Patent Publication Number: US-2005135472-A1

Title: Adaptive equalizer, decoding device, and error detecting device

Description:
BACKGROUND OF THE INVENTION  
      1. Field of the Invention  
      The present invention relates to an adaptive equalizer for equalizing a reproduction waveform to a partial response (PR) in an optical recording apparatus or magnetic recording apparatus, a decoding device using the adaptive equalization, and an error detecting device.  
      2. Description of the Related Art  
      Conventionally, an adaptive equalizer for performing adaptive equalization using a least mean square (LMS) algorithm has been known.  
      An FDTS/DFE, that is, an decision feedback equalizer (DFE) that uses fixed delay tree search (FDTS) as signal-determining means is also known from, for example, J. Moon and L. R. Carley, “Performance comparison of detection methods in magnetic recording”, IEEE Transaction on magnetics, Vol. 26, No.  6 , November 1990, pp.  3155 - 3172 .  
      When adaptive equalization is performed using the above-noted LMS algorithm, original data must be provisionally determined from a waveform. When data having a large amount of noise and equalization error and having a low signal difference-to-noise ratio (SDNR) is detected with respect to a threshold to perform provisional determination, the determination result contains a large amount of noise, thus making it difficult to achieve a high-speed prediction with an increased adaptive gain.  
      This can also be true for a phase locked loop (PLL), auto gain control (AGC), and so on that require a dynamic high-speed operation. That is, detection of data having a low SDNR with respect to a threshold to obtain an error signal leads to a large amount of error, thus making it difficult to achieve a high-speed operation.  
      Even when an attempt is made to equalize an input waveform having an insufficient output or having a missing portion in a frequency range required for partial response, a frequency range that cannot be equalized remains. Such error remains as an equalization error that strongly depends on the pattern of input data. This causes the performance of a decoding device to greatly decreases, thus leading to an increase in bit error rate (BER).  
      In the above-described FDTS/DFE, a feed-forward filter (FFF) needs to equalize an input waveform to a waveform that satisfies causality. If leading-edge inter-symbol interference (ISI), i.e., the leading portion of the ISI, of a waveform equalized by the FFF remains to cause a waveform that does not satisfy causality is input to the FDTS/DFE, the DFE structure cannot remove trailing-edge ISI (i.e., a portion subsequent to the leading-edge ISI). Thus, equalization error resulting from the leading-edge ISI cannot be removed. With the FDTS, therefore, equalization error resulting from the leading-edge ISI leads to an increase in error rate.  
      Typically, FFFs are provided with a noise-whitening function. This is intended to allow the FDTS to improve the determination performance based on noise whitening. However, depending on an input waveform, it is quite difficult to design an FFF having a noise-whitening capability while satisfying the causality.  
      Further, when an FFF is selected based on the criterion that satisfies the causality with a noise-whitening capability, a detection distance in the FDTS is prone to be shorter compared to known PR equalization.  
      With an FFF performing equalization that dos not satisfy the causality, even when an attempt is made to provide an adaptive structure by using an LMS algorithm in order to cause the FDTS/DFE to control the FFF, such a structure still does not work properly. The reason is that, with the error detection provided by the FDTS/DFE, it is impossible to determine whether the error is due to the leading-edge ISI or the trailing-edge ISI. As a result, the determination settles to a local minimum solution to only permit equalization with a large amount of equalization error left.  
     SUMMARY OF THE INVENTION  
      Accordingly, an object of the present invention is to provide an adaptive equalizer that is capable of performing adequate equalization processing using an FDTS/DFE or the like, a decoding device, and an error detecting device.  
      In order to achieve the foregoing object, the present invention provides an adaptive equalizer. The adaptive equalizer includes a feed-forward filter (FFF) for equalizing a waveform and an equalization circuit for performing response according to a partial-response (PR) scheme on only a leading-edge portion of inter-symbol interference (ISI) of the waveform equalized by the feed-forward filter and for performing equalization that does not consider trailing-edge inter-symbol interference subsequent to the leading-edge portion. The equalization circuit has a configuration of a decision feedback equalizer (DFE). The adaptive equalizer further includes a feed-back filter (FBF) for generating a response for the trailing-edge inter-symbol interference. The equalization circuit subtracts the response generated by the feed-back filter from a response provided by the feed-forward filter so that a result of the subtraction provides a partial response.  
