Abstract:
The invention relates to Run length Limited-codes storage systems. In modern storage systems, the inter-track spacing is chosen to be relatively small to allow for high storage densities. As a result, when reading a target track, data written on side tracks may appear in the recovered signal. This inter-track interference is called cross-talk. The invention proposes a cross-talk cancellation scheme based on the minimization of the mismatch between the actual (dm+1m) and the expected (exp) run length between two transitions (xm, xm+1) of the (dm+1,m) signal. The proposed solution significantly improves the ramp-up properties of the receiver and allows more efficient hardware implementation.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to a cross-talk cancellation method, a computer program for implementing a cross-talk cancellation method, a signal processor comprising cross-talk cancellation means, and an apparatus for reading a signal stored along a track on a storage medium, said apparatus comprising cross-talk cancellation means.  
         [0002]     The present invention relates to storage systems in which data are stored along tracks on a storage medium. In modern storage systems, the inter-track spacing is chosen relatively small to allow for high storage densities. As a result, when reading a target track, data written on side tracks may appear in the recovered signal. This inter-track interference is called cross-talk.  
         [0003]     The invention is advantageously used in such storage systems to improve the recovered signal by removing the cross-talk. For example, the invention applies to optical storage systems (DVD, Blu-ray Disc, Small Form Factor Optical Disc . . . ), magnetic storage systems (hard disks notably), magneto-optical storage systems.  
         [0004]     With optical storage systems, the cross-talk is even more severe when radial tilt is present in the system because then the optical spot extends more onto the side tracks.  
       BACKGROUND OF THE INVENTION  
       [0005]     A cross-talk removing device is described in U.S. Pat. No. 6,134,211. This device has three reading elements simultaneously reading a main track and two adjacent tracks. The three signals that are read by the three reading elements are sampled so as to provide three sequences of samples. A cross-talk removing circuit applies adaptive signal processing (for example an LMS adaptive algorithm) to the three sequences of samples to produce a cross-talk-removed sequence of samples associated with the main track that is free of cross-talk components from the adjacent tracks.  
         [0006]     The adaptive processing comprises an adaptive filtering, the filter coefficients being updated so as to converge to zero an error value present in the cross-talk-removed sequence of samples.  
         [0007]     This convergence is achieved by using a reference sample extracting circuit. When the values of three successive samples transit from positive to negative or from negative to positive, the reference sample extracting circuit extracts the central sample value of three successive sample values. The extracted sample value is supplied to a subtractor that calculates the difference between the extracted sample value and a reference value. This difference is used as the error (e) that has to be converged to zero to update the filter coefficients.  
         [0008]     In this scheme it is assumed that the central sample value is the sample value at ideal zero-crossing time. This assumption can only be made if the samples are bit-synchronous samples.  
         [0009]     In U.S. Pat. No. 6,134,211 this is achieved by running the analog-to-digital converters and the cross-talk removing circuit on a clock that is driven by a time recovery circuit. As a consequence, the cross-talk cancelling scheme is only operational when the time recovery circuit has acquired both the frequency and the phase lock.  
         [0010]     In U.S. Pat. No. 6,134,211, when the sample sequences remain in an asynchronous state (that is, when the time recovery circuit is not locked), the sequences are filtered on the basis of fixed predetermined coefficients. This helps to avoid divergence of the filter coefficients but leads to a ramp-up problem: if the time recovery circuit cannot converge because of strong cross-talk, the cross-talk cancellation scheme will remain inefficient and the system will be stuck.  
         [0011]     Another problem of the prior art system is that it is hardly compatible with asynchronous receiver architectures.  
