Abstract:
A method and apparatus are provided for determining a plurality of filter tap weights or biases (or both) for a noise predictive filter used to generate one or more signal dependent branch metrics. A filter tap weight or filter bias (or both) are adaptively accumulated for each possible data condition. The data conditions may comprise, for example, each possible data pattern for a given data dependency length. The appropriate accumulated filter tap weight or bias to update can be selected based on a data condition associated with the current received data. The filter tap weights associated with a delay 0 tap can be adapted for each filter condition except for a single normalizing condition, whose corresponding delay 0 tap remains fixed.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates generally to channel equalization and decoding techniques and, more particularly, to sequence estimation techniques with noise compensation.  
       BACKGROUND OF THE INVENTION  
       [0002]     A magnetic recording read channel converts an analog read channel into an estimate of the user data recorded on a magnetic medium. Read heads and magnetic media introduce noise and other distortions into the read signal that correlate with the written user data. A number of techniques have been proposed or suggested for taking statistical correlations between the written user data and distortions into account in order to improve read channel performance.  
         [0003]     Previous techniques that used data dependent statistics to improve detector error rates were unwieldy because they required off-board processing to calculate detector parameters from statistics that were off-loaded from the device. This off-load, calculate, and on-load cycle becomes prohibitively time consuming and complex when the number of distinct data conditions used, and the number of correlation lags used, are large enough to realize significant gains in error rate performance.  
         [0004]     A need therefore exists for a method and apparatus for adapting to these data correlations without relying on external calculations or circuits. A further need exists for a method and apparatus that can adapt to these data correlations during normal read operations and provide parameter values to the sequence detector (or to a post-processor acting on AN initial NRZ estimate produced by a sequence detector).  
       SUMMARY OF THE INVENTION  
       [0005]     Generally, a method and apparatus are provided for determining a plurality of filter tap weights or biases (or both) for a noise predictive filter used to generate one or more signal dependent branch metrics. A filter tap weight or filter bias (or both) are adaptively accumulated for each possible data condition to thereby permit the computation of data dependent branch metrics. The data conditions may comprise, for example, each possible data pattern for a given data dependency length. The accumulation may be performed by selecting the appropriate accumulated filter tap weight or bias to update based on a data condition associated with the current received data.  
         [0006]     Once determined, the accumulated filter tap weights or biases (or both) can be provided, for example, to a Viterbi detector for computation of the one or more branch metrics, or to a post-processor acting on an initial data estimate produced by a Viterbi detector. According to another aspect of the invention, the filter tap weights associated with a delay 0 tap are adapted for each filter condition except for a single normalizing condition, whose corresponding delay 0 tap remains fixed.  
         [0007]     A more complete understanding of the present invention, as well as further features and advantages of the present invention, will be obtained by reference to the following detailed description and drawings. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0008]      FIG. 1  is a schematic block diagram of an adaptive circuit that determines the predictive filter tap weights and biases that are needed to compute branch metrics in accordance with the present invention;  
         [0009]      FIG. 2  is a schematic block diagram illustrating the bias compensation block of  FIG. 1  in further detail;  
         [0010]      FIG. 3  is a schematic block diagram illustrating an exemplary 16-register read and replace accumulator of  FIG. 2  in further detail;  
         [0011]      FIG. 4  is a schematic block diagram of an exemplary positive delay filter tap of  FIG. 1 ;  
         [0012]      FIG. 5  is a schematic block diagram illustrating an exemplary 8-register dual read single write accumulator of  FIG. 4 ;  
         [0013]      FIG. 6  is a schematic block diagram of an exemplary delay 0 filter tap of  FIG. 1 ;  
         [0014]      FIG. 7  is a table illustrating how eight exemplary filter conditions α collapse together in pairs with each decrement in the data dependency parameter; and  
         [0015]      FIG. 8  is a control circuit for a programmable number of data dependencies. 
     
