Abstract:
A method and device for error analysis particularly adoptable for a recording medium such as an optical disc are disclosed. The present invention executes an encoding-like operation such as an interleaving operation to error flags during reproducing data from the optical disc, so as to obtain number and distribution of the errors on the disc.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application claims priority to and incorporates by reference the disclosure set forth, in its entirety, in U.S. Provisional Patent Application No. 60/729,279, entitled “AN INFORMATION RECORDING AND REPRODUCING APPARATUS WITH ERROR ANALYZER” filed Oct. 21, 2005. 
     
    
     TECHNICAL FIELD OF THE INVENTION  
       [0002]     The present invention relates to error analysis, more specifically, for a method and device for analyzing errors in a recording medium such as an optical disc.  
       BACKGROUND OF THE INVENTION  
       [0003]     It is advantageous to know the quality of a recording medium, for example, an optical disc such as a CD, DVD+, DVD−, DVD-RAM, HD-DVD, Blu-ray disc or the like. A method to know the disc quality well is to obtain the number and distribution of errors in the disc. From error analysis, errors due to a recording apparatus or the disc per se can be distinguished. The respective manufacturers of the recording apparatus and the disc can improve their products according to result of the error analysis.  
         [0004]     Generally, when an optical disc is read by a disc drive, a kind of errors so called “burst errors” in the present invention are essentially caused by defects of the disc per se. In contrast, another kind of errors so called “random errors” are mainly caused by the recording apparatus. For monitoring the recording or writing quality, it is necessary to omit the burst errors due to the inherent disc defects when calculating the total errors.  
         [0005]     An erroneous byte is a data byte in which at least one bit is of a wrong value. An error burst is defined as a sequence of bytes in which there are not more than a predetermined number m (m=2 in a usual case) correct bytes between any two erroneous bytes. A length of the error burst is defined as the total number of bytes counted from a first erroneous byte separated by a series of continuous correct bytes, which has at least m+1 (3 in a usual case) correct bytes to a final erroneous byte also separated by at least m+l (3 in a usual case) continuous correct bytes.  FIG. 1  is a diagram schematically illustrating an example of an error burst of an optical disc. In this example, the length of the error burst is 10 bytes. In addition, the number of the erroneous bytes in this error burst is 7.  
         [0006]     An error burst of a length longer than or equal to n (n=40 in a usual case) bytes can be referred to a burst error. On the other hand, an error burst of a length less than 40 bytes is referred to a random error. There is a need for a method to obtain information of the different types of errors during data reproduction. The error profile such as the numbers and distribution of different types of errors including burst errors and random errors can be used to estimate the recording or writing quality or other applications.  
       SUMMARY OF THE INVENTION  
       [0007]     An objective of the present invention is to provide a method for error analysis, which is particularly adoptable for a recording medium such as an optical disc. The method in accordance with the present invention is to execute an encoding-like operation to error flags during decoding data of the optical disc, so as to obtain number and distribution of the errors.  
         [0008]     Another objective of the present invention is to provide a device for error analysis, which is particularly adoptable for a recording medium such as an optical disc. The apparatus in accordance with the present invention has a unit for executing an encoding-like operation to error flags during decoding data of the optical disc, so as to obtain number and distribution of the errors.  
         [0009]     In accordance with an aspect of the present invention, the method for error analysis of an optical disc includes obtaining error information such as error flags of data recorded on the optical disc; writing the error information to a buffer and reading the error information from the buffer, so that the read error information is of a format as the data recorded on the disc; and analyzing the read error information. Specifically, the data recorded on the disc is de-interleaved during reproduction. In the method of the present invention, the error flags are interleaved, and the interleaved error flags are calculated, so that the number and distribution of the errors can be obtained and used in statistics and/or analysis for the errors of the optical disc.  
         [0010]     In accordance with another aspect of the present invention, the device for error analysis of an optical disc includes an interleave unit and an error rate controller. In reproducing data recorded on the optical disc, which is processed by a de-interleaving operation, the error rate controller receives error information of the data and requests the interleave unit to conduct an interleaving operation to the error information such as error flags. The interleaved error information can be used in statistics and/or analysis for the errors of the disc. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]     The present invention will be further described in detail in conjunction with the accompanying drawings, wherein:  
         [0012]      FIG. 1  is a diagram schematically illustrating an example of an error burst of an optical disc;  
         [0013]      FIG. 2  is an illustration showing data reproduction for a blu-ray disc;  
         [0014]      FIG. 3  is a block diagram generally showing a recording and reproduction apparatus with an error analyzer in accordance with the present invention;  
         [0015]      FIG. 4A  is a block diagram generally showing a structure of the error analyzer in accordance with an embodiment of the present invention;  
         [0016]      FIG. 4B  is a block diagram generally showing a structure of the error analyzer in accordance with another embodiment of the present invention;  
         [0017]      FIG. 5  shows a configuration of an LDC block of a Blu-ray disc;  
         [0018]      FIG. 6  shows a configuration of an LDC cluster error flag map;  
         [0019]      FIG. 7  shows the LDC cluster error flag map of  FIG. 6  processed by a two-step interleaving operation in accordance with the present invention;  
         [0020]      FIG. 8  shows a configuration of a LDC no-solution bit map;  
         [0021]      FIG. 9  shows a configuration of a BIS block of a Blu-ray disc;  
         [0022]      FIG. 10  shows a configuration of BIS cluster error flag map;  
         [0023]      FIG. 11  shows a configuration of a BIS no-solution bit map;  
         [0024]      FIG. 12  illustrates a fetch sequence of the LDC error flags and BIS error flags;  
         [0025]      FIG. 13  shows a configuration of a HD-DVD ECC block;  
         [0026]      FIG. 14  shows a configuration of a HD-DVD ECC block error flag map;  
         [0027]      FIG. 15A  shows a configuration of a PO no-solution bit map; and  
         [0028]      FIG. 15B  shows a configuration of a PI no-solution bit map.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0029]     The present invention will be described in details in conjunction with the drawings.  
         [0030]     A symbol error rate (SER), which is used in error analysis, is defined as the total number of all erroneous bytes in respective data units (e.g. ECC clusters) divided by the total number of bytes in those data units as represented by the following equation:  
             SER   =         ∑     i   =   1     N     ⁢     number   ⁢           ⁢   of   ⁢           ⁢   all   ⁢           ⁢   erroneous   ⁢           ⁢   bytes   ⁢           ⁢   in   ⁢           ⁢   ECC   ⁢           ⁢   Cluster   ⁢           ⁢   i         N   ×   M               (   1   )             
 
