Abstract:
Multiword information is based on multibit symbols disposed in relative contiguity with respect to a medium, and is encoded with a wordwise interleaving and wordwise error protection code for providing error locative clues across multiword groups. In particular, the clues originate in high protectivity clue words (BIS) that are interleaved among clue columns, and also in synchronizing columns constituted from synchronizing bit groups. The synchronizing columns are located where the clue columns are relatively scarcer disposed. The clues are directed to low protectivity target words (LDS) that are interleaved in a substantially uniform manner among target columns which form uniform-sized column groups between periodic arrangements of clue columns and synchronizing columns.

Description:
BACKGROUND OF THE INVENTION 
     The invention relates to a method according to the preamble of claim  1 . U.S. Pat. No. 4,559,625 to Berlekamp et al, and U.S. Pat. No. 5,299,208 to Blaum et al disclose decoding of interleaved and error protected information words, wherein an error pattern found in a first word may give a clue to locate errors in another word of the same group of words. The references use a fault model with multisymbol error bursts across plural words. An error in a particular word yields a high probability for an error to occur at a corresponding symbol position pointed at in a next word or words. The procedure may raise the number of corrected errors. A clue will however only materialize when the clue word has been fully corrected. Furthermore, the medium stores information as well as synchronization bit groups which represent an appreciable amount of redundancy that may also be used to signal errors in the target words, so that to some extent clue words may be exchanged for synchronization bit groups. Part of the errors is due to so-called bit slips that are more frequent further away from the sync bit groups. Therefore, interleaving the clue words amongst clue columns and also interleaving the target words amongst target columns may further improve the error protection. 
     SUMMARY TO THE INVENTION 
     In consequence, amongst other things, it is an object of the present invention to provide a coding format allowing clue words to cooperate with synchronizing bit groups in a systematic format, while also smoothing out possibly negative effects of bit slips more evenly among the various words. Now therefore, according to one of its aspects the invention is characterized as recited in the characterizing part of claim  1 . A clue can point to an erasure symbol. Pointing can make error correction more powerful. In fact, many codes will correct at most t errors when no error locative indication is known. Given the erasure locations, generally a larger number e&gt;t of erasures may be corrected. Also protection against a combination of bursts and random errors may improve. The invention may be used both for storage and for transmission. 
     Advantageously, the method has the features of claim  2 . This is a relatively simple arrangement. Alternatively, the number of synchronizing columns may be larger than one, and the number of clue columns may be even if preferred. 
     Advantageously, the method has the features of claim  3 . In video recording, user data will relate to the image and accompanying sound to be presented to a user, whereas system data may indicate the program name, time, addresses, and various other parameters that may be useful without reference to the video or audio proper. This feature allows fast access to the system data without necessity for decoding the target words. 
     Advantageously, the method has the features of claim  4 . If error-free, this feature will immediately indicate to a user device whether the processed frame of information is correct. 
     Advantageously, the method has the features of claim  5 . This is a straightforward organization. Advantageously, the method has the features of claim  6 . This has proven to raise the worst case to the average level attainable for this code format. Advantageously, the method has the features of claim  7 . Optical storage has been proven a fortuitous medium. 
     The invention also relates to a method for decoding information so encoded, to an encoding and/or decoding device for use with the method, and to a carrier containing information so encoded. Further advantageous aspects of the invention are recited in dependent claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     These and further aspects and advantages of the invention will be discussed more in detail hereinafter with reference to the disclosure of preferred embodiments, and in particular with reference to the appended FIGURES that show: 
     FIGS. 1 a,    1   b,  a record carrier; 
     FIG. 2, a playback device; 
     FIG. 3, a recording device; 
     FIG. 4, a system with encoder, carrier, and decoder; 
     FIG. 5, a code format principle; 
     FIG. 6, a schematic representation of a physical cluster on the carrier; 
     FIG. 7, a data frame; 
     FIG. 8, a composition of a data sector from two data frames; 