    
     DETAILED DESCRIPTION  
       [0016]     The present invention provides an adaptive circuit  100 , discussed below in conjunction with  FIG. 1 , that generates tap weights and biases for a noise predictive filter. The tap weights and biases are used to compute branch metrics. In one implementation of the self-adaptive circuit  100 , the generated tap weights and biases provide signal dependent, noise predictive, bias compensated branch metrics. Initially, the computation of branch metrics is discussed in the section entitled “Maximum Likelihood Branch Metrics,” before details of the self-adaptive circuit  100  are discussed.  
         [0017]     Maximum Likelihood Branch Metrics  
         [0018]     A Viterbi detector and an event-based post-processor compute the log-likelihood of a received sequence, given a corresponding NRZ sequence, as a sum of bit-cycle log-likelihood increments, referred to as branch metrics, along the sequence. The underlying assumption behind computing the log-likelihood of a sequence as a sum of increments is that the statistical events whose log-likelihoods correspond to the increments are statistically independent. Statistical independence is approached by using classical linear predictive filtering. When the noise and data are correlated, statistical independence is even more closely approached by conditioning the noise predictive filtering on the given NRZ sequence.  
         [0019]     The underlying assumption behind computing each log-likelihood increment (branch metric) as a square difference is that the difference, as a random variable, has a mean zero Gaussian probability distribution. Thus, bias in the filtered noise sample should be subtracted before the squaring operation.  
         [0020]     These considerations lead to a definition of data-dependent filtered, bias compensated noise statistics as follows. First, notation for the NRZ conditions for noise predictive filtering and bias compensation are introduced. A data condition length d is then fixed. A partition of the set of all 2 d  length d blocks of bits is fixed into disjoint sets β: 
 
{0,1} d =∪β. 
 
         [0021]     Each set β is a bias condition. Another coarser partition of {0,1} d  is fixed into disjoint sets α, so that each set β is contained in some set α. Each set α is a filtering condition.  
         [0022]     The most important example of the two partitions of {0,1} d  into bias conditions and filter conditions is where each bias condition β is a singleton set consisting of one bit sequence, 
 
β={ b   −d+1    . . . b   0 }, 
 
 and each filtering condition comprises two polar opposite bit sequences: 
 
α={ b   −d+1    . . . b   0   ,{overscore (b)}   −d+1    . . . {overscore (b)}   0 }. 
 
         [0023]     These partitions are important in practice because empirical second order conditional noise statistics are close to invariant under polarity reversal, while the first order conditional biases change sign under polarity reversal.  
         [0024]     Finally, the number of elements in a set α is denoted as m(α).  
         [0025]     A correlation length, c, corresponding to the maximum tap delay in the noise predictive filters is also fixed. An equalization target length, e, is fixed, where each ideal equalized sample y i  depends on NRZ bits b i−e+1  . . . b i . It is assumed for notational simplicity that the data-dependency length d≦c+e (which is true in practical cases).  
         [0026]     Having fixed the correlation length c, the data-dependency length d, the equalization target length e, the partition of {0, 1} d  into bias condition sets β, and the coarser partition of {0, 1} d  into filter condition sets α, a data-dependent filtered, bias compensated noise statistic underlying the branch metric corresponding to an NRZ sequence 
 
a −c−e+1  . . . a −1 a 0  
 
 can be defined, as follows. 
 
         [0027]     Let β be the bias condition with 
 
a −d+1  . . . a −1 a 0εβ,  
 
 and let α be the filter condition with β⊂α. 
 
