Two stage coding method

Abstract

Errors which arise in recording and reproducing data in a recording material are corrected with the use of an error correction code such as an RS (Reed-Solomon) code, and a two stage C 2 and C 1 coding method is conducted at an interval of repetition of a combination of [k 2 /n 2 ] and [k 2 /n 2 ]+1 on digital data having a two dimensional arrangement of k 1 in the first direction and k 2 in the second direction, whereby burst error correction ability is enhanced by the enhancement of error correction capacity.

We claim: 
     
       1. A two stage coding system for encoding digital information arranged in a matrix of k 1  ×q digits in a first direction, and k 2  digits in a second direction orthogonal to the first direction, wherein K 1 , q, and k 2  are integers,   K 1  <k 2  ; q=the number of digits per data word, and   K 1 , K 2  =the number of data words in said first and second directions respectively, comprising:   C 2  encoder means for encoding said digital information with a C 2  code on a Galois Field GF (2 q ), including means for .[.numbering.]. .Iadd.selecting .Iaddend.data words in said matrix diagonally from an arbitrary data word a 1  and establishing a 2  to a n2 , wherein n 2  is the length of .[.code.]. .Iadd.the .Iaddend.C 2  encoded data, such that ##EQU8## wherein h 1  to h n2-1  satisfy the following   h.sub.2i-1 =[K.sub.2 /n.sub.2 ]       h.sub.2i =[k.sub.2 /n.sub.2 ]+1 1≦i≦(n.sub.2 -1)/.Badd.2       .Iadd.said C 2  encode means including .Iaddend.means for C 2  encoding said .[.numbered.]. .Iadd.selected .Iaddend.data words, and means for adding the obtained C 2  code to an end of said matrix in said first direction; and   C 1  encoder means for encoding said C 2  encoded matrix with a C 1  code having a .Iadd.predetermined .Iaddend.length .[.of n 1  .]. on a GF (2 q ) for each row of data words in said first direction, and adding the obtained C 1  code to an end of said matrix in said first direction. .Iadd.   
     
     
       2.  The two stage coding system of claim 1 wherein said means for C 2  encoding further encodes said selected data words in each said diagonal; said means for adding a C 2  code to the end of each said diagonal to form a C 2  code field at the end of said matrix in said first direction. .Iaddend. .Iadd.3. The two stage coding system of claim 2 wherein said C 2  encoder means subtracts n 2  ×k 2  from any initially calculated value of a 2  to a n2  that exceed n 2  ×k 2  to select data words in said matrix diagonally. .Iaddend. .Iadd.4. The two stage coding system of claim 1 wherein said C 2  encoder means subtracts n 2  ×k 2  from any initially calculated value of a 2  to a n2  that exceed n 2  ×k 2  to select data words in said matrix diagonally. .Iaddend. .Iadd.5. The two stage coding system of claim 1 wherein additional data added to said rows of data words in said first direction prior to encoding of said C 2  encoded matrix with a C 1  code is also encoded with this C 1  code by said C 1  encoder means. .Iaddend. .Iadd.6. A two stage coding system for encoding digital information arranged in an information matrix of k 1  ×q digits in a first direction, and k 2  digits in a second direction orthogonal to the first direction, wherein   k 1 , q, and k 2  are integers,   k 1  <k 2  ; q=the number of digits per data word, and   k 1 , k 2  =the number of data words in said first and second directions respectively, comprising:   C 2  encoder means for encoding said digital information with a C 2  code on a Galois field GF(2 2 ), said C 2  encoder means selecting data words in said information matrix diagonally from an arbitrary data word a 1  and including a 2  to a n2 , wherein n 2  is the length of the C 2  encoded data, such that   a.sub.2 =a.sub.1 +n.sub.2 ×h.sub.1 +1       a.sub.3 =a.sub.2 +n.sub.2 ×h.sub.2 +1       :       a.sub.k1 =a.sub.k1-1 +n.sub.2 ×h.sub.k1-1 +1       :       a.sub.n2 =a.sub.n2-1 +n.sub.2 ×h.sub.n2-1 +1,     h 1  to h 2n-1  each being selected from one of h A  and h B , wherein,     h.sub.A =[k.sub.2 /n.sub.2 ],       h.sub.B =[k.sub.2 /n.sub.2 ]+1, and       h.sub.A ×l.sub.1 +h.sub.B ×l.sub.2 ≦k.sub.2, where       l.sub.1 +l.sub.2 =n.sub.2       said C 2  encoder means forming said C 2  code from said selected data words and adding the obtained C 2  code to an end of said information matrix in said first direction thereby forming a C 2  encoded matrix; and   C 1  encoder means for encoding each line in said first direction of said C 2  encoded matrix with a C 1  code having a predetermined length on a GF(2 q ), and adding the obtained C 1  code to an end of each said line of said matrix in said first direction to form a C 2     
     