         [0012]     In such asynchronous architectures, the analog-to-digital converters and the filters are run on a fixed clock. A transition from the fixed clock domain to the bit-synchronous domain is done at the output of the cross-talk cancellation circuit by means of a sample rate converter controlled by a time recovery circuit. An additional sample rate controller, locked to the time recovery circuit, would be needed for each adjacent track to produce the bit-synchronous samples that are needed to derive the above-described error (e).  
         [0013]     Moreover, if the fixed clock (at which the filters are running) and the clock driven by the time recovery circuit (at which the filters coefficients are updated) differ substantially from each other, inverse sample rate converters would also be required to interpolate the filter coefficients from the domain of the clock driven by the time recovery circuit to the domain of the fixed clock.  
         [0014]     This would lead to an increased complexity of the architecture.  
       SUMMARY OF THE INVENTION  
       [0015]     One of the objects of the invention is to propose a solution for cross-talk cancellation that solves the above-mentioned problems.  
         [0016]     This is achieved with a cross-talk cancellation method as claimed in claim  1 , a program as claimed in claim  2 , a signal processor comprising cross-talk cancellation means as claimed in claims  3  to  5 , and an apparatus for reading a signal stored along a track on a storage medium as claimed in claims  6  to  8 .  
         [0017]     The cross-talk cancellation means according to the invention are intended for receiving a main signal associated with a target track and satellite signals associated with side tracks, said main signal showing transitions and runs of various lengths between two transitions. They comprise:  
         [0018]     filtering means for filtering the satellite signals with adaptive filters, thereby generating filtered versions of the satellite signals,  
         [0019]     updating means for updating the coefficients of the adaptive filters by minimizing the mismatch between the actual and the expected run length between two transitions of the main signal,  
         [0020]     processing means for generating an improved main signal from said main signal by subtraction of said filtered versions of the satellite signals.  
         [0021]     According to the invention the error that is to be minimized when updating the filter coefficients is the mismatch between the actual and the expected run length between two transitions of the main signal. Contrary to the prior art minimization scheme, the minimization scheme of the invention does not use the notion of ideal transition time. Therefore it does not require the use of bit-synchronous samples. The proposed minimization scheme requires frequency lock but not phase lock.  
         [0022]     A first advantage of the proposed minimization scheme is that it resolves the above-mentioned ramp-up problem.  
         [0023]     A second advantage of the proposed minimization scheme is that it can be implemented in an asynchronous architecture without any additional hardware complexity.  
         [0024]     Advantageously, when used in an asynchronous receiver having a bit clock that is driven by a time recovery circuit, the cross-talk cancellation means of the invention are operated at a fixed clock that is asynchronous with respect to this bit-clock.  
         [0025]     In such a case, if the bit clock frequency is different from the fixed clock frequency, additional time recovery means are provided to derive the ratio between the bit clock frequency and the fixed clock frequency, said ratio being used by said updating means for updating said coefficients. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0026]     These and other aspects of the invention will be further described with reference to the following drawings:  
         [0027]      FIGS. 1 and 2  are functional block diagrams of examples of an apparatus according to the invention for reading a storage medium;  
         [0028]      FIGS. 3 and 4  are schematic representations of a first and a second configuration of tracks and light spots used in a 3-spot cross-talk cancellation scheme;  
         [0029]      FIG. 5  is a functional block diagram of the cross-talk cancellation means according to the invention;  
         [0030]      FIG. 6  is a schematic representation of a received signal showing two transitions and a run between the two transitions. 
     