         [0028]     In the following formula for the data-dependently filtered, bias compensated noise f i   [β]  the bit sequence b i−f+1  . . . b i  is denoted as b i−d+1   i ,  
           f   i     [   β   ]       =       ∑     j   =   0     c     ⁢       p   j     [   α   ]       ⁡     (       n     i   -   j       -     E   ⁡     (       n     i   -   j       |       b     i   -   d   +   1     i     ∈   β       )         )           ,       
 
 where p 0   [α] =1, and the p j   [α]  satisfy  
             ∑     j   =   0     c     ⁢       R   kj     [   α   ]       ⁢           ⁢     p   j     [   α   ]           =   0     ,     (     0   &lt;   k   ≤   c     )     ,       
 
 and where the conditional covariance matrix R [α]  is defined by  
               R   kj     [   α   ]       =       ⁢       ∑     β   ⋐   α       ⁢         m   ⁡     (   β   )         m   ⁡     (   α   )         ⁢     E   ⁡     (         n     i   -   k       ⁡     (       n     i   -   j       -     E   ⁡     (       n     i   -   j       |       b     i   -   d   +   1     i     ∈   β       )         )       |       b     i   -   d   +   1     i     ∈   β       )                       =       ⁢       E   ⁡     (         n     i   -   k       ⁡     (       n     i   -   j       -     E   ⁡     (       n     i   -   j       |       b     i   -   d   +   1     i     ∈   β       )         )       |     β   ⋐   α       )       .               
 
         [0029]     The statistic f i   [β]  is the residual noise after signal dependent noise predictive filtering and bias compensation.  
         [0030]     It is noted that R [α]  is a symmetric matrix, because it can be expressed in the form 
 
 R   kj   [α]   =E (( n   i−k   |b   i−d+1   i ββ))( n   i−j   −E ( n   i−j   |b   i−f+1   i εβ))|β⊂α) 
 
         [0031]     This follows from E(n i−j −E(n i−j |b i−d+1   i εβ)|b i−d+1   i εβ)=0.  
         [0032]     If it is assumed that the conditional covariance matrix R [α]  is positive definite, then it is invertible, and it follows that the vector p [α] =[p o   [α] , . . . , p c   [α] ] r  of noise predictive filter taps is uniquely determined (because p 0   [α] =1 fixes the scale). One can verify that the data-dependently filtered, bias compensated noise samples f i   [β]  satisfy: 
 
 E ( f   i   [β]   |b   i−d+1   i εβ)=0 
 
         [0033]     For each filter condition α, the choices of noise predictive filter taps and compensating biases minimizes the mean variance, as follows:  
             (     σ     [   α   ]       )     2     =         ∑     β   ⋐   α       ⁢         m   ⁡     (   β   )         m   ⁡     (   α   )         ⁢     E   ⁡     (         (     f   i     [   β   ]       )     2     |       b     i   -   d   +   1     i     ∈   β       )           =     E   ⁡     (         (     f   i     [   β   ]       )     2     |     β   ⋐   α       )           ,       
 
 over all filter tap weight sets with p 0   [α] =1. In the case where each bias condition β consists of a single NRZ sequence, each filter condition α consists of a polar opposite pair of NRZ sequences, and where the second order noise statistics are invariant under polarity reversal 
 
 E =(( f   i   [β] ) 2   |b   i−d+1   i εβ)= E (( f   i   [{overscore (β)}] ) 2   |b   i−d+1   i β{overscore (β)}), 
 
 so the variance becomes 
 
(σ [α] ) 2   =E ( f   i   [β] ) 2   |b   i−d+1 εβ)= E (( f   i   [{overscore (β)}] ) 2   |b   i−d+1   i ε{overscore (β)}). 
 
 The independence condition, 
 
 E ( n   i−j   f   i   [β]   |b   i−d+1   i εα)=0, (1 ≦j≦c ), 
 
 shows, under certain assumptions regarding the noise statistics (including that the noise is multivariate Gaussian) that the statistics f i   [β]  are approximately independent along the true NRZ trellis path. 
 
         [0034]     These three points, taken together, argue that the log-likelihood increment corresponding to the branch with NRZ sequence, a i−c−e+1  . . . a i−1 a i  with a i−d+1  . . . a i−1 a i εβ⊂α, can be expressed using the following (negative) log probability:  
             (     f   i     [   β   ]       )     2       2   ⁢       (     σ     [   α   ]       )     2         +       log   (       2   ⁢           ⁢   π   ⁢           ⁢     σ     [   α   ]           )     .         
 