      The present invention provides a decoding device. The decoding device includes a feed-forward filter (FFF) for equalizing a waveform and an equalization circuit for performing response according to a partial-response (PR) scheme on only a leading-edge portion of inter-symbol interference (ISI) of the waveform equalized by the feed-forward filter and for performing equalization that does not consider trailing-edge inter-symbol interference subsequent to the leading-edge portion. The equalization circuit has a configuration of a decision feedback equalizer (DFE) having a feed-back loop. The decoding device further includes a feed-back filter (FBF) for generating a response for the trailing-edge inter-symbol interference, a noise predictor provided in the feedback loop, and a decoder for performing noise-predictive maximum-likelihood decoding on a signal output from the noise predictor. The equalization circuit subtracts the response generated by the feed-back filter from a response provided by the feed-forward filter so that a result of the subtraction provides a partial response.  
      The present invention further provides an error detecting device. The error detecting device includes a feed-forward filter (FFF) for equalizing a waveform and an equalization circuit for performing response according to a partial-response (PR) scheme on only a leading-edge portion of inter-symbol interference (ISI) of the waveform equalized by the feed-forward filter and for performing equalization that does not consider trailing-edge inter-symbol interference subsequent to the leading-edge portion. The equalization circuit has a configuration of a decision feedback equalizer (DFE). The error detecting device further includes a feed-back filter (FBF) for generating a response for the trailing-edge inter-symbol interference, a noise predictor provided in the feedback loop, and an error detection circuit. The equalization circuit includes a determination circuit using a fixed delay tree search (FDTS) and subtracts the response generated by the feed-back filter from a response provided by the feed-forward filter so that a result of the subtraction provides a partial response, and the error detection circuit detects error information to be fed back to at least one of automatic gain control and a phase-locked loop by using a determination value provided by the fixed delay tree search.  
      The present invention further provides an adaptive equalization method. The method includes a step of causing an equalization circuit to perform response according to a partial-response (PR) scheme on only a leading-edge portion of inter-symbol interference (ISI) of a waveform equalized by a feed-forward filter (FFF) and to perform equalization that does not consider trailing-edge inter-symbol interference subsequent to the leading-edge portion, a step of causing a feed-back filter (FBF) to generate a response for the trailing-edge inter-symbol interference, and a step of subtracting the generated response for the trailing-edge inter-symbol interference from a response provided by the feed-back filter so that a result of the subtraction provides a partial response.  
      According to the adaptive equalizer, the decoding device, and the error detecting device, partial response is performed on only a first portion of ISI of a waveform equalized by the upstream FFF and equalization that does not consider trailing-edge ISI subsequent to the first portion is performed. The FBF generates a response for the trailing-edge ISI and the DFE structure subtracts the generated response from a response provided by the FFF so that a result becomes a PR response. As a result, the present invention allows appropriate equalization processing using FDTS/DFE and so on while performing PR equalization. Further, the present invention can be applied to effective decode processing and error detection. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  is a block diagram showing a basic configuration of an optical recording apparatus or a magnetic recording apparatus according to an embodiment of the present invention;  
       FIG. 2  is a block diagram showing details of the PR equalizer shown in  FIG. 1 ;  
       FIG. 3  is a graph showing an input waveform of the PR equalizer shown in  FIG. 2 ;  
       FIG. 4  is a block diagram showing the configuration of an FFF provided in the PR equalizer shown in  FIG. 2 ;  
       FIG. 5  is a block diagram showing the configuration of an FBF provided in the PR equalizer shown in  FIG. 2 ;  
       FIG. 6  is a block diagram of the configuration of a predictor provided in the PR equalizer shown in  FIG. 2 ;  
       FIG. 7  illustrates a tree structure of the FDTS for T= 1 ;  
       FIG. 8  is block diagram of the configuration of the FBW provided in the PR equalizer shown in  FIG. 2 ;  
       FIG. 9  is a block diagram of the configuration of the FDTS unit provided in the PR equalizer shown in  FIG. 2 ;  
       FIG. 10  is a block diagram of the configuration of the LMS-FFF provided in the PR equalizer shown in  FIG. 2 ;  