    
     DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0031]     The invention applies to storage media having tracks each forming a 360° turn of a spiral line. Encoded data are recorded along the tracks. The encoding scheme that is used in optical recording system is a Run Length Limited encoding scheme (RLL). When the data recorded along the tracks are encoded with an RLL encoding scheme, the tracks exhibit marks corresponding to runs of a same value, and the edges of a mark correspond to a transition between two runs. The size of the mark corresponds to the length of the run. It is an integer multiple of a reference unit size mark.  
         [0032]      FIGS. 1 and 2  show block diagrams of a first and a second example of an apparatus for reading such a disc. The apparatus shown in  FIG. 1  carries reference number  6 - 1 . The apparatus of  FIG. 2  carries reference number  6 - 2 . According to  FIGS. 1 and 2 , the apparatuses  6 - 1  and  6 - 2  comprise an optical unit  8  having three reading elements: a main reading element  12  for reading a main signal associated with a main track, and two satellite reading elements  11  and  13  for reading two satellite signals associated with the two tracks that are adjacent to the main track. In the subsequent description, one of these satellite signal is called upper satellite signal, and the other satellite signal is called lower satellite signal. The three reading elements transmit three light spots  21 ,  22  and  23 .  
         [0033]      FIGS. 3 and 4  show the locations of the three light spots  21 ,  22  and  23  with respect to the three tracks to be read  31 ,  32  and  33 . The main light spot  22  is centered on the main track  32 . The satellite light spots  21  and  23  may be centered either on the satellite tracks  31  and  33  as represented in  FIG. 3 , or between the main track  32  and the adjacent tracks  31  and  33  as represented in  FIG. 4 . The satellite signals read by the satellite light spots  21  and  23  in  FIGS. 3 and 4  are said to be “associated with” the adjacent tracks because the light spots  21  and  23  overlap with at least part of the adjacent tracks.  
         [0034]     The embodiment of  FIG. 4  is advantageous for rewritable optical disc systems because it allows reusing the 3-spot push-pull radial tracking means which are currently available in all such systems (the signal read by the reading elements  11 ,  12  and  13  and the main light spots  21 ,  22  and  23  can be used both for tracking and for cross-talk cancellation).  
         [0035]     Returning to  FIGS. 1 and 2 , the three signals that are read by the three reading elements  11 ,  12  and  13  are input to a signal processor  40  comprising cross-talk cancellation means  42  and decoding means  44 . The signal produced by the decoding means  44  is input to a reproduction circuit  46  that generates an output signal (for example an audio or a video signal).  
         [0036]      FIG. 5  is a functional representation of the cross-talk cancellation means  42 . The cross-talk cancellation means  42  comprise three analog-to-digital converters  51 ,  52  and  53  for sampling the main signal, the upper satellite signal and the lower satellite signal. The three analog-to-digital converters  51 ,  52  and  53  operate at a fixed clock  55  and generate a sequence of main samples  62 , a sequence of lower satellite samples  61 , and a sequence of upper satellite samples  63 . The sequences of lower and upper satellite samples  61  and  63  are processed by a lower adaptive filter  71  and an upper adaptive filter  73 , respectively, which generate a filtered version  81  of the sequence of lower satellite samples and a filtered version  83  of the sequence of upper satellite samples. The sequence  62  of main samples is processed by an optional equalizer  90 , which generates an equalized sequence of main samples  92 . Then a subtractor  93  subtracts the filtered version  81  of the sequence of lower satellite samples and a filtered version  83  of the sequence of upper satellite samples from the equalized sequence  92  of main samples, thereby generating an improved sequence of main samples  102 .  
         [0037]     Alternatively, if the equalizer  90  is omitted, the improved sequence of main samples  102  is generated by subtraction of the filtered version  81  of the sequence of lower satellite samples and a filtered version  83  of the sequence of upper satellite samples from the sequence  62  of main samples.  
         [0038]     The improved sequence of main samples  102  is input to a sample rate converter  120  driven by a time recovery circuit  130  (for example a Phase Lock Loop circuit). The output of the sample rate converter  120  is the input of the decoding means  44 .  
         [0039]     The improved sequence of main samples  102  and the sequences of lower and upper satellite samples  61  and  63  are processed by lower and upper coefficient updating means  111  and  113 . The lower and upper coefficient updating means  111  and  113  update the respectively coefficients used by the lower filter  71  and by the upper filter  73 .  
         [0040]     The behaviour of the cross-talk cancellation means  42  can be formalized by the following mathematical expression:  
                 C   ~     m     =       C   m     -       ∑   k     ⁢       f   k   +     ⁢     S     m   -   k     +         -       ∑   k     ⁢       f   k   -     ⁢     S     m   -   k     -                   (     equation   ⁢           ⁢   1     )             
 