 If the log term is neglected, and the above expression is normalized by multiplying by 2(σ [α     0     ] ) 2 , where α 0  is a fixed, normalizing filter condition, the branch metric may be expressed as follows:  
           (         σ     [     α   0     ]         σ     [   α   ]         ⁢     f   i     [   β   ]         )     2     .       
 
 In practice, the normalizing condition α 0  is chosen to minimize σ [α] . 
 
         [0035]     This branch metric can be calculated in hardware by first filtering the noise estimate using an FIR with tap weights set to the normalized noise predictive filter coefficients (i.e., tap weights):  
           q   j     [   α   ]       =         σ     [     α   0     ]         σ     [   α   ]         ⁢           ⁢     p   j     [   α   ]           ,     (     0   ≤   j   ≤   c     )     ,       
 
 and then subtracting the normalized bias  
           μ     [   β   ]       =         σ     [     α   0     ]         σ     [   α   ]         ⁢           ⁢       ∑     j   =   0     c     ⁢       p   j     [   α   ]       ⁢     E   ⁡     (       n     i   -   j       |       b     i   -   d   +   1     i     ∈   β       )               ,       
 
 from the filter output, and finally performing the squaring operation. In summary, the branch metric m (b i−c−e+1   i ) corresponding to the NRZ sequence, b i−c−e+1   i =b i−c−e+1  . . . b i−1 b i  with b i−d+1  . . . b i−1 b i εβ⊂α, is given by:  
         m   ⁡     (     b     i   -   c   -   e   +   1     i     )       =         (         σ     [     α   0     ]         σ     [   α   ]         ⁢           ⁢     f   i     [   β   ]         )     2     =         (       (       ∑     j   =   0     c     ⁢       q   j     [   α   ]       ⁢           ⁢     n     i   -   j           )     -     μ     [   β   ]         )     2     .           
 
         [0036]     The present invention provides a self-adaptive circuit  100  that determines the normalized noise predictive tap weights q j   [α]  and normalized biases μ [β]  that are used in this calculation of the branch metrics m(b i−c−e+1   i ).  
         [0037]     Generation of Tap Weights and Biases for Branch Metric Computation  
         [0038]      FIG. 1  is a schematic block diagram of an adaptive circuit  100  that finds the branch metric filters and biases in accordance with the present invention. Generally, the adaptive circuit  100  includes accumulation registers  300 ,  500  whose values converge to the normalized biases μ [β]  and normalized noise predictive tap weights q j   [α]  respectively, that are used to calculate the branch metrics m(b i−c−e+1   i ) presented above.  
         [0039]     As shown in  FIG. 1 , the exemplary implementation of the adaptive circuit  100  includes three positive delay filter taps  400 - 1  through  400 - 3 , discussed further below in conjunction with  FIG. 4 . In other words, the correlation length, c, is equal to three. The adaptive circuit  100  is embodied as a noise predictive FIR as modified herein to provide a number of new features and functions. According to a data dependency feature of the present invention, the filter tap weights for the filter taps  400 - 1  through  400 - 3  and compensating biases for a bias compensation block  200 , discussed further below in conjunction with  FIG. 2 , that are used in any one update cycle are controlled (multiplexed) by an estimate of the NRZ data aligned with the noise estimate. According to a bias compensation feature of the present invention, the output of the filter is compensated by a bias cancellation circuit that is inside the filter tap weight adaptation loops. According to a conditional variance normalization feature of the present invention, the delay 0 tap weights w 0   [α]  adapt for each filter condition α except for a single normalizing condition α 0 , whose corresponding delay 0 tap remains fixed at w 0   [α     0     ] =1 (instead of being fixed as would be the case with classical linear noise prediction).  
         [0040]     The adaptive noise prediction block  100  includes a number of delay elements  150 , multipliers  160  and adders  170  that operate in a conventional manner to properly align the various data elements and integrate the values from each cycle.  
         [0041]     Once the tap weights and biases generated by the adaptive noise prediction block  100  of  FIG. 1  converge (reach equilibrium), they can be provided to a circuit (not shown) that actually computes signal dependent, noise predictive, bias compensated branch metrics. An exemplary circuit for computing such signal dependent, noise predictive, bias compensated branch metrics is described, for example, in A. Kavcic, “Decision Feedback Equalization in Channels with Signal-Dependent Media Noise,” IEEE Transactions on Magnetics, Vol 37, 1909-11 (July 2001) or U.S. Pat. No. 6,594,094, each incorporated by reference herein.  
         [0042]     Data Dependency and Bias Compensation  
         [0043]     As shown in  FIG. 1 , the adaptive noise prediction block  100  receives a noise estimate, n i , and four consecutive NRZ estimates b i−3 b i−2  . . . b i . The noise estimate, n i , and NRZ estimate are aligned as usual, so that n i  is computed as the difference between the equalized sample y i  and the bi-polar NRZ b i =b i −½ convolved with the target, [t 0 t 1  . . . t e−1 ], as follows:  
         n   i     =       y   i     -       ∑     j   =   0       e   -   1       ⁢       t   j     ⁢           ⁢         b   ~       i   -   j       .               
 