 Here, M is the total number of data bytes in one ECC cluster. For example, under the Blu-Ray standard, the total number of data bytes in one ECC cluster is 76880, and hence M is 76880. 
 
 Further, a random symbol error rate (RSER), which is also useful in error analysis, is calculated by excluding the error bursts with lengths thereof longer than or equal to n bytes (i.e. the burst errors, where n=40 in a usual case)) as represented by the following equation:  
             RSER   =               ∑     i   =   1     N     ⁢     (       number   ⁢           ⁢   of   ⁢           ⁢   all   ⁢           ⁢   erroneous   ⁢           ⁢   bytes     -                       number   ⁢           ⁢   of   ⁢           ⁢   all   ⁢           ⁢   erroneous   ⁢           ⁢   bytes   ⁢           ⁢   in   ⁢           ⁢   bursts     ≥     n   ⁢           ⁢   bytes       )               in   ⁢           ⁢   ECC   ⁢           ⁢   Cluster   ⁢           ⁢   i                       N   ×   M     -       ∑     i   =   1     N     ⁢     number   ⁢           ⁢   of   ⁢           ⁢   all   ⁢           ⁢   erroneous   ⁢           ⁢   bytes   ⁢           ⁢   in   ⁢           ⁢   bursts         ≥               n   ⁢           ⁢   bytes   ⁢           ⁢   in   ⁢           ⁢   ECC   ⁢           ⁢   Cluster   ⁢           ⁢   i                     (   2   )             
 