 where: 
 
 S m   +  is the sample m of the upper satellite signal; 
 
 S m   −  is the sample m of the lower satellite signal; 
 
 C m  is the sample m of the main signal; 
 
 f k   +  are the coefficients of the upper filter and f k   −  are the coefficients of the lower filter; 
 
 {tilde over (C)} m  is the improved main sample m obtained at the output the subtractor  93 . 
 
         [0041]     Advantageously, the algorithm used to update the filter coefficients is the LMS algorithm (Least Mean Square). According to the invention the driving term Z m  of the algorithm (that is the term to be minimized) is the mismatch between the actual and the expected run length between two transitions of the main signal. 
 
 This means that:  
                 (     f   k   ±     )       m   +   1       =         (     1   -   μ     )     ⁢       (     f   k   ±     )     m       -     μ   ⁢     ∂     ∂     f   k   ±         ⁢       (     Z   m     )     2                 (     equation   ⁢           ⁢   2     )             
 
         [0042]     The cross-talk minimization scheme of the invention will be described below with reference to  FIG. 6 . As will be apparent from this description, for the proposed scheme to operate properly, the ratio α between the PLL-driven bit clock and the fixed clock that runs the analog-to-digital converters  51 ,  52  and  53  must be available. In  FIG. 5 , two arrows  141  and  143  indicate that the frequency ratio α is supplied to the first and second coefficient updating means  111  and  113 . The arrows  141  and  143  are represented in dashed lines because they may be omitted if the frequency ratio α is equal to 1.  
         [0043]     The ratio α is advantageously supplied by a time recovery circuit external to the cross-talk cancellation means  42  and specifically designed for fast approximate recovery of the bit frequency. Such an external time recovery circuit is already present in most reading apparatuses.  
         [0044]     For example, in some systems (mostly in writable/rewritable systems), the wobble clock can be conveniently used for estimating the ratio α.  FIG. 1  gives an example of an implementation that will be advantageously used in such systems: in  FIG. 1 , the external time recovery circuit carries reference number  50 - 1  and is connected In the path between the main reading element  12  and the cross-talk cancellation means  42 . In other systems (mostly in ROM systems), average run length measurements can be used for the same purpose.  FIG. 2  gives an example of an implementation that will be advantageously used in such systems: in  FIG. 2 , the external time recovery circuit carries reference number  50 - 2  and is connected In the path between the cross-talk cancellation means  42  and the decoding means  44 .  
         [0045]      FIG. 5  is a schematic representation of the received main signal. Two successive transitions X m  and X m+1 , are represented.  
         [0000]     {tilde over (C)} (m,L)  is the improved main sample on the left of the transition X m ;  
         [0000]     {tilde over (C)} (m,R)  is the improved main sample on the right of the transition X m ;  
         [0000]     {tilde over (C)} (m+1,L)  is the improved main sample on the left of the transition X m+1 ;  
         [0000]     {tilde over (C)} (m+1,R)  is the improved main sample on the right of the transition X m+1 ;  
         [0000]     {tilde over (C)} (m,L)+1  is the improved main sample that precedes sample {tilde over (C)} (m,L) ;  
         [0000]     {tilde over (C)} (m,L)+1  is the improved main sample that follows sample {tilde over (C)} (m,L) ;  
         [0000]     {tilde over (C)} (m,R)−1  is the improved main sample that precedes sample {tilde over (C)} (m,R) ;  
         [0000]     {tilde over (C)} (m,R)+1  is the improved main sample that follows sample {tilde over (C)} (m,R) ;  
         [0000]     φ m  is the time interval between the ideal time of the transition X m  and the actual time of the transition X m  (in  FIG. 5 , φ m &lt;0);  
         [0000]     φ m+1  is the time interval between the ideal time of the transition X m+1  and the actual time of the transition X m+1  (in  FIG. 5 , φ m+1 &lt;0);  
         [0000]     d m+1,m  is the actual run length between the two transitions X m  and X m+1 .  
         [0046]     In the following it is assumed for simplification purposes, without loss of generality, that:  
         [0047]     the time interval between two samples is equal to 1,  
         [0048]     the transition moment m=1 corresponds to a rising transition,  
         [0049]     and the time interval φ m  takes values from the interval  
         [       -     1   2       ,     +     1   2         ]     .       
 