         [0044]     The NRZ stream acts as a control signal for the tap update blocks  400 - 1  through  400 - 3  and the bias compensation block  200 .  
         [0045]     As previously indicated, the compensating biases for the bias compensation block  200  that are used in any one update cycle are correlated with the data and are thus controlled (multiplexed) in accordance with the present invention by an estimate of the NRZ data aligned with the noise estimate.  FIG. 2  is a schematic block diagram illustrating the bias compensation block  200  of  FIG. 1  in further detail. The bias compensation block  200  implements data dependent offset control. The bias compensation block  200  drives each conditional mean of the error signal e i  to zero. So, at equilibrium, 
 
 E ( e   i   |b   i−d+1    . . . b   i εβ)=0, (β) 
 
         [0046]     The bias compensation block  200  can be implemented as a separate accumulator (read and replace function) for each bias condition, β. In the exemplary implementation where the data dependency, d, is 4 bits, each having two potential values, there are 16 distinct bias conditions, β, and thus 16 accumulation registers  300 , discussed further below in conjunction with  FIG. 3 . Since only one bias condition β holds on any bit cycle, the accumulators can share a single adder  210  to perform the accumulation and multiplier  220  to perform gain control.  
         [0047]      FIG. 3  is a schematic block diagram illustrating the 16-register read and replace accumulator  300  of  FIG. 2  in further detail. The choice of the appropriate register to update, namely, the register corresponding to bias condition β with b i=d+1  . . . b i ββ, is controlled by the block of NRZ bits b i−d+1  . . . b i  via a multiplexer  310  and demultiplexer  330 , for the case d=4. The “read-and-replace” circuit  300  reads o i   [β]  from an appropriate register  320  (indexed by the block of NRZ bits b i−d+1  . . . b i ) and replaces the value in the register with the updated version, o i+1   [β] =o i   [β] +ge i , using adder  210  and multiplier  220 .  
         [0048]     As previously indicated, the exemplary implementation of the adaptive circuit  100  includes three positive delay filter taps  400 - 1  through  400 - 3 .  FIG. 4  is a schematic block diagram of an exemplary positive delay filter tap  400 . Generally, the positive delay filter tap  400  implements a separate accumulator for each filter condition α. As indicated above, where each bias condition β consists of a single NRZ sequence, each filter condition α consists of a polar opposite pair of NRZ sequences. Due to the symmetric properties, the filter conditions α associated with the 16 distinct bias conditions β in the exemplary embodiment can be collapsed two-fold into eight distinct filter conditions a (see also, the discussion below in conjunction with  FIG. 7 ). For example, the bit patterns 0110 and 1001 share the same noise conditions and the corresponding filter conditions, α, can be collapsed into a single condition. Since only one filter condition α holds on any bit cycle, the eight accumulators can share a single adder  410  to perform the accumulation and multipliers  420 ,  430  to calculate the accumulated increment based on the noise estimate, error, and gain factor.  