       FIG. 11  is a detailed block diagram illustrating an i-th tap coefficient fi in the FIR coefficient update unit shown in  FIG. 10 ;  
       FIG. 12  is a detailed block diagram illustrating an i-th tap coefficient hi in the IIR coefficient update unit shown in  FIG. 10 ;  
       FIG. 13  is a block diagram of the configuration of the LMS-FBF provided in the PR equalizer shown in  FIG. 2 ;  
       FIG. 14  is a detailed block diagram illustrating an i-th tap coefficient bi in the FIR coefficient update unit shown in  FIG. 13 ;  
       FIG. 15  is a detailed block diagram illustrating an i-th tap coefficient ci in the IIR coefficient update unit shown in  FIG. 13 ;  
       FIG. 16  is a block diagram of the configuration of the LMS-predictor provided in the PR equalizer shown in  FIG. 2 ;  
       FIG. 17  is a detailed block diagram illustrating an i-th tap coefficient fi in the coefficient update unit shown in  FIG. 13 ;  
       FIG. 18  is a graph illustrating one example of an equalized waveform having leading-edge ISI;  
       FIG. 19  illustrates an example of characteristic of a phase shifter;  
       FIG. 20  is illustrates a waveform provided by passing the equalized waveform shown in  FIG. 18  through the phase shifter;  
       FIG. 21  is a block diagram showing details of a PR equalizer that incorporates the block of the phase shifter;  
       FIG. 22  is a block diagram of the configuration of a phase controller provided in the PR equalizer shown in  FIG. 21 ;  
       FIG. 23  is a block diagram of the configuration of a level error detector provided in the PR equalizer shown in  FIG. 21 ; and  
       FIG. 24  is a block diagram of the configuration of a timing error detector provided in the PR equalizer shown in  FIG. 21 . 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT  
      According to an embodiment of the present invention, in a waveform equalizer for a communication apparatus, a magnetic recording apparatus, or an optical recording/reproducing apparatus, a feed-forward filter (FFF) is provided and, at a subsequent stage, a decision feedback equalizer (DFE) or a fixed delay tree search/decision feedback equalizer (FDTS/DFE) employing FDTS for a determination unit is provided. Partial response (PR) is performed on only a first portion of inter-symbol interference (ISI) of a waveform equalized by the FFF and equalization that does not consider subsequent response (herein after referred to as “trailing-edge ISI”) is performed. A feed-back filter (FBF) generates a response for the trailing-edge ISI and the DFE structure subtracts the generated response from a response provided by the FFF so that a result becomes a partial response.  
      An embodiment of the present invention will now be described with reference to the accompanying drawings.  
       FIG. 1  is a block diagram showing a basic configuration of an optical recording apparatus or a magnetic recording apparatus according to an embodiment of the present invention.  
      As shown in  FIG. 1 , the apparatus includes a modulation circuit  10 , a recording control circuit  20  for controlling recording current for a recording laser or a magnetic head in accordance with a modulation signal, a laser pickup or magnetic head  30  for recording/reproducing various types of data to/from a medium  100 , a reproduction amplifier  40 , an automatic gain control (AGC)  50 , a phase-locked loop (PLL)  60 , a partial-response (PR) equalizer  70 , a maximum-likelihood decoder  80 , and a demodulation circuit  90 .  
       FIG. 2  is a block diagram showing details of the PR equalizer  70  shown in  FIG. 1 .  
      As shown, the PR equalizer  70  includes a feed-forward filter (FFF)  110 , a least-mean-square feed-forward filter (LMS-FFF)  111 , a least-mean-square feed-back filter (LMS-FBF)  112 , an FBF  113 , a Feed Back Whitener (FBW)  114 , a fixed delay tree search (FDTS) unit  115 , a delay unit  116 , an LMS predictor  117 , and a predictor  118 .  
      The PLL  60  samples discrete data so that a reproduction input waveform is produced at the timing of a PR detecting point and supplies the discrete data to the FFF  110  based on a clock. All the blocks shown in  FIG. 2  are digital circuits that operate based on the clock.  
      A description is now given in conjunction with an example of an input waveform and an equalized waveform. The description, however, is merely one example and thus does not restrict the claims of the present invention.  
      First, a sampled readout waveform, as indicated by waveform (a) in  FIG. 3 , is input to the FFF  110  shown in  FIG. 2 . For example, when an attempt is made to equalize a waveform for first two pieces of data to PR( 11 ), an output having an equalized waveform as indicated by waveform (b) shown in  FIG. 3  is obtained.  
      The FFF  110  is a digital filter for performing the calculation:  
               y0   n     =         ∑     i   =   0       N   1       ⁢           ⁢       f   i     ·     x     n   -   i           -       ∑     i   =   0       N   2       ⁢           ⁢       h   i     ·     y0     n   -   i                     (   1   )             
 