         [0031]      FIG. 2  shows data formats of a blu-ray disc in respective stages during data reproduction. As shown, in reproducing data from the disc, data bit stream read from the disc is demodulated into ECC cluster format. An ECC cluster contains 155 columns×496 rows of data, and is divided into four LDC (long distance code) groups and three BIS (burst indicator subcode) groups disposed alternately. Each LDC group has 38 columns, and each BIS group has 1 column. Then, the four LDC groups are extracted from the ECC cluster to form LDC cluster and the three BIS groups are also derived from the ECC cluster to form BIS cluster. After de-interleaving, the LDC cluster is mapped to LDC block, and the BIS cluster is mapped to BIS block. The LDC block has 304 codewords and each LDC codeword is of a length of 248 bytes including 216 bytes of data and 32 bytes of parity. The LDC block has 24 codewords and each BIS codeword is of a length of 62 bytes including 30 bytes of information and 32 bytes of parity. The LDC and BIS blocks are used for ECC decoding.  
         [0032]      FIG. 3  shows a recording and reproduction apparatus with an error analyzer in accordance with the present invention. As shown, an optical disc  1  is rotated by a spindle motor  2 , which is driven by a motor driver  3  The motor driver  3  is controlled by a servo circuit  4  A pick-up head  5  used to read/write the optical disc  1  is also controlled by the servo circuit  4  via the motor driver  3 . In reading, data read from the optical disc  1  by the pick-up head  5  are amplified by an amplifier  6  and are fed into a data decoder  7  and an address decoder  12  In the data decoder  7 , demodulation, de-interleaving operation as shown in  FIG. 2  and error correction are carried out. The address decoder  12  derives address information recorded on the optical disc  1  The decoded data and address information are fed back to the servo circuit  4 . A buffer manager  9  stores the decoded data into a data buffer  10 , and transfers the decoded data to a host computer via a host interface  11 . To record data to the optical disc  1 , data are sent to a data encoder  13 . The data encoder  13  affixes ECC codes to the data to be recorded and performs interleaving operation and modulation to the data. The encoded data are then written to the optical disc  1  by the pick-up head  5 . The power of the pick-up head  5  is controlled by a laser control circuit  14 . In accordance with the present invention, the apparatus includes an error analyzer  8 . The details of the error analyzer  8  will be further described later.  
         [0033]      FIG. 4A  is a block diagram generally showing a structure of the error analyzer  8  in accordance with an embodiment of the present invention. The error analyzer  8  includes an error rate controller  80 , an interleave unit  81 , an error buffer  82  and an error counter  84 .  
         [0034]     During data reproduction, the decoding results including error flags (bits) and no-solution flags (bits) generated by the data decoder  7  are stored into the error buffer  82 . The error flag indicates if a codeword has an error. The no-solution flag indicates if the error cannot be solved.  
         [0035]     An error rate controller  80  of the error analyzer  8  accesses the error flags and the no-solution flags from the error buffer  82  for calculation of random error rate and burst error rate of each ECC cluster. An interleave unit  81  has a write address generator  811  and a read address generator  813 . The writing address generator  811  generates write addresses for the error flags and no-solution flags to be stored in an error buffer  82  in a sequence order according to the codeword numbers and/or error location numbers from the data decoder  7 . The reading address generator  813  generates access addresses to fetch the error flags and no-solution flags stored in the error buffer  82  according to a sequence order corresponding to the sequence order of the data recorded on the disc. After the error flags and no-solution flags are stored in and read from the error buffer  82  according to the write addresses generated by the write address generator  811  and the access addresses generated by the read address generator  813 , those flags are disposed as the format of the ECC data before de-interleaving. The error counter  84  calculates the total error numbers, the total random error number or total burst error number under the control of the error rate controller  80 . In a normal situation, the total error number equals to the sum of the total random error number and the total burst error number. The symbol error rate (SER) and the random symbol error rate (RSER) can be obtained based on the total error number, the total random error number and the total burst error number.  
         [0036]     The error rate controller  80  receives the error flags and no-solution flags from the data decoder  7  and stores the flags to the error buffer  82  according to the write addresses generated by the write address generator  811 . When the data decoder  7  completely decodes an ECC cluster, the error rate controller  80  triggers the read address generator  813  to generate access addresses, so as to fetch the flags stored in the error buffer  82  according to a sequence order corresponding to the sequence order of the data recorded on the disc  1 . An error counter  84  counts the flags. After the error rate controller  80  fetches the error flags and no-solution flags of the complete ECC cluster for calculating the SER and/or RSER, the location of the error buffer  82  occupied by the flags of the ECC cluster is released, so that the error flags and no-solution flags of the next ECC cluster from the data decoder  7  can be stored therein. When the error buffer  82  has sufficient space to store error flags and no-solution flags of the next ECC cluster, for example, the error rate controller  80  informs the data decoder  7  to continue decoding the data reproduced from the optical disc  1 . Otherwise, the error rate controller  80  requests the data decoder  7  to suspend decoding. Further, when the error buffer  82  receives error flags and no-solution flags of a complete ECC cluster, for example, the error rate controller  80  notifies the error counter  84  to calculate the total error number, and the total random error number or total burst error number. Otherwise, the error rate controller  80  requests the error counter  84  stops calculating. Although a complete ECC cluster is used herein as a unit to start or stop these operations, the present invention is not limited to this. Other units can be also used as desired. The boundary of an ECC cluster should be obtained in order to analyze the error configuration.  
         [0037]      FIG. 4B  is a block diagram generally showing a structure of the error analyzer in accordance with another embodiment of the present invention. The essential difference between this embodiment and the embodiment shown in  FIG. 4A  is that the error buffer  82 ′ is combined with the data buffer  10 . That is, the data buffer  10  is divided out a portion to be used as the error buffer  82 ′. In the present embodiment, accessing to the error buffer  82 ′ is performed via the buffer manager  9 .  
         [0038]     As described above, the interleave unit  80  executes a re-interleaving operation to the error flags and the no-solution flags of an ECC cluster, so that the error flags and the no-solution flags are disposed in a format as the data recorded on the optical disc  1 . Accordingly, not only the number of the errors can be counted, but also the distribution of the errors can be observed. The SER and RSER can be calculated accordingly.  
         [0039]     The address generation will be further described in detail. For a blu-ray disc example, the buffer  82  should be divided into four parts: an LDC error buffer for storing error flags of the LDC cluster, an LDC no-solution flag buffer for storing no-solution flags of the LDC cluster, a BIS error buffer for storing error flags of the BIS cluster, and a BIS no-solution flag buffer for storing no-solution flags of the BIS cluster.  
         [0040]      FIG. 5  shows a configuration of an LDC block of a Blu-ray disc, the LDC block is to be decoded by the data decoder  7 . As shown, the 216 data bytes in a column L of the LDC block are numbered from the top as codeword numbers: C 0,L , C 1,L , C 2,L , . . . , C 215, L , where L is the column number between  0  to  313 . Each column of the LDC block further has 32 parity bytes, which are numbered as P 216,L , P 217,L , P 218,L , . . . , P 247,L .  
         [0041]      FIG. 6  shows a configuration of a LDC error flag (bit) map. In the present embodiment, error flags are written to the buffer  82  in the format of the error flag map as a first interleaving stage. The first interleaving stage can be mathematically represented by the following formulas. The error flag (bit) E R,L  of the byte C R,L  or P R,L  of the LDC Block shown in  FIG. 5  is written to the LDC error buffer as:  
                                               For row:   Q = 2 × R + mod(L, 2)   0 ≦ Q ≦ 495   (3)       For column   P = div(L, 2)   0 ≦ P ≦ 151   (4)                    
 where R is the row number of the LDC block, Q and P are respectively the row and column numbers of the LDC Cluster at the first interleaving stage. 
 