         [0049]      FIG. 5  is a schematic block diagram illustrating the 8-register dual read single write accumulator  500  of  FIG. 4  in further detail. The choice of which accumulator to update is controlled by the NRZ block b i−d+ 1 . . . b i  via a multiplexer  510  and demultiplexer  530 . The multiplexer  510  and demultiplexer  530  choose the filter condition α for which b i−d+1  . . . b i εα. The register value (w j   [α] )i for the delay j tap is updated as follows: 
 ( w   j   [α] ) i+1 =( w   j   [α] ) i   −gn   i−j   e   i , (1≦j≦c),  
 using adder  410  and multipliers  420 ,  430 . It follows that at equilibrium, 
   E ( n   i−j   e   i   |b   i−d+1    . . . b   i εα)=0, (1≦j≦c).  
         [0050]     As shown in  FIG. 5 , the choice of which accumulated value to use as a tap weight in filtering the noise is controlled by a differently delayed version of the block of four NRZ bits, labeled “tap wt sel” in  FIG. 5 . The relative delay between “tap wt sel” and “adapt sel” is shown in  FIG. 1 . In particular, the “adapt sel” signal controlling the tap block at delay j, (as well as the noise estimate) (for 1≦j≦c), is delayed by j bit cycles (using delay elements  145 ) compared to the “tap wt sel” signal controlling the same tap block. It is noted that the delays on the “tap wt sel” signal are arranged so that all of the summands contributing to a single filter output sample are computed using tap weights w j   [α]  corresponding to a single condition α. It is also noted that the delays on the “adapt sel” signal are arranged so that the condition α for which tap weight w j   [α]  is updated is the same condition that was used j cycles earlier to select the tap weights in the computation of the filter output sample used in the update.  
         [0051]     As previously indicated, the delay 0 tap weights w 0   [α]  for the delay 0 filter tap  600 , shown in  FIG. 6 , adapt each filter condition α except for a single normalizing condition α 0 , whose corresponding delay 0 tap remains fixed at w 0   [α     0     ] =1 (instead of being fixed as would be the case with classical linear noise prediction).  FIG. 6  is a schematic block diagram of an exemplary delay 0 filter tap  600 . As shown in  FIG. 6 , the adaptive loops implemented by block  600  drive the delay 0 tap weight w 0   [α]  for each condition a α≠α 0  to the following stable value:  
         w   0     [   α   ]       =         σ     [     α   0     ]         σ     [   α   ]         .         
 
         [0052]     Again, the delay 0 tap weight w 0   [α     0     ]  for the normalizing condition α 0  is fixed at value one (1). The delay 0 tap weight w 0   [α]  for each of the other conditions is only constrained (saturated) to be non-negative. This constraint forbids a second, undesirable stable point for α that is the negative of the desired stable point.  
         [0053]     The circuit  600  implements the following update equations. Let μ i  be the register value held in the register  610  labeled “abs accum” in  FIG. 6 . The update equations for μ i  implemented using the register  610 , adders  615 ,  650 , multiplexer  640  and multiplier  625  are as follows:  
         μ     i   +   1       =     {                 ⁢       μ   i     +       g   ′     ⁡     (            e   i          -     μ   i       )                       if   ⁢           ⁢     b     i   -   d   +   1     i       ∈     α   0       ,     ⁢                       ⁢     μ   i             otherwise   ⁢               .           
 