      Referring to  FIG. 4 , the FFF  110  has a configuration in which delay units  120 , multipliers  121 , and adders  122  are connected as shown. Coefficients fi and hi (i is an integer) are defined by values supplied from an LMS block (described below) for the FFF  110 . Delay elements corresponding to an FDTS tree length (“2” in this case) are provided in order to obtain x(n−N1−2) and y 0 (n−N2−2), respectively. These values are irrelevant to the above-noted digital filter calculation but are required for calculation of the LMS block (described below) for the FFF  110 .  
      The FBF  113  shown in  FIG. 2  has tap coefficients, bi (i=0, 1, . . . , and L1) and ci (i=0, 1, . . . , and L2), supplied from an LMS block (described below) for the FBW  113  in order to cancel the trailing-edge ISI after the third pieces of data in the equalized waveform indicated by waveform (b) shown in  FIG. 3 . The FBF  113  is a digital filter for calculating the following:  
               y1   n     =         ∑     i   =   0       L   1       ⁢           ⁢       b   i     ·       a   ^       n   -   2   -   i           -       ∑     i   =   0       L   2       ⁢           ⁢       c   i     ·     y1     n   -   i                     (   2   )             
 
      The FBF  113  has a configuration in which delay units  140 , multipliers  141 , and adders  142  are connected as shown in  FIG. 5 . The above description, however, has been given based on an assumption that the values of hk (k=0, 1, and L2) are all 0s. Coefficients fi and hi (i is an integer) are defined by values supplied from the LMS block (described below) for the FFF  110 . Delay elements corresponding to the FDTS tree length (“2” in this case) are also provided in order to obtain a(n−2−L1−2) and y 1 (n−L2−2). These values are irrelevant to the above-noted digital filter calculation but are required for calculation (described below) of an FBF LMS block. Data a(n−2), i.e., 0 or 1, which is an FDTS determination result, is input to the FBF  113 .  
      However, when the trailing-edge ISI does not exist and the values of bk (k=0, 1, . . . , and L1) are all 0s, this is equivalent to a case in which no FBF is provided and thus the FBF is not necessarily required.  
      The determination result is then subtracted from the FFF equalized waveform (i.e., waveform (a) shown in  FIG. 3 ) by a subtractor and the resulting waveform is shaped to have waveform PR( 11 ) in waveform (c) shown in  FIG. 3 . The shaped waveform, y 2 ( n ), can be expressed as: 
 
 y   2   n   =y   0   n   −y   1   n   (3) 
 
      The predictor  118  shown in  FIG. 2  is a block for whitening noise and has a prediction coefficient pk (k=1, 2, . . . , and N) therefor. How to determine pk will be described later. The predictor  118  is a digital filter for calculating the following:  
               y3   n     =       y2   n     -       ∑     i   =   1     N     ⁢           ⁢       p   i     ·     y2     n   -   i                     (   4   )             
 
      The predictor  118  has a configuration in which delay units  150 , multipliers  151 , and an adder  152  are connected as shown in  FIG. 6 .  
      Next, the operation of the FDTS  115  will be described.  
      Branch metric calculation for the FDTS is performed according to expression (7) described in E. Eleftheriou and W. Hirt, “Noise-predictive maximum-likelihood (NPML) detection for the magnetic recording channel” in IEEE Conf. Records, ICC&#39;96, June 1996, pp. 556-560. Herein, however, it is assumed that a minimum metric is used and the symbol of the expression is reversed. In addition, although the paper describes an example of RP4, the calculation herein is performed for an example of PR( 11 ). Further, an example of the FDTS cut-off depth of T=1 is discussed herein.  
      The transfer function, P(D), can be given by: 
 
 P ( D )= p   1   ·D+p   2   ·D   2   + . . . +p   N   ·D   N   (5) 
 
      Since the predictor transfer function for PR ( 11 ) is 1+D, G(D) is defined as: 
 
 G ( D )=(1+ D )·(1− P ( D ))−1− g   1   ·D . . . −g   N+1   ·D   N+1   (6) 
 
      This coefficient gi is calculated by a G(D) calculation block in the LMS predictor  117 , which is described below and shown in  FIG. 16 .  
      Branch metric for time n is given by:  
               λ   n     =       (       y3   n     +       ∑     i   =   2       N   +   2       ⁢       a     n   -   i       ·     g   i         +       a     n   -   1       ·     g   1       -     a   n       )     2             (   7   )             
 
      The FBW unit  114  in the DFE structure uses a provisional determination value to calculate the following:  
               y5   n     =       ∑     i   =   2       N   +   2       ⁢       a     n   -   i       ·     g   i                 (   8   )             
 
      The FBW includes delay units  160 , multipliers  161 , and an adder  162 , as shown in  FIG. 8 .  
      Next, the expression of the branch metric is rewritten using y 4  shown in  FIG. 2 . 
 