         [0042]     The error flags (bits) stored in the LDC error buffer are then read out in a second interleaving stage.  FIG. 7  shows the LDC cluster error flag map of  FIG. 6  processed by the second interleaving stage. In the second interleaving stage, each of the error flags is shifted over mod(3×div(Q,2), 152) units to the left, and the error flags shifted out of the left side are re-filled in the array from the right side. The read address generator  813  generates addresses so that the error rate controller reads out the error flags according to the sequence achieved by the second interleaving stage. The LDC error flags are stored in the LDC error buffer and are fetched by calculating the read addresses, which will be described further, to execute the second interleaving stage.  
         [0043]     The addresses generated by the read address generator  813  start incrementally from the first row (Q=0) to the last row (Q=495). For each row, the addresses for the error flags to be read out start from mod(3×div(Q,2), 152) and are incrementally counted up to 151 with a step of 1, and then are counted from 0 to mod(3×div(Q,2), 152)−1. In this way, the error flags stored in the LDC error buffer are read out in a sequence consistent with the recording sequence for error calculation.  
         [0044]      FIG. 8  shows a configuration of a LDC no-solution flag (bit) map. In  FIG. 8 , the 304 no-solution flags (bits) in the LDC no-solution flag map are numbered starting from the left as NS 0 , NS 1 , . . . , NS L , . . . , NS 303 , which corresponds to the 304 codewords in the LDC Block. Mathematically, when the error flag E q,p  is read out from the LDC error buffer for error calculation, the corresponding no-solution flag NS w  from the LDC no-solution bit buffer is also read out. The relationship between the LDC error flag E q,p  and the LDC no-solution flag NS w  could be represented by the following formulas: 
   w= 2 ×p +mod( q, 2)  (5)  
 where w is the corresponding LDC codeword number ranging from 0 to 303 
 