 Also, μ i+1  is saturated to be non-negative: 
 
μ i+1 ≧0. 
 
         [0054]     Thus, μi is a low-passed version of |e i |, restricted to cycles i when b i−d+1   i εα 0 . This filtering of |e i | for the normalizing condition α 0  ensures that variations in μ i  from its mean are only weakly correlated with |e i |. Furthermore, it follows from the update equations for μ i  that at equilibrium, 
 
μ i   =E (| e   i   ||b   i−d+1   i εα 0 ). 
 
         [0055]     The read and replace register  670 , together with the adder  620 , multiplier  630  and multiplexer  640  implements the following update equations for the register values w 0   [α]  corresponding to the delay 0 taps for conditions α≠α 0 :  
           (     ⁢     w   0     [   α   ]       ⁢       )       i   +   1         =     {                 ⁢         (     ⁢     w   0     [   α   ]       ⁢       )     i       -     g   ⁡     (            e   i          -     μ   i       )                       if   ⁢           ⁢     b     i   -   d   +   1     i       ∈   α     ,     ⁢                       ⁢       (     ⁢     w   0     [   α   ]       ⁢       )     i               otherwise   ⁢               .           
 
 It is noted that the read and replace register  670  may be implemented in a similar manner to the register  300 , described above in conjunction with  FIG. 3 . It follows from the update equations that at equilibrium, 
 
 E (| e   i   ||b   i−d+1   iεα)=μ   i   =E (| e   i   ||b   i−d+1   i εα 0 ), (α). 
 
         [0056]     This, together with 
 
 E (| e   i   ||b   i−d+1   i    . . . b   i εβ)=0, (β). 
 
 and the assumption that the noise is multivariate Gaussian, give equal conditional variances of the filtered, bias compensated noise e i  for the filter conditions α and α 0 : 
 
 E ( e   i   2   |b   i−d+1   i εα)= E ( e   i   2   |b   i−d+1   i εα 0 ), (α). 
 
         [0057]     Adaptive Circuit Variations  
         [0058]     In this section, a minor modification to the adaptive circuit  100  is described that allows the dependency length d to be programmable from d=0 up to a maximum value. In practice, the dependency length should be programmed to be the smallest value that saturates the performance gains provided by increasingly refined data-dependency. There are two advantages in doing this. First, adaptation time is approximately cut in half for each decrement of d by one. Second, if d exceeds the true data-dependency window of the noise and distortion, then any differences between the adaptation for two conditions having the same statistics are due to adaptation noise. Such differences will only degrade performance.  
         [0059]      FIG. 7  is a table  700  illustrating how eight exemplary filter conditions α (each comprising a polar opposite pair of length 4 NRZ sequences) collapse together in pairs with each decrement in d by 1 starting at d=4.  
         [0060]     It is noted that the control lines that control the multiplexers and demultiplexers in  FIGS. 3, 5  and  6  comprise a bus of four consecutive delays of the binary NRZ estimate.  FIG. 8  is a control circuit  800  for a programmable number of conditions (from d=4 to d=0).  FIG. 8  shows a modification to these four delays that would be situated upstream from the multiplexers and demultiplexers. A programmable number of the oldest bits are forced to zero, thus forcing a corresponding subset of the accumulation registers in the adaptation circuits to be used during adaptation.  
         [0061]     In one exemplary application, the adaptive circuit serves to calibrate parameters used in a Viterbi detector. In another application, the adaptative circuit serves to calibrate parameters used in a post-processor acting on the initial NRZ estimate produced by a Viterbi detector.  
         [0062]     It is to be understood that the embodiments and variations shown and described herein are merely illustrative of the principles of this invention and that various modifications may be implemented by those skilled in the art without departing from the scope and spirit of the invention. For example, the invention can be implemented in magnetic recording system, and other applications, such as Ethernet in general and a future 10 Gigabit Ethernet over copper system in particular, as well as wireless communications.