     FIG. 9, renumbering data bytes and forming an ECC sector by adding parities; 
     FIG. 10, a composition of an ECC cluster by multiplexing 16 ECC sectors; 
     FIG. 11, a renumbered ECC cluster before interleaving; 
     FIG. 12, an interleaved ECC cluster; 
     FIG. 13, multiplexing of the BIS cluster with the interleaved ECC cluster; 
     FIG. 14, a BIS block containing 24 BIS code words; 
     FIG. 14A, the mapping of the BIS block into the BIS cluster; 
     FIG. 15, the frame structure for explaining main data interleaving; 
     FIG. 16, the interleaving proper; 
     FIG. 17, an example of the partial mapping of BIS bytes on the first eight sectors; 
     FIG. 18, an example of the partial mapping of BIS bytes on the last eight sectors; 
     FIG. 19, a schematic representation of the overall encoding process. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 1 a  shows a disc-shaped record carrier  11  with track  19  and central hole  10 . Track  19  is arranged in a spiral pattern of turns forming substantially parallel tracks on an information layer. The carrier may be an optical disc with a recordable or prerecorded information layer. CD-R, CD-RW, and DVD-RAM are recordable, whereas audio-CD is an example of a prerecorded disc. The prerecorded type can be manufactured in a known way by first recording a master disc and then pressing consumer discs. On a recordable carrier the track is indicated by a pre-embossed track structure provided during manufacture of the blank carrier. The track may be structured as a pregroove  14  to enable a read/write head to follow the track  19  during scanning. Information is represented on the information layer by optically detectable marks, e.g. pits and lands. 
     FIG. 1 b  is a cross-section along line b—b of the record carrier  11  of the recordable type, transparent substrate  15  being provided with recording layer  16  and protective layer  17 . Pregroove  14  may be implemented as an indentation or an elevation, or as a material property deviating from its surroundings. 
     The record carrier may carry user information, that for user convenience has been sub-divided into smaller items, that each may have a duration of a few minutes e.g. songs of an album or movements of a symphony. Access information for identifying the items can also be provided on the carrier, e.g. a so-called Table Of Contents (TOC) or a file system like ISO 9660 for CD-ROM. The access information may include playing time and start address for each item, and further information like a song title. Such information may represent system information. The information is recorded in a digital manner after analog to digital (A/D) conversion. 
     FIG. 2 shows a playback apparatus according to the invention for reading a record carrier  11  such as shown in FIG.  1 . The device has a drive  21  for rotating the record carrier  1 , and read head  22  for scanning the track on the record carrier. The apparatus has positioning means  25  for coarse radial positioning of the read head  22 . The read head comprises an optical system of a known type for generating a radiation beam  24  guided through optical elements focussed to a radiation spot  23  on a track of the information layer. The radiation beam  24  is generated by a known radiation source. The read head further has a focusing actuator for moving the focus of the radiation beam  24  along the optical axis of the beam and a tracking actuator for fine positioning of the spot  23  in a radial direction on the track centre. The tracking actuator may comprise coils for radially moving an optical element or may be arranged for changing the angle of a reflecting element. The radiation reflected by the information layer is detected by a detector of a usual type, e.g. a four-quadrant diode, in the read head  22  for generating a read signal and further detector signals including a tracking error and a focusing error signal coupled to said tracking and focusing actuators. The read signal is processed by reading means  27  to retrieve the data, which reading means are of a usual type for example comprising a channel decoder and an error corrector. The retrieved data is sent to data selection facility  28  to select certain information from the data read and sends it to buffer  29 . The selection is based on data type indicators recorded on the record carrier, e.g. headers in a framed format. The compressed information is sent from buffer  29  to de-compressor  31  via signal  30 . This signal may also be externally available. The de-compressor  31  decodes the data to reproduce the original information on output  32 . The de-compressor may be fitted separately, as indicated by the rectangle  33  in FIG.  2 . Alternatively, the buffer may be positioned before the data selection. Control unit  20  furthermore receives control commands from a user or from a host computer via control lines  26  such as a system bus, connecting drive  21 , positioning means  25 , reading means  27  and data selection means  28 , and possibly also buffer  29  for buffer filling level control. Thereto, control unit  20  comprises control circuitry, such as a microprocessor, a program memory and control gates, or a state machine. 