λ n =( y   4   n   +a   n−1   ·g   1   −a   n ) 2   (9) 
 
      The tree structure of FDTS for T=1 is shown in  FIG. 7 . The internal structure of the FDTS calculation unit is shown in  FIG. 9 . As shown in  FIG. 9 , the FDTS calculation device includes path-metric calculation blocks  161  and  162 , branch metric calculation units  163  to  166 , adders  167  to  170 , minimum-value selection circuits  171  and  172 , and a comparator circuit  173 .  
      Here, in accordance with the values a(n) and a(n−1) of branches shown in  FIG. 7 , the following calculations are performed for branch metrics b 11 , b 10 , b 01 , and b 00 . 
 
 b   11 =( y   4   n   +g   1 −1) 2  
 
 b   10 =( y   4   n   +g   1 ) 2  
 
 b   01 =( y   4   n −1) 2  
 
 b   00 =( y   4   n ) 2   (10) 
 
      These calculations correspond to the branch-metric calculation units  163  to  166 , respectively. For path metrics p 11 , p 10 , p 01 , and p 00 , the following calculations are performed. 
 
 p   11 = p   1 + b   11  
 
 p   10 = p   1 + b   10  
 
 p   01 = p   0 + b   01  
 
 p   00 = p   0 + b   00   (11) 
 
      These calculations correspond to the adders  167  to  170  for adding outputs from the path-metric calculation blocks  161  and  162  and outputs from the branch-metric calculation blocks  163  to  166 .  
      In order to determine the value of a(n−1), the minimum-value selection circuits  171  and  172  shown in  FIG. 9  perform calculations of MIN 1 =min(p 11 , p 10 ) and MIN=mini(p 01 , p 00 ), respectively. When the comparator circuit  173  yields the result of MIN 1 &lt;MIN 0 , it is determined as a(n−1)= 1 , and when the comparator circuit  173  yields the result of MIN 1 ≧MIN 0 , it is determined as a(n−1)=0.  
      Path-metrics p 11 , p 10 , p 01 , and p 00  are input to the comparator circuit  173  shown in  FIG. 9 , and the comparator circuit  173  selects next candidates p 1  and p 0  for output. Specifically, the comparator circuit  173  performs update so that p 1 =p 11  and p 0 =p 10  are satisfied for MIN 1 &lt;MIN 0  and p 1 =p 01  and p 0 =p 00  are satisfied for MIN 1 ≧MIN 0 .  
      Next, the operation of the LMS-FFF  111 , which is an LMS block for the FFF  110 , will be described.  
       FIG. 10  is an internal block diagram of the LMS-FFF  111 . As shown, the LMS-FFF  111  includes a finite-impulse-response (FIR) coefficient update unit  181  and an infinite-impulse-response (IIR) coefficient update unit  182 . The results of coefficient updates are output to corresponding FIR and IIR tap-coefficient terminals. An evaluation function, F(n), for an FFF output waveform is given as follows: 
   F ( n )={ y   2   n −( a   n   +a   n−1 )} 2   (12)  
 where n indicates current time. 
 
      In the LMS algorithm, filter coefficients are controlled so as to minimize square error.  
      For example, when partial differentiation is performed with respect to coefficient fi for an FIR section with FFF tap number i, the following is given:  
                 ∂     ∂     f   i         ⁢     F   ⁡     (   n   )         =     2   ⁢       {       y2   n     -     (       a   n     +     a     n   -   1         )       }     ·     x     n   -   i                   (   13   )             
 
      In practice, however, since the FDTS in this system has a fixed delay, a determination result with a delay of τ+1=2 is provided and thus the following partial differentiation is performed.  
                 ∂     ∂     f   i         ⁢     F   ⁡     (     n   -   2     )         =     2   ⁢       {       y2     n   -   2       -     (       a     n   -   2       +     a     n   -   3         )       }     ·     x     n   -   2   -   i                   (   14   )             
 
      This calculation is performed internally by the FIR coefficient update unit  181  shown in  FIG. 10 .  
       FIG. 11  is a detailed block diagram illustrating the i-th tap coefficient fi in the FIR-coefficient update unit  181  shown in  FIG. 10 . Although FIR coefficient update sections (only one of which is shown in  FIG. 11 ) are provided such that the number thereof is equal to the number of tap coefficients, i.e., N1+1, an example of the i-th tap coefficient is described since all the structures of the FIR coefficient update sections are the same.  
      As shown, the FIR coefficient update section includes an FIR partial-differential calculation unit  191  and a moving average calculation unit  192 , a multiplier  193 , a subtractor  194 , and a delay unit  195 .  
      The above-noted partial differentiation is performed by the FIR partial-differential calculation unit  191 . The result of the partial differentiation is used to perform moving-average calculation with respect to moving averages M 0  provided by the moving average calculation unit  192 . The result is then multiplied by an update coefficient α0 and the resulting value is subtracted from fi obtained during the previous clock cycle, thereby performing update.  
      Similarly, partial differentiation with respect to coefficient hi in the IIR unit  182  is given by:  
                 ∂     ∂     h   i         ⁢     F   ⁡     (   n   )         =     2   ⁢       {       y2   n     -     (       a   n     +     a     n   -   1         )       }     ·     (     -     y0     n   -   i         )                 (   15   )             
 
