simulation on random input data, the variance of the charge is about 1.74 over a significant number of consecutive codewords. This result is satisfactory for dealing with perpendicular recording hard-disks.
The decoder in this example is also such that:
B
i
=C
i
+μC
i−1,
where Bi is an m-tuple output by the decoder and Ci is an m-tuple currently input to the decoder
The efficiency of the modulation in reducing charge may be increased by increasing m and k, whereby there will be more values to try for β1.
If several values of β1 happen to reduce the charge, then preferably the one causing most transitions in codeword C is selected, whereby clock-recovery is also promoted. Alternatively, if a precoder 14 is present, the value causing C to have most is is selected instead.
If multiple properties are to be satisfied by the codewords, r may be chosen equal to the number of properties, whereby there will be as many factors β to search for as desired properties. Factors β will not be independent and it may be necessary to optimize them through several iterations, i.e. if an optimal first factor is found for a first property, a subsequently found optimal second factor for a second property may affect the optimality of the first factor, whereby the first factor is searched for again, which may in turn affect the optimality of the second factor. This may continue until a compromise is found for both factors.
Disk drive assembly 107, e.g., an HDD system, implements physical mass storage typically on a plurality of magnetic disks and read/write head electronics for transferring data with the disks. Disk drive assembly 107 typically includes read channel hardware for preprocessing and amplifying data read from the magnetic media as well as a spin motor for spinning the disks and voice coil motor (VCM) for positioning the read/write head electronics at specific locations with respect to the disk surface(s).
A servo control 108 generates drive signals that control the VCM and/or spin motors. These drive signals are in the form of precision voltage or current signals that drive the motors directly.
Host 101 typically comprises a data processing device such as a personal computer, server, workstation or the like that requires access to bulk data storage capabilities of disk drive assembly 107. Host 101 sends write commands and data via controller 103 to write data onto the disks as well as read commands to retrieve previously written data from disks within disk drive assembly 107. On both read and write operations the data transmitted from the host 101 to the disk controller 103 includes an indication of a specific location or set of locations on the disk drive assembly that contains the data that is to be accessed.
The data that is exchanged through disk controller 103 is typically buffered in buffer memory 104 that is accessible via memory controller 109 and subsequently transmitted to disk assembly 107 or host 101. Buffer memory 104 is used to overcome differences between the speed at which host 101 operates as compared to the speed at which disk assembly 107 operates. In place of or in addition to buffer memory 104, a cache memory may be implemented by appropriate changes (e.g., tag management, hit/miss detection and the like) to memory controller 109.
The present invention may be implemented in hardware within the read/write subsystem 105, in software executed within the system processor 113, or in a combined hardware and software mode in processor 113 and subsystem 105.
Although the invention has been described and illustrated with a certain degree of particularity, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the combination and arrangement of parts can be resorted to by those skilled in the art without departing from the spirit and scope of the invention, as hereinafter claimed.
| Number | Date | Country | |
|---|---|---|---|
| Parent | 11016283 | Dec 2004 | US |
| Child | 12345561 | US |