     Compression and de-compression are well-known. During de-compression an inverse process is applied to reconstruct the original signal. If the original digitized signal is reconstructed exactly, the (de-)compression is lossless, but in lossy (de)-compression some details of the original signal will not be reproduced. Such omitted details are substantially undetectable by the human ear or eye. Most known systems, such as MPEG, use lossy compression for audio and video; lossless compression is used from storing computer data. 
     The data selection  28  is arranged for retrieving control information from the data read, and for discarding any stuffing data that had been added during recording. The rotation rate may be adjusted using the average filling level of the buffer  29 , e.g. decreasing the rotation rate when the buffer is more then 50% full on average. 
     FIG. 3 shows a recording device for writing information on a (re)writable record carrier  11 . During a writing operation, marks representing the information are formed on the record carrier. The marks may be in any optically readable form, e.g. in the form of areas whose reflection coefficient differs from their surroundings, through recording in materials such as dye, alloy or phase change, or in the form of areas with a direction of magnetization different from their surroundings, when recording in magneto-optical material. Writing and reading of information for recording on optical disks and usable formatting, error correcting and channel coding rules are well-known in the art, e.g. from the CD system. The marks can be formed through a spot  23  generated on the recording layer via a electromagnetic radiation beam  24  from a laser diode. The recording device comprises similar basic elements as the apparatus for reading described above in FIG. 2, i.e. control unit  20 , drive means  21  and positioning means  25 , but it has a write head  39 . The information is presented on the input of compression means  35 , that may be placed in a separate housing. The variable bitrate compressed information on the output of the compression means  35  is passed to buffer  36 . From the buffer  36  the data is passed to data combination means  37  for adding stuffing data and further control data. The total data stream to be recorded is passed to writing means  38 . The write head  39  is coupled to the writing means  38 , which comprise a formatter, an error encoder and a channel modulator. The data presented to the input of the writing means  38  is distributed over logical and physical sectors according to formatting and encoding rules discussed infra, and converted into a write signal for write head  39 . Unit  20  is arranged to control the buffer  36 , the data combination means  37  and the writing means  38  via control lines  26  and for performing the positioning procedure as described above for the reading apparatus. The recording apparatus may be arranged for reading through the features of a playback apparatus and a combined write/read head. 
     FIG. 4 shows a comprehensive system according to the invention, provided with an encoder, a carrier, and a decoder. The embodiment is used for encoding, storing, and finally decoding a sequence of samples or multibit symbols derived from an audio or video signal, or from data. Terminal  120  receives a stream that may have eight bit symbols. Splitter  122  recurrently and cyclically transfers first symbols intended for the clue words to encoder  124 , and all other symbols to encoder  126 . In encoder  124  the clue words are formed by encoding the data into code words of a first multi-symbol error correcting code. This code may be a Reed-Solomon code, a product code, an interleaved code, or a combination. In encoder  126  the target words are formed by encoding into code words of a second multi-symbol error correcting code. In FIG. 5, all code words have a uniform length, but this is not a restriction. The clue words may have a much higher degree of error protection. This may be effected by a larger number of check symbols, by a smaller number of data symbols, or by a combination thereof. 
     In block  128 , the code words are transferred to one or more outputs of which an arbitrary number has been indicated, so that the distribution on a medium to be discussed later will become uniform. Block  130  symbolizes the unitary medium such as tape or disc that receives the encoded data. This may relate to direct writing in a write-mechanism-plus-medium combination. Alternatively, the medium may be a copy from a master encoded medium such as a stamp. Storage may be optical and fully serial, but other configurations may be used. In block  132 , the various words are read again from the medium. Then the clue words of the first code will be sent to decoder  134 , and decoded as based on their inherent redundancies. Furthermore, as will become apparent in the discussion of FIG. 5 hereinafter, such decoding may present clues on the locations of errors in other than these clue words. Moreover, the information from synchronizing bit columns may be analyzed as to interferences therein, to immediately produce additional clues for the target words. Box  135  receives all clues and contains a program for using one or more different strategies to translate such clues to erasure locations. The target words are decoded in decoder  136 . With help from the erasure locations, the error protection of the target words is raised to a higher level. Finally, all decoded words are demultiplexed by means of element  138  to output  140  conforming to the original format. For brevity, electromechanical interfaces between the various subsystems were ignored. 