         [0045]     The algorithms above are described for exemplification. Other algorithms can also be used. For example, if the final format of the LDC error flag map is achieved in the first interleaving stage, that is, the LDC error flags are written to the LDC error buffer in the format shown as the lower format in  FIG. 7 , then in the second interleaving stage, the LDC error flags only need to be sequentially read out.  
         [0046]      FIG. 9  shows a configuration of a BIS Block to be decoded by the data decoder  7 . As shown, the 30 information bytes in each column of the BIS Block are numbered in a sequence starting from the top of each column as B 0,H , B 1,H , B 2,H , . . . , B 29,H , where H is the BIS codeword number, that is the column number (0 to 23). Each column of the BIS Block is provided with 32 parity bytes according to a long distance RS code. The parity bytes are numbered as: Pb 30,H , Pb 31,H , Pb 32,H , . . . , to Pb 6l,H .  
         [0047]      FIG. 10  is a view showing a configuration of a BIS error flag map. As shown, the error flag map corresponds to a BIS Cluster map. Mathematically, the interleaving of the BIS error flags in a format of a BIS block into a format of a BIS cluster can be represented by the following formulas. The error flag D V,H  of the byte B V,H  or Pb v,H  of the BIS Block (see  FIG. 9 ) is stored in BIS error buffer as:  
                                                           For unit   u = mod({div(V, 2) + 8 − div(H, 3)}, 8) +   (6)               8 × mod(V, 2)           For row   r = div(V, 2)   (7)           For column   e = mod({H + div(V, 2)}, 3)   (8)                        
 where V is the corresponding row number (0 to 61) of the BIS Block. 
 
         [0048]     The error flag number s, giving the sequence number of the error flag D S , of the BIS block to be interleaved in the sequence of the corresponding BIS Cluster written to the disc, is: 
 
 s =( u× 31 +r )×3 +e   (9) 
 
 The error flag number is the sequential reading address to fetch the BIS error flag stored in the buffer for error calculation. The value of the error flag number s starts from 0 and ends at 1487, which is the sequence order for the data to be recorded to the disc. 
 