      In practice, however, since the FDTS in this system has a fixed delay, a determination result with a delay of τ+1=2 is provided and thus the following partial differentiation is performed.  
                 ∂     ∂     h   i         ⁢     F   ⁡     (     n   -   2     )         =     2   ⁢       {       y2     n   -   2       -     (       a     n   -   2       +     a     n   -   3         )       }     ·     (     -     y0     n   -   2   -   i         )                 (   16   )             
 
      This calculation is performed by the IIR coefficient update unit  182  shown in  FIG. 10 .  
       FIG. 12  is a detailed block diagram illustrating the i-th tap coefficient hi in the IIR-coefficient update unit  182  shown in  FIG. 10 . Although IIR coefficient update sections (only one of which is shown in  FIG. 12 ) are provided such that the number thereof is equal to the number of tap coefficients, i.e., N2+1, an example of the i-th tap coefficient is described since all the structures of the IIR coefficient update sections are the same.  
      As shown, the IIR coefficient update section includes an IIR coefficient calculation unit  201 , a moving average calculation unit  202 , a multiplier  203 , a subtractor  204 , and a delay unit  205 .  
      The above-noted partial differentiation is performed by the IIR partial-differential calculation unit  201 . The result of the partial differentiation is used to perform moving-average calculation with respect to moving averages M 1  provided by the moving average calculation unit  192 . The result is then multiplied by an update coefficient al and the resulting value is subtracted from hi obtained during the previous clock cycle, thereby performing update.  
      Next, the operation of the LMS-FBF  112 , which is an LMS block for the FBF  113 , will be described.  
       FIG. 13  is a block diagram of the internal configuration of the LMS-FBF  112 . As shown, the LMS-FBF  112  includes an FIR coefficient update unit  211  and an IIR coefficient update unit  212 . The results of coefficient updates are output to corresponding FIR and IIR tap-coefficient terminals.  
      An evaluation function, F(n), for an FBF output waveform is discussed similarly to the case of the FFF.  
      For example, when partial differentiation is performed with respect to coefficient bi for tap number i in the FIR unit for the FBF  113 , the following is given:  
                 ∂     ∂     b   i         ⁢     F   ⁡     (   n   )         =     2   ⁢       {       y2   n     -     (       a   n     +     a     n   -   1         )       }     ·     (     -     a     n   -   2   -   i         )                 (   17   )             
 
      In practice, however, since the FDTS in this system has a fixed delay, a determination result with a delay of τ+1=2 is provided and thus the following partial differentiation is performed.  
                   ∂               ∂     b   i         ⁢     F   ⁡     (     n   -   2     )         =     2   ⁢       {       y2     n   -   2       -     (       a     n   -   2       +     a     n   -   3         )       }     ·     (     -     a     n   -   4   -   i         )                 (   18   )             
 
      This calculation is performed internally by the FIR coefficient update unit  211 .  
       FIG. 14  is a detailed block diagram illustrating the i-th tap coefficient bi in the FIR-coefficient update unit  211 . Although FIR coefficient update sections shown in  FIG. 14  (only one of which is shown) are provided such that the number thereof is equal to the number of tap coefficients, i.e., L1+1, an example of the i-th tap coefficient is described since all the structures of the FIR coefficient update sections are the same.  
      As shown, the FIR coefficient update section includes an FIR partial-differential calculation unit  221  and a moving average calculation unit  222 , a multiplier  223 , a subtractor  224 , and a delay unit  225 .  
      The above-noted partial differentiation is performed by the FIR partial-differential calculation unit  221 . The result of the partial differentiation is used to perform moving-average calculation with respect to moving averages M 2  provided by the moving average calculation unit  222 . The result is then multiplied by an update coefficient α2 and the resulting value is subtracted from bi obtained during the previous clock cycle, thereby performing update.  
      Similarly, partial differentiation with respect to coefficient ci of the IIR unit is given by:  
                   ∂               ∂     c   i         ⁢     F   ⁡     (   n   )         =     2   ⁢       {       y2   n     -     (       a   n     +     a     n   -   1         )       }     ·     y1     n   -   i                   (   19   )             
 
      This calculation is performed by the IIR coefficient update unit  212 .  
      In practice, however, since the FDTS in this system has a fixed delay, a determination result with a delay of τ+1=2 is provided and thus the following partial differentiation is performed.  
                   ∂               ∂     c   i         ⁢     F   ⁡     (     n   -   2     )         =     2   ⁢       {       y2     n   -   2       -     (       a     n   -   2       +     a     n   -   3         )       }     ·     y1     n   -   2   -   i                   (   20   )             
 