     FIG. 5 illustrates a simple code format. The coded information has been shown arranged in a 480 symbol block with 15 horizontal rows and 32 vertical rows. Storage on a medium starts at the top left and proceeds along vertical rows. The hatched region contains check symbols: horizontal rows  4 ,  8 , and  12  have 8 check symbols each and constitute clue words. The other rows contain 4 check symbols each and constitute target words. The whole block has 408 information symbols and 72 check symbols. The latter may be localized in a more distributed manner over respective words. Further to the above, the top horizontal row contains a representation of synchronizing bit groups. These are present on the medium to synchronize a reader device to the format, but generally contain neither system data nor user data and have a prescribed format with much redundancy. Therefore, it is often easy to detect an interference, and the occurrence of a single one or a plurality of disturbed synchronizing bit groups that are physically close to each other or to distributed clue symbols can be used to signal occurrence of a burst error. This will produce clues in similar manner as the clue words. 
     The Reed-Solomon code allows to correct in each clue word up to four symbol errors. Actual symbol errors have been indicated by a crosses. In consequence, all clue words may be decoded correctly, inasmuch as they do not have more than four errors. Notably words  2  and  3  may however not be decoded on the basis of their own redundancy alone. In the Figure, all errors, except  62 ,  66 ,  68  represent error strings. Only strings  52  and  58  cross at least three consecutive clue words and are considered as error bursts, causing at least all intermediate symbol locations to get an erasure flag. Also, target words just before the first clue word error of the burst and target words just after the last clue word error of the burst may get an erasure flag at that location, depending on the strategy followed. String  54  is not considered a burst, because it is too short. 
     As a consequence, two of the errors in word  4  produce an erasure flag in the associated vertical rows. This renders words  2  and  3  correctable, each with one error symbol and two erasure symbols. However, random errors  62 ,  68 , nor string  54  constitute clues for words  5 ,  6 ,  7 , because each of them contains only one clue word. Sometimes, an erasure cause a zero error pattern, because an arbitrary error in an 8-bit symbol has a {fraction (1/256)} probability to cause again a correct symbol. Likewise, a long burst crossing a particular clue word may produce a correct symbol therein. By a bridging strategy between preceding and succeeding clue symbols of the same burst, this correct symbol is then incorporated into the burst, and in the same manner as erroneous clue symbols translated into erasure values for appropriate target symbols. The above decisions may vary according to decoding policy. The clues by the sync bit groups may be used in similar manner as those from the clue words. 
     The relevance of the present invention is brought about by newer methods for digital optical storage. A particular feature is that in the case of substrate incident reading the upper transmissive layer is as thin as 100 micron. The channel bits have a size of some 0.14 micron, so that a data byte at channel rate of ⅔ will have a length of only 1.7 microns. At the top surface the beam has a diameter of some 125 microns. A caddy or envelope for the disc will reduce the probability of large bursts. Non-conforming particles of less than 50 microns may cause short faults, although the invention is also useful against longer faults. A fault model has been used wherein 50 micron faults through error propagation may lead to bursts of 200 microns, corresponding to some 120 Bytes. A particular model has fixed size bursts of 120B that start randomly with a probability per byte of 2.6*10 −5 , or on the average one burst per 32 kB block. The invention has been conceived for optical disc storage, but other configurations such as multitrack tape, and other technologies such as magnetic and magneto-optical would also benefit from the improved approach. 
     Discussion of a Preferred Format of the Information 