         [0050]     A first implementation of the updating scheme of the invention will now be described. This first implementation is applicable when the fixed system clock is (nearly) equal to the PLL driven bit clock (that is when the ratio α is close to 1), but there is no phase lock between the two clocks.  
         [0051]     The LMS driving parameter to be minimized Z m  is chosen to be equal to the difference between the actual run length d m+1,m  and the expected run length d m+1,m   (exp) . Taking into account that an integer number of clock intervals should ideally fit between the transitions in the RLL encoded signal when there is no inter-symbol interference and no clock frequency variations, d m+1,m   (exp)  can be approximated as d m+1,m   (exp) =round(d m+1,m ) where round(x) is defined as the integer number that is closest to the real number x.  
         [0000]     Thus: 
 
 Z   m =ζ( d   m+1,m ) 
 
where ζ( x )= x −round( x ) 
 
with  d   m+1,m =[( m+ 1 , L )−( m,L )]+φ m+1 −φ m   (equation 3) 
 
 where [(m+1,L)−(m,L)] denotes the integer number of sampling intervals between the samples {tilde over (C)} (m,L)  and {tilde over (C)} (m+1,L) . 
 
 In the following it is assumed that the cross-talk is not extremely large, so that for small variations of the filter coefficients  
              ζ   ⁡     (     d       m   +   1     ,   m       )            &lt;       1   2     .         
 
 With this assumption, Z m  can be approximated as follows: 
 
 Z m =ζ(d m+1,m )≈φ m+1 −φ m +E where E is an integer independent of the filter coefficients.  
               ⇒       ∂     Z   m         ∂     f   k   ±           =       ∂     (       φ     m   +   1       -     φ   m       )         ∂     f   k   ±                 (     equation   ⁢           ⁢   4     )             
 
         [0052]     The time interval φ m  can be computed approximately as a function g m  of the improved main samples: 
 
φ m   ≈g   m ( {tilde over (C)}   (m,L)   ,{tilde over (C)}   (m,L)−1   , . . . ,{tilde over (C)}   (m,L)−N     L     ,{tilde over (C)}   (m,R)−1   , . . . ,{tilde over (C)}   (m,R)−N     R   )·(−1) m  
 
 The general form of a linear approximation is:  
         φ   m     ≈       (         ∑     k   =   0       N   L       ⁢       η     k   ,   L       ⁢       C   ~         (     m   ,   L     )     -   k           +       ∑     k   =   0       N   R       ⁢       η     k   ,   R       ⁢       C   ~         (     m   ,   R     )     -   k             )     ·       (     -   1     )     m           
 
 A simple 2-term linear approximation may be used, which gives: 
 
φ m ≈η·( {tilde over (C)}   (m,L)   +{tilde over (C)}   (m,R) )·(−1) m  
 
with η k,L =η k,R =η&gt;0 
 
and φ m+1 ≈η·( {tilde over (C)}   (m+1,L)   +{tilde over (C)}   (m+1,R) )·(−1) m+1  
 
 Based on this simple 2-term linear approximation and on equation 3 above: 
 
 Z   m ≈ζ(η R   m ·(−1) m+1 +[( m+ 1 ,L )−( m,L )])=ζ(η R   m )·(−1) m+1  
 
where  R   m   ={tilde over (C)}   (m,L)   +{tilde over (C)}   (m,R)   +{tilde over (C)}   (m+1,L)   +{tilde over (C)}   (m+1,R)  
 
 The term  
         ∂     ∂     f   k   ±         ⁢       (     Z   m     )     2         
 
 in equation 2 can be computed as follows:  
           ∂     ∂     f   k   ±         ⁢       (     Z   m     )     2       =         2   ·     Z   m     ·       ∂     Z   m         ∂     f   k   ±           ≈     2   ·     ζ   ⁡     (     η   ⁢           ⁢     R   m       )       ·       (     -   1     )       m   +   1       ·       ∂     (       φ     m   +   1       -     φ   m       )         ∂     f   k   ±             ⇒         ∂     ∂     f   k   ±         ⁢       (     Z   m     )     2       ≈     2   ·   η   ·     ζ   ⁡     (     η   ⁢           ⁢     R   m       )       ·     [       S       (     m   ,   L     )     -   k     ±     +     S       (     m   ,   R     )     -   k     ±     +     S       (       m   +   1     ,   L     )     -   k     ±     +     S       (       m   +   1     ,   R     )     -   k     ±       ]               
 