       FIG. 15  is a detailed block diagram illustrating the i-th tap coefficient ci in the IIR coefficient update unit  212 . Although FIR coefficient update sections (only one of which is shown in  FIG. 15 ) are provided such that the number thereof is equal to the number of tap coefficients, i.e., L2+1, an example of the i-th tap coefficient is described since all the structures of the FIR coefficient update sections are the same.  
      As shown, the IIR coefficient update section includes an IIR partial-differential calculation unit  231  and a moving average calculation unit  232 , a multiplier  233 , a subtractor  234 , and a delay unit  235 .  
      The above-noted partial differentiation is performed by the IIR partial-differential calculation unit  231 . The result of the partial differentiation is used to perform moving-average calculation with respect to moving averages M 3  provided by the moving average calculation unit  232 . The result is then multiplied by an update coefficient α3 and the resulting value is subtracted from ci obtained during the previous clock cycle, thereby performing update.  
      The LMS predictor  117  will be described next.  
       FIG. 16  is an internal block diagram of the LMS predictor  117 .  
      The LMS predictor  117  has a coefficient update unit  241 , a G(D) calculation block  242 , and so on. To the LMS predictor  117 , y 2   n  and FDTS determination result a(n−2) are input, and an error signal w(n−2) at time n- 2  is calculated. This w(n−2) is input to an FIR noise predictor, and the result and a signal indicating w(n−2−i) are input to the coefficient update unit  241 , so that each tap coefficient pi (i=1, 2, . . . , and N) is updated.  
      Now, the following e 2 (n) is considered as a predictor evaluation function.  
                 e   2     ⁡     (   n   )       =       {       w   n     -       ∑     i   =   1     N     ⁢           ⁢       w     n   -   i       ·     p   i           }     2             (   21   )             
 
 where n indicates current time. 
 
      Now, a method for minimizing the value by using an LMS algorithm is considered.  
      For example, when partial differentiation is performed with respect to coefficient pi for tap number i in the predictor, the following is given.  
                   ∂               ∂     p   i         ⁡     [       e   2     ⁡     (   n   )       ]       =     2   ⁢       {       w   n     -       ∑     j   =   1     N     ⁢           ⁢       w     n   -   j       ·     p   j           }     ·     w     n   -   i                   (   22   )             
 
      In practice, however, since the FDTS in this system has a fixed delay, a determination result with a delay of τ+1=2 is provided and thus the following partial differentiation is performed.  
                   ∂               ∂     p   i         ⁡     [       e   2     ⁡     (     n   -   2     )       ]       =     2   ⁢       {       w     n   -   2       -       ∑     j   =   1     N     ⁢           ⁢       w     n   -   2   -   j       ·     p   j           }     ·     w     n   -   2   -   i                   (   23   )             
 
      This calculation is performed internally by the coefficient update unit  241 .  
       FIG. 17  is a detailed block diagram illustrating the i-th tap coefficient pi in the coefficient update unit  241 . Although coefficient update sections (only one is shown in  FIG. 17 ) are provided such that the number thereof is equal to the number of tap coefficients, i.e., N, an example of the i-th tap coefficient is described since all the structures of the coefficient update sections are the same.  
      As shown, the coefficient update section includes a partial-differential calculation unit  251  and a moving average calculation unit  252 , a multiplier  253 , a subtractor  254 , and a delay unit  255 .  
      The above-noted partial differentiation is performed by the partial-differential calculation unit  251 . The result of the partial differentiation is used to perform moving-average calculation with respect to moving averages M 4  provided by the moving average calculation unit  252 . The result is then multiplied by an update coefficient α4 and the resulting value is subtracted from pi obtained during the previous clock cycle, thereby performing update.  
      As described above, the PR( 11 ) adaptive equalizer has the hybrid configuration of the FFF and the FDTS/DFE.  
      The above description has been given for a case in which an equalized waveform lacks leading-edge ISI, as shown in  FIG. 3 . Now, a method for equalizing an equalized waveform having leading-edge ISI, as shown in  FIG. 18 , will be described.  
      First, an operation for, for example, rotating the phase of the equalized waveform having the leading-edge ISI is considered. Rotating phase θ means, when viewed along a frequency axis, multiplication of phase θ by a characteristic as shown in  FIG. 19 . The character, fs, represents a sampling frequency.  
      Now, an FIR having a tap coefficient obtained by performing Inverse Discrete Fourier Transform (IDFT) on the frequency characteristic shown in  FIG. 19  is defined as a phase shifter.  
       FIG. 20  shows a waveform obtained by passing an equalized waveform through the phase shifter.  
      It is shown that an increase in phase θ causes overshoot in the leading-edge ISI to increase and a decrease in phase θ causes an increase in undershoot in the leading-edge ISI. Thus, applying feedback to θ with automatic control so as to reduce the leading-edge ISI can achieve such equalization that the leading-edge ISI displays a moderately small value.  
       FIG. 21  is a block diagram showing an entire system incorporating the block of the phase shifter.  
      In addition to the block configuration shown in  FIG. 2 , this system further includes a phase shifter  261 , a phase controller  262 , a level error detector  263 , and a timing error detector  264 .  
      The phase controller  262  calculates θ and supplies it to the phase shifter  261  and the phase shifter  261  then rotates the phase of an input waveform by θ.  
      The overshoot shown in  FIG. 20  will appear as interference with the leading-edge ISI at a waveform detecting point. When θ is large as shown in  FIG. 20 , error at a detecting point increases in a positive direction, and when θ is small, error at a detecting point increases in a negative direction. Thus, calculating the following expression can yield a value proportional to the error of θ. 
 