     Before recording, User Data received from a source, that may be an application or a host, is formatted in a number of successive steps, that will be explained more in detail with reference to FIG. 19, as follows: Data Frames, Data Sectors, ECC Sectors, an ECC Cluster, a BIS Cluster, a Physical Cluster and Recording Frames. 
     The data is recorded in 64 k partitions, called Physical Clusters, that each contain 32 Data Frames with 2048 bytes of User Data. A Physical Cluster is protected by two error correction mechanisms: 
     firstly, a Long Distance (LDS) (248,216,33) Reed-Solomon (RS) error correction code; 
     secondly, the data is multiplexed with a Burst Indicator Subcode (BIS), that consists of (62,30,33) Reed-Solomon (RS) codewords. The number of parity symbols is equal for the two code categories, which allows to use the same decoder hardware for both cases. The BIS code is used to indicate long burst errors, by which the LDS code can more efficiently perform erasure corrections. All data is arranged in an array as shown in FIG.  6 . Note that the horizontal and vertical directions have been interchanged with respect to FIG.  5 . The array is read along a horizontal direction, and is recorded on the disc after inserting synchronization patterns and additional d.c. control bits, and after modulation. 
     The error correction codes are applied in vertical direction, which gives a good basic break-up of burst errors on the disc. Additionally, the LDS codewords have been interleaved in a diagonal direction. For the purpose of addressing, a whole Physical Cluster is subdivided into 16 Physical Sectors, each consisting of 32 consecutive rows. 
     A Data Frame consists of 2052 bytes: 2048 User Data bytes numbered d o to d 2047  and 4 Error Detection Code (EDC) bytes numbered e 2048  to e 2051 . The bytes e 2048  to e 2051  contain an Error Detection Code computed over 2048 bytes of the Data Frame. The Data Frame is considered as a field of single bits, starting with the most significant bit of the first User Data byte d 0  and ending with the least significant bit of the last EDC byte e 2051 . The msb is b 16415  and the lsb is b 0 . Each bit b i  of the EDC is shown as follows for i=0 to 31:          EDC        (   x   )       =       ∑     i   =   31     0                       b   i          x   i          I        (   x   )          mod                   G        (   x   )                                  
     where:                  I        (   x   )       =       ∑     i   =   16415     32                       b   i          x   i           ,       G        (   x   )       =       x   32     +     x   31     +     x   4     +   1               (   1   )                                
     Next, two Data Frames (A, B) are placed in an array of 19 columns by 216 rows, called a Data Sector. The filling of the array is done column by column, starting at the top of the first one with byte do 0,A  and ending at the bottom of the last column with byte e 2051,B , cf. FIG.  8 . 
     Next in FIG. 9, the bytes in each column of the Data Sector are renumbered starting from the top of the column as follows: d L,0 , d L,1  . . . d L,i  . . . to d L,215 , L being the column number (0 . . . 18). The ECC Sector is completed by extending each column with 32 Parity bytes of a (248,216,33) long distance RS code. The Parity bytes are: P L,216 , P L,217 , . . . P L,j  . . . to P L,247 . 
     The long distance RS code is defined over the finite field GF(2 8 ). Non-zero elements of the finite field GF(2 8 ) are generated by a primitive element α that is a root of the primitive polynomial p(X)=X 8 +X 4 +X 3 +X 2 30 1. The symbols of GF(2 8 ) are represented by 8-bit bytes, using a polynomial base representation with (α 7 , α 6 , α 5 , . . . α 2 , α, 1) as a basis. The root α is represented as α=00000010. Each LDS codeword, represented by the vector lds=(d L,0  . . . d L,i  . . . d L,215  P L,216 —P L,j —P L,247 ), belongs to a Reed-Solomon code over GF(2 8 ), with 216 information bytes and 32 parity bytes. Such codeword can be represented by a polynomial lds(x) of degree 247, that may have some coefficients zero, the highest degrees corresponding to the information part of the vector (d L,0  . . . etc.) and the lowest degrees corresponding to the parity part (P L,216  . . . etc.). Now, lds(x) is a multiple of the generator polynomial g(x) of the LDS codeword. The generator polynomial is:          g        (   x   )       =       ∏     i   =   0     31                     (     x   -     α   i       )                              
     The LDS code is systematic: the 216 information bytes appear unaltered in the highest order positions of each codeword. The parity check matrix of code lds is such that: H LDS *lds T  =0 for all LDS codewords lds. 
     The second row H LDS 2  of the parity check matrix H LDS  is given by H LDS 2  =(α 247  α 246 . . .  α 2  α 1) and corresponds to the zero α of the generator polynomial g(x) which defines the codeword positions to be used for error locations. 
     After generating the LDS codewords in the ECC Sectors, 16 consecutive ECC Sectors are combined to one ECC Cluster by multiplexing the 16*19 columns of height 248, 2 by 2, including the parities. In this way 152 new columns are formed with a height of 496 bytes as shown in FIG.  10 . The numbering of the bytes is according to d L,M,N  where: 