         [0049]      FIG. 11  shows a configuration of a BIS no-solution flag map. As shown, the 24 no-solution flags in the BIS no-solution flag map are numbered starting from the left as NSb 0 , NSb 1 , . . . , NSb H , . . . , NSb 23 , which corresponds to the 24 codewords in the BIS Block. When the error flag D s  is read out from the BIS error buffer for error calculation, the corresponding no-solution flag NSb t  is also read out from the BIS no-solution flag buffer. The relationship between the BIS error flag number s and the BIS no-solution flag number t could be drawn by the following deductive equations: 
   u =div( s, 93)  (10)    r =div(mod( s, 93),3)  (11)    e =mod(mod( m, 93),3)  (12)  t=mod(24−3×mod( u, 8)+3×( r +div(((2 ×e ) +mod( r, 3)),3))+ e -mod( r, 3),24)  (13)  
 where t is the corresponding BIS codeword number ranging from 0 to 23. 
 
         [0050]     Returning to  FIG. 2 , the ECC cluster is constructed by multiplexing the LDC cluster and BIS cluster. Similarly, the LDC error flags read from the LDC error buffer are split into 4 groups, and each group has 38 columns. Then,3 columns of the BIS error flags from the BIS error buffer are respectively inserted between the LDC error flag groups, so that the LDC error flag groups and the BIS error flags are alternately disposed, as shown in  FIG. 12 .  
         [0051]     To simplify the complexity of the error analyzer  8 , the errors of the BIS cluster may be neglected because there are only 3 bytes of BIS data in a recording frame of 155 bytes, as shown in  FIG. 2 . In this situation, only the error flags of the LDC cluster are considered in error calculation. Hence, the SER represented by the formula (1) is reduced as  
             SER   =         ∑     i   =   1     N     ⁢     number   ⁢           ⁢   of   ⁢           ⁢   erroneous   ⁢           ⁢   bytes   ⁢           ⁢   in   ⁢           ⁢   LDC   ⁢           ⁢   Cluster   ⁢           ⁢   i         N   ×     M   LDC                 (   14   )             
 
 Here, M LDC  is the total number of data bytes in one LDC cluster. For example, under the Blu-Ray standard, the total number of data bytes in one LDC cluster is 75392, and hence MLDC is 75392. 
 
 In addition, the RSER represented by the formula (2) is reduced as:  
             RSER   =               ∑     i   =   1     N     ⁢     (       number   ⁢           ⁢   of   ⁢           ⁢   all   ⁢           ⁢   erroneous   ⁢           ⁢   bytes     -                       number   ⁢           ⁢   of   ⁢           ⁢   all   ⁢           ⁢   erroneous   ⁢           ⁢   bytes   ⁢           ⁢   in   ⁢           ⁢   bursts     ≥     n   ⁢           ⁢   bytes       )               in   ⁢           ⁢   LDC   ⁢           ⁢   Cluster   ⁢           ⁢   i                       N   ×     M   LDC       -       ∑     i   =   1     N     ⁢     number   ⁢           ⁢   of   ⁢           ⁢   all   ⁢           ⁢   erroneous   ⁢           ⁢   bytes   ⁢           ⁢   in   ⁢           ⁢   bursts         ≥               n   ⁢           ⁢   bytes   ⁢           ⁢   in   ⁢           ⁢   LDC   ⁢           ⁢   Cluster   ⁢           ⁢   i                     (   15   )             
 