 Eventually the expression for updating the filters coefficients is: 
 
( f   k   ± ) m+1 =(1−μ)( f   k   ± ) m −2·μ·η·ζ(η R   m )·( S   (m,L)−k   ±   +S   (m,R)−k   ±   +S   (m+1,L)−k   ±   +S   (m+1,R)−k   ± )  (equation 5) 
 
         [0053]     A second implementation of the updating scheme of the invention will now be described that can be used when the fixed system clock (under which the filters are running) is not equal to the PLL driven bit clock (that is when the ratio α≠1).  
         [0054]     In this second implementation, the LMS driving parameter to be minimized Z m  is also chosen to be equal to the difference between the actual run length d m+1,m  and the expected run length d m+1,m   (exp) , but the mathematical formulae used for computing d m+1,m ,φ m  and φ m+1  have to be modified so as to take into account the frequency ratio α.  
         [0055]     Namely, in order to measure the run length in bit intervals, the number of samples between two transitions has to be multiplied by α, which means that: 
 
 d   m+1,m =α·[( m+ 1 ,L )−( m,L )]+φ m+1 −φ m  
 
 The transition phases φ m  also have to be multiplied by α. This means that the general form of the linear approximation of φ m  is:  
         φ   m     ≈     α   ·     (         ∑     k   =   0       N   L       ⁢       η     k   ,   L       ⁢       C   ~         (     m   ,   L     )     -   k           +       ∑     k   =   0       N   R       ⁢       η     k   ,   R       ⁢       C   ~         (     m   ,   R     )     -   k             )     ·       (     -   1     )     m           
 
 and the simple 2-term expression of the linear approximation is: 
 
         φ m ≈α·η·( {tilde over (C)}   (m,L)   +{tilde over (C)}   (m,R) )·(− 1 ) m  
 
 Eventually the expression for updating the filters coefficients is: 
 
( f   k   ± ) m+1 =( 1 −μ)( f   k   ± ) m −2·α·μ·η·ζ(η R   m )·└ S   (m,L)−k   ±   +S   (m,R)−k   ±   +S   (m+1,L)−k   ±   +S   (m+1,R)−k   ± ┘  (equation 6) 
 
         [0056]     It will be noted from equations 5 and 6 that the minimization scheme of the invention does not use the notion of ideal transition time.  
         [0057]     With respect to the described cross-talk cancellation method, signal processor and reading apparatus, modifications or improvements may be proposed without departing from the scope of the invention. The invention is not limited to the examples provided. In particular:  
         [0058]     The first and second implementations that were described are based on a simple 2-term linear approximation for the calculation of the time intervals φ m  and φ m+1 . This is not restrictive. Other approximations can be used. For example, a linear approximation using more than 2 terms may be used. The LMS updating scheme for these other approximations can be derived in a similar fashion as for the 2-term linear approximation.  
         [0059]     The minimization algorithm used in the above described implementations is the LMS algorithm. This is not restrictive. Other minimization algorithms may be used to minimize Z m . The corresponding coefficient updating equations may be readily derived by using the same principles as those described above for the LMS algorithm.  
         [0060]     In the cross-talk cancellation means described with reference to  FIG. 5 , the main signal is equalized. In an alternative embodiment, the main signal may be processed by an adaptive filter in a similar fashion as the lower and upper satellite signal.  
         [0061]     The functions described above may be implemented either in hardware or in software.  FIGS. 1, 2  and  5  are functional representations of an apparatus and a signal processor according to the invention. A hardware implementation thereof may differ from this functional block representation.  
         [0062]     The word “comprising” does not exclude the presence of elements or steps other than those listed.