     L=0 . . . 18 is the LDS code word number within the ECC Sector 
     M=0 . . . 247 is the byte number within the IDS code word 
     N=0 . . . 15 is the ECC Sector number. 
     For further improving the burst error correcting capabilities, extra interleaving is introduced by renumbering the bytes are in horizontal direction through all rows of the ECC Cluster, cf. FIG.  11 . Now all rows of an ECC Cluster are shifted two by two over mod(k*3,152) bytes to the left, starting from row  2  onwards, the first row being row 0; k=div(row-number, 2). The bytes that shift out at the left side re-enter the array from the right side, cf. FIG.  12 . After this process the bytes are renumbered once more in horizontal direction through all rows, resulting in the numbering D 0  to D 75391  indicated in FIG.  6 . The renumbering of the bytes causes non-uniform mapping of logical addresses on physical addresses. Consequences thereof will be discussed infra. 
     After interleaving, the interleaved ECC Cluster is split into 4 groups of 38 columns each. In between the 4 groups, 3 columns of one byte width each are inserted. These columns carry the address information relating to the data contained in the interleaved ECC Cluster. They consist of (62,30,33) RS BIS codewords with 30 bytes of information and 32 bytes of parity. Due to the high error protection capabilities and an advanced interleaving scheme, these columns may also offer a reliable indication of burst errors. 
     A 3 by 496 byte array formed by the 3 BIS columns from the Physical Cluster, is called a BIS Cluster. The content of the BIS Cluster is formed by placing all BIS codewords of a BIS Cluster in the 24 columns of a 24 by 62 byte array, cf. FIG.  14 . 
     The BIS RS code is defined over the finite field GF(2 8 ). The non-zero elements of the finite field GF(2 8 ) are generated by a primitive element α, that is a root of the primitive polynomial p(x)=X 8 +X 4 +X 3 +X 2 +1. The symbols of GF(2 8 ) are represented by 8-bit bytes, using the polynomial base representation, with (α 7 , α 6 , . . . α 2 , α, 1) as a basis. The root α is represented as α=00000010. 
     Each BIS codeword is represented by a vector bis=(b c,0  . . . , b c,i  . . . , b c,29 , Pb c,30 , . . . Pb c,j  . . . Pb c,61 ) in a Reed-Solomon code over GF(2 8 ), with 32 parity bytes and 30 information bytes. Such codeword may be represented by a polynomial bis(x) of degree 61, that may have some coefficients zero, the highest degrees representing the information part of the vector (b c,0  . . . etc.) and the lowest degrees the parity part of the vector (Pb c,30  . . . etc.). Each codeword is a multiple of the generator polynomial g(x) of the BIS codeword:          g        (   x   )       =       ∏     i   =   0     31                     (     x   -     α   i       )                              
     The BIS code is systematic: the 30 information bytes appear unaltered in the highest order positions of each codeword. The parity check matrix of code bis is such that H BIS *bis T +0 for all BIS codewords bis. The second row h BIS 2  of the parity check matrix H BIS  is given by h BIS 2 =(α 61 ,α 60  . . . α 2 , α, 1) It corresponds to the zero α of the generator polynomial g(x), and defines the codeword positions to be used for error locations. 
     FIG. 15 shows the frame structure for explaining main data interleaving. The various physical sectors and columns carry appropriate numbering. There are 304*[248,216,33] LDS code words, and 24*[62,30,33] BIS code words. 
     A 2 kB logical sector contains 9.5 LDS code words in which 2048 User Data bytes and 4 EDC bytes have been encoded, and further 22.5 BIS Bytes for storing a header, 4ID+2EDC bytes, copyright data, and 6 Copyright Management Information CPR_MAI. Furthermore, 10.5 BIS Bytes have been reserved for possible future use. A 4 kB Physical Sector consists of 31 rows, where the header bytes of two 2 kb logical sectors are stored in physically prescribed positions. FIG. 16 shows the interleaving proper. Here, the i-th LDS code word with 0≦i≦303, contains 248 bytes d_j, where j is of the form: j=[(i mod 2)+2*a]*152+{[(i div 2)−3*a ]mod 152} for certain values 0≦a≦247. Various locations are feasible for putting the parities, such as at the bottom, or permutated according to a+31*i, a≧22 . . . 
     Next, the generating of a BIS cluster will be discussed. After generating the BIS codewords, the BIS Block is mapped in an interleaved manner on an array of 496=(16×31) rows*3 columns. This new array is called a BIS Cluster shown in FIG.  14 A. The positioning of the bytes from a BIS Block (FIG. 14) in a BIS Cluster will first be given by mathematical expressions. For this purpose, the BIS Cluster is subdivided according to the Physical Sectors shown in FIG.  6 . The sectors are numbered s=1 . . . 15, the rows in such sector are numbered r=0 . . . 30, and the columns are numbered e=0 . . . 2, cf. FIG. 14 a . Now byte b N,C  gets the following position: 
     