         [0052]     In addition to a blu-ray disc, the present invention is also suitable for other recording mediums, a HD-DVD disc, for example.  FIG. 13  shows a configuration of an HD-DVD ECC block to be decoded by the data decoder  7  For each ECC block, the  208  information bytes in each column are numbered starting from the top of each column as B 0,L , B 1,L , B 2,L , . . . , B 207,L , where L represents the column number (0 to 207) of the ECC Block. The  364  information bytes in each row are numbered starting from the left of each row as B R,0 , B R,1 , B R,2 , . . . , B R,363 , where R represents the column number (0 to 363) of the ECC Block. The ECC Block comprises 172×2×192 bytes information fields, 172×2×16 PO parities of the outer code of RS, and 208×2×10 PI parities of the inner code of RS.  
         [0053]     Also, to describe the address generation for the HD-DVD error flag interleaving, the error buffer  82  is divided into three parts: an ECC error buffer for storing the error flags of the ECC block, a PO no-solution flag buffer for storing the PO no-solution flags of the ECC block, and a PI no-solution flag buffer for storing the PI no-solution flags of the ECC block.  
         [0054]      FIG. 14  shows a configuration of an ECC error flag map. As shown, the error flag map corresponds to an ECC Block map after interleaving process. The error flag G R,L  corresponding to the byte B R,L  of the ECC Block (see  FIG. 13 ) is placed in ECC error buffer according to rules mathematically represented as:  
                                           for row   R′ = 2 × R + div(L, 182) + div(R, 6) for R &lt;= 191,   (16)           and R′ = (2 × (R − 192) + div(L, 182)) × 13 +           12 for R &gt; 191       for column   L′ = mod(L, 182)   (17)                    
 where R′ and L′ are row number and column number of the ECC error buffer, respectively. Then, the error flags G R′,L′ are fetched one by one for error calculation. The fetch sequence of the ECC error buffer is from the top row (R′=0) to the bottom row (R′=415) and is from the left bit (L′=0) to the right bit (L′=181) within each row. When all the 182 bits of a row are fetched completely, the next row is fetched sequentially until all the 416 rows of the ECC block are fetched completely. Hence, the fetch sequence number s is deduced as 182×R′+L′. 
 
         [0055]      FIG. 15  shows a configuration of a PO no-solution flag map and a PI no-solution flag map of the ECC block of the HD-DVD disc. The 364 PO no-solution flags in the PO no-solution flag map are numbered starting from the left as NSpo 0 , NSpo 1 , . . . , NSpo 363 , which corresponds to the 364 columns in the ECC Block as shown in  FIG. 13 . The 2×208 PI no-solution flags in the PI no-solution flag map are numbered starting from the left as NSpi 0,0 , NSpi 0,1 , . . . , NSpi 0,207 , and Nspi 1,0 , Nspi 1,1 , . . . , Nspi, 1,207 . The first row of the PI no-solution flag map corresponds to the left half row in the ECC block, and the second row of the PI no-solution flag map corresponds to the right half row in the ECC block as shown in  FIG. 13 . When the error flag G R′,L′ is read out from the ECC error buffer for error calculation, the corresponding PO no-solution flag NSpo 1  and PI no-solution bit NSPi h,r  are also respectively read out from the PO no-solution flag buffer and PI no-solution flag buffer. The relationship between the error flag G R′,L′ and the PO no-solution flag NSpo 1 , as well as the PI no-solution flag NSPi h,r  can be derived as follows: 
 if mod(div( R′,  13), 12)═0    l=L′+ 182×mod(div( R′,  13), 2)    h =mod(div( R′,  13), 2)    r= 192+div( R′,  13×2)  else if mod(div(R′, 13), 12)≠0    l=L′+ 182×mod( R ′+div( R′,  13), 2)    h =mod(( R ′−div( R′,  13)), 2)    r =div(( R ′−div( R′,  13)), 2).  (18)  
         [0056]     As described above, during reproducing the data from the optical disc, the decoded error information such as error flags and no-solution flags are processed with an interleave operation. Accordingly, the number and distribution of the errors on the disc can be obtained for analysis of the disc quality and/or the recording quality.  
         [0057]     While the preferred embodiments of the present invention have been illustrated and described in detail, various modifications and alterations can be made by persons who are skilled in this art. The embodiment of the present invention is therefore described in an illustrative but not restrictive sense. It is intended that the present invention should not be limited to the particular forms as illustrated, and that all modifications and alterations that maintain the spirit and realm of the present invention are within the scope as defined in the appended claims.