     
        C 1  encoded matrix. .Iaddend. .Iadd.7.  The two stage coding system of claim 6 wherein a group of two or more adjacent lines h 1 , h 2 , . . . utilize a repetition pattern having at least one of each of h A  and h B  contained therein, said selection of data words a 1  to a n  by said C 2  encoder means utilizing said repetition pattern for selection of all said data words (a) in said information matrix. .Iaddend. .Iadd.8. The two stage coding system of claim 7 wherein said repetition pattern is selected from the group consisting of h A , h B  ; h B , h A  ; and h A , h B , h B . .Iaddend. .Iadd.9. The two stage coding system of claim 6 wherein:   h.sub.2i-1 =h.sub.A,       h.sub.2i =h.sub.B,     where 1<i<(n 2  -1)/2. .Iaddend. .Iadd.10. The two stage coding system of claim 6 wherein:     h.sub.2i-1 =h.sub.B,       h.sub.2i =h.sub.A,     where 1<i<(n 2  -1)/2. .Iaddend. .Iadd.11. The two stage coding system of claim 6 wherein said C 2  encoder means repeatedly selects data words in said information matrix from an arbitrary data word a 1  and including a 2  to a n2 , said C 2  encoder means repeatedly forming said C 2  code and adding said C 2  to the end of the matrix, each repetition starting from a different arbitrary data word a 1 . .Iaddend. .Iadd.12. The two stage coding system of claim 11 wherein said C 2  encoder means selects k 2  arbitrary data words from which to perform selecting, forming and adding to thereby form a complete C 2  encoded matrix. .Iaddend. .Iadd.13. The two stage coding system of claim 6 wherein said means for C 2  encoding further encodes said selected data words in each said diagonal;   said means for adding a C 2  code to the end of each said diagonal to form a C 2  code field at the end of said information matrix in said first direction. .Iaddend. .Iadd.14. The two stage coding system of claim 6 wherein additional data added to said rows of data words in said first direction prior to encoding of said C 2  encoded matrix with a C 1  code is also encoded with this C 1  code by said C 1  encoder means to thereby form said C 2  C 1  encoded matrix. .Iaddend. .Iadd.15. The two stage coding system of claim 14 wherein the length of said C 2  C 1  encoded data matrix in the first direction is (n 1  +k 3 )×q digits, where k 3  is an integer. .Iaddend. .Iadd.16. The two stage coding system of claim 6 wherein said C 2  encoder means subtracts n 2  ×k 2  from any initially calculated value of a 2  to a n2  that exceed n 2  ×k 2  to select data words in said matrix diagonally. .Iaddend. .Iadd.17. The two stage coding system of claim 6 wherein the length of said C 2  C 1  encoded data matrix in the first direction is n 1  ×q digits. .Iaddend. .Iadd.18. A two stage coding system for encoding digital information arranged in an information matrix of k 1  ×q digits in a first direction, and k 2  digits in a second direction orthogonal to the first direction, wherein   k 1 , q, and k 2  are integers,   k 1  <k q  ; q=the number of digits per data word, and   k 1 , k 2  =the number of data words in said first and second directions respectively,   said system further single stage coding additional information of k 3  ×q digits in the first direction, where k 3  is an integer and k 2  digits in the second direction, comprising:   C 2  encoder means for encoding said digital information with a C 2  code on a Galois field GF(2 q ), said C 2  encoder means selecting data words in said information matrix diagonally from an arbitrary data word a 1  and including a 2  to a n2 , wherein n 2  is the length of the C 2  encoded data, such that   a.sub.2 =a.sub.1 +n.sub.2 ×h.sub.1 +1       a.sub.3 =a.sub.2 +n.sub.2 ×h.sub.2 +1       :       a.sub.k1 =a.sub.k1-1 +n.sub.2 ×h.sub.k1-1 +1       :       a.sub.n2 =a.sub.n2-1 +n.sub.2 ×h.sub.n2-1 +1     h 1  to h n2-1  each being selected from one of h A  and h B , wherein,     h.sub.A =[k.sub.2 /n.sub.2 ],       h.sub.B =[k.sub.2 /n.sub.2 ]+1, and       h.sub.A ×l.sub.1 +h.sub.B ×l.sub.2 ≦k.sub.2, where       l.sub.1 +l.sub.2 =n.sub.2       said C 2  encoder means forming said C 2  code from said selected data words and adding the obtained C 2  code to an end of said information matrix in said first direction to form a C 2  encoded matrix; and   said additional data of k 3  words and said C 2  encoded matrix collectively forming an added data matrix having k 2  lines;   C 1  encoder means for encoding each of said k 2  lines extending in said first direction of said added data matrix with a C 1  code having a predetermined length on a GF(2 q ), and adding the obtained C 1  code to an end of each said line of said added data matrix in said first   
     