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 sector 
                 s = 
                 mod {[div(N,2) + 8 − div(C,3)], 8 } + 8 * mod (N,2) 
               
               
                 number 
                   
                   
               
               
                 row 
                 r = 
                 div(N,2) 
               
               
                 number 
                   
                   
               
               
                 column 
                 e = 
                 mod {[C + div(N,2)] , 3} 
               
               
                 number 
               
               
                   
               
             
          
         
       
     
     The byte number m gives the sequence number B m  as the Physical cluster is written to the disc as shown in FIG. 6 according to m=(s*31+r)*3+e. The essentials of the interleaving scheme are exemplified in FIGS. 17,  18 , and pertain to: 
     each row of the BIS Block is split into 8 groups of 3 bytes each, which three-byte groups are each placed in a respective row of the BIS Cluster. 
     the even rows of the BIS Block are mapped on Sectors  0  through  7 , the odd rows of the BIS Block are mapped on Sectors  8  through  15 . 
     the eight three-byte groups from an even row of the BIS Block are each put on the same row of eight successive sectors, using the Sectors in a direction that is reverse to their numbering. 
     It has been found that this reversal is effective for better dispersing of burst errors. The starting sector for each row of the BIS Block is one sector higher than for the previous row. 
     row N=0 of the BIS block is placed on rows r=0 of the sectors  0 ,  7 ,  6 ,  5 , . . .  2 ,  1 . 
     row N=2 of the BIS block is placed on rows r=1 of the sectors  1 ,  0 ,  7 ,  6 , . . .  3 ,  2 . 
     row N=4 of the BIS block is placed on rows r=2 of the sectors  2 ,  1 ,  0 ,  7 , . . .  4 ,  3 . 
     this procedure is cyclically repeated until row N=60, that is placed on the rows r=30 of the sectors  6 ,  5 ,  4 , . . .  0 ,  7 . 
     Now, within each sector, each row is shifted cyclically to the right by mod(r, 3) positions: so, row 
     r=0 is not shifted at all, row r=1 is shifted 1, row r=2 is shifted 2, row r=3 is not shifted, row 
     r=4 is shifted 1, etc. For the odd rows of the BIS Block a corresponding procedure is followed. 
     In this respect, FIG. 17 shows an example of the partial mapping of BIS bytes on the first eight sectors, and FIG. 18 an example of the partial mapping of BIS bytes on the last eight sectors, that after the foregoing are self-explanatory. 
     FIG. 19 by way of recapitulation gives a schematic representation of the overall encoding process. The user data as received from a source that may be a host or an application are first divided into data frames that each consist of 2048+4 bytes; as shown in block  200  of the FIG., 32of these frames are taken into account for the next encoding step. In block  202 , a Data Block is formed and arranged into 304 columns of 216 rows each. In block  204  a Long Distance Code block is formed through adding 32 rows parity. In block  206  an ECC cluster is arranged according to 152 columns and 496 rows. This is arranged to fill the four sections labeled ECC in the Physical Cluster block  218 , that is the comprehensive code format entity. 
     The address and control data added by the Recording System are converted also in successive steps. First the Logical Address and Control Data is arranged in 32*18 bytes in block  208 . The logical addresses are those that pertain to user functionalities, and may indicate aspects that relate to a duration of the rendering of a user program. Also the physical addresses are arranged into 16*9 bytes in block  210 . The physical addresses relate to physical distances on the carrier. Due to the repeated renumbering and interleaving, the relation between physical and logical addresses has been broken. Items that follow each other closely in a program, may be spaced from each other by an appreciable physical distance, and vice versa. Also, the mapping is not uniformly progressing. In block  212 , the addresses are combined in an Access Block of 24 columns by 30 rows. In block  214 , there are 32 rows of parity added. In block  216 , these arranged into a BIS cluster of 3 columns and 496 rows. These fill the three BIS columns in block  218 . Also a column of sync bit groups is added, so that a physical cluster of 155 columns by 496 rows is formed. Together these form 16 Physical Sectors that are grouped into 496 Recording Frames as shown.