{y 2   n −(a n +a n−1 )}·(a n+1 +a n )  (24) 
 
      In practice, however, data obtained by the FDTS is delayed by an amount of time corresponding to two clocks. Further, since a(n+1) in expression  24  is data subsequent to data obtained at time n, the data cannot be obtained until the next determination. Thus, a determination value obtained with a delay corresponding to another one clock, i.e., a determination value obtained with a delay of total of three clocks is used to calculate the following expression. 
 
{y 2   n-3 −(a n-3 +a n−3−1 )}·(a n−3+1 +a n−3 )  (25) 
 
      The phase controller  262  is a block that uses the above-noted calculation to update θ.  FIG. 22  is a detailed block diagram of the phase controller  262 . The phase controller  262  has a θ calculation unit  271 , a moving average calculation unit  272 , a multiplier  273 , a subtractor  274 , and a delay unit  275 . The θ calculation unit  271  performs the above-noted calculation. A moving average among M 5  is determined by the moving average calculation unit  272  and is multiplied by an update coefficient α5, and the resulting value is subtracted from θ obtained during the previous clock cycle.  
      The level error detector  263  will be described next.  FIG. 23  is a block diagram of the configuration of the level error detector  263 . The level error detector  263  has a configuration in which delay units  281 , adders  282 , and a multiplier  283  are connected as shown in  FIG. 23 .  
      The level error detector  263  calculates a level error by using the following expression. 
 
{Y 2   n −(a n +a n−1 )}·(a n +a n−1 )  (26) 
 
      In practice, however, since data provided by the FDTS is delayed by an amount of time corresponding to two clocks, the following partial differentiation is performed. 
 
{Y 2   n−2 −(a n−2 +a n−2−1 )}·(a n−2 +a n−2−1 )  (27) 
 
      The timing error detector  264  will be described next.  FIG. 24  is a block diagram of the configuration of the timing error detector  264 . The timing error detector  264  has a configuration in which delay units  291 , adders  292 , and multipliers  293  are connected as shown in  FIG. 24 .  
      The timing error detector  264  calculates timing error by using the following expression. 
 
−y 2   n ·(a n−1 +a n−2 )+y 2   n−1 ·(a n +a n−1 )  (28) 
 
      In practice, however, since data provided by the FDTS is delayed by an amount of time corresponding to two clocks, the following partial differentiation is performed. 
 
−y 2   n−2 ·(a n−2−1 +a n−2−2 )+y 2   n−2−1 ·(a n−2 +a n−2−1 )  (29) 
 
      The embodiment having the above-described configuration can provide a determination value based on FDTS with an improved performance compared to a case in which a threshold determining unit is used, while performing PR equalization.  
      Performing partial response on a first response of a waveform output from the FFF allows a maximum-likelihood decoder suitable for, for example, Viterbi decoding PR, to be arranged at a subsequent stage.  
      Further, a combination with the noise predictor improves the determination performance of the FDTS. In addition, supplying an output of the noise predictor to the NPML decoder allows for NPML decoding for a waveform having decreased ISI.  
      Further, conventionally, when a waveform having leading-edge ISI is input to an FDTS/DEF, whether equalization error is due to the leading-edge ISI or the trailing-edge ISI cannot be identified, and thus the leading-edge ISI of the FFF output cannot be adaptively removed. However, according to the present invention, since the phase shifter is provided, it is possible to perform equalization by differentiating equalization error due to the leading-edge ISI.  
      Additionally, according to the present invention, level error and phase error can be detected from a waveform having a decreased ISI, through the use of a determination provided by the FDTS having an improved determination performance.