     
        direction to form a C 2  C 1  encoded matrix. .Iaddend. .Iadd.19. The two stage coding system of claim 18 wherein a group of two or more adjacent lines h 1 , h 2 , . . . utilize a repetition pattern having at least one of each of h A  and h B  contained therein, said selection of data words a 1  to a n  by said C 2  encoder means utilizing said repetition pattern for selection of all said data words (a) in said information matrix. .Iaddend. .Iadd.20. The two stage coding system of claim 19 wherein said repetition pattern is selected from the group consisting of h A , h B  ; h B , h A  ; and h A , h B , h B . .Iaddend. .Iadd.21. The two stage coding system of claim 18 wherein:   h.sub.2i-1 =h.sub.A,       h.sub.2i =h.sub.B,     where 1<i<(n 2  -1)/2. .Iaddend. .Iadd.22. The two stage coding system of claim 18 wherein:     h.sub.2i-1 =h.sub.B,       h.sub.2i =h.sub.A,     where 1<i<(n 2  -1)/2. .Iaddend. .Iadd.23. The two stage coding system of claim 18 wherein said C 2  encoder means repeatedly selects data words in said information matrix from an arbitrary data word a 1  and including a 2  to a n2 , said C 2  encoder means repeatedly forming said C 2  code and adding said C 2  to the end of the matrix, each repetition starting from a different arbitrary data word a 1 . .Iaddend. .Iadd.24. The two stage coding system of claim 23 wherein said C 2  encoder means selects k 2  arbitrary data words from which to perform selecting, forming and adding to thereby form a complete C 2  encoded matrix. .Iaddend. .Iadd.25. The two stage coding system of claim 18 wherein said means for C 2  encoding further encodes said selected data words in each said diagonal;   said means for adding a C 2  code to the end of each said diagonal to form a C 2  code field at the end of said information matrix in said first direction. .Iaddend. .Iadd.26. The two stage coding system of claim 18 wherein said C 2  encoder means subtracts n 2  ×k 2  from any initially calculated value of a 2  to a n2  that exceed n 2  ×k 2  to select data words in said information matrix diagonally. .Iaddend. .Iadd.27. The two stage coding system of claim 18 wherein the length of said C 2  C 1  encoded matrix in the first direction is (n 1  +k 3 )×q digits. .Iaddend.