US RE34245 E 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.Claims(4) 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, whereinK _{1}, q, and k_{2} are integers,K _{1} <k_{2} ; q=the number of digits per data word, andK _{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 followingh h .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; andC _{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, whereink _{1}, q, and k_{2} are integers,k _{1} <k_{2} ; q=the number of digits per data word, andk _{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 thata a : a : a h _{1} to h_{2n-1} each being selected from one of h_{A} and h_{B}, wherein,h h h l 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; andC _{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 h where 1<i<(n _{2} -1)/2. .Iaddend. .Iadd.10. The two stage coding system of claim 6 wherein:h h 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, whereink _{1}, q, and k_{2} are integers,k _{1} <k_{q} ; q=the number of digits per data word, andk _{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 thata a : a : a h _{1} to h_{n2-1} each being selected from one of h_{A} and h_{B}, wherein,h h h l 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; andsaid 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 h where 1<i<(n _{2} -1)/2. .Iaddend. .Iadd.22. The two stage coding system of claim 18 wherein:h h 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.Description The present invention relates to a two stage coding method having a high burst error correction ability and also a random error correction ability equivalent to that of the prior art when an error correction code such as a Reed Solomon code (hereinafter referred to as "RS code") is used in order to correct data errors which arise in reproducing data recorded in a recording material such as a magnetic disk. Generally, in recording and reproducing data into and from a recording material such as a magnetic disk a data error may arise dependent on the state of the recording material. A data error may be a burst error caused by a signal drop out .[.on.]. .Iadd.or .Iaddend.a random error caused by a deterioration in SN ratio. In order to correct these errors a two stage coded error correction code is used. As an example, a two stage code using RS codes on a GF .[.(2 A specific coding example will be described with reference to FIGS. 5 and 2. When it is established that k
a and similarly check codes are added to the data successively. Herein, if the calculated result of a Next, C In the prior art two stage coding method with such a construction, the C
h=[k .Iadd.where [A] denotes an integer which does not exceed A .Iaddend.The C The prior art two stage coding method is constructed in such a manner, and the error correction ability by one code amounts to n
(n but h becomes as follows:
h=[k and k The present invention is directed to solve the problems pointed out above and an object is to provide a two stage coding method in which the above-described deterioration in a burst error correction ability is improved and a higher burst error correction ability than that of the prior art device is obtained. According to the coding method of the present invention, assuming that data of k
[k (herein, l In the two stage coding method of the present invention, C
(n and this exceeds 432 which is the burst error correction ability of the prior art device against the same number of data and the same number of check codes. In this way, it is possible to conduct a two stage coding having a higher burst error correction ability than that of the prior art, and having a random error correction ability equivalent to that of the prior art due to the C FIG. 1 is a diagram showing a data arrangement for conducting a C FIG. 2 is a diagram showing a data arrangement for conducting a prior art two stage coding method and a C FIG. 3 is a block diagram showing a two stage encoding circuit; FIG. 4 is a block diagram showing a two stage decoding circuit; and FIG. 5 is a diagram showing a data arrangement for conducting the C Embodiments of the present invention will be described with reference to the drawings. In FIGS. 1 and 2, the constants are established that q=8, k
h
h (i: integer, 1≦i≦(n and a
a and similarly inspection codes are added to the data successively. a Next, C In the two stage coding method of the present invention, the C In the above-illustrated embodiment a repetition pattern of (h
h
l Furthermore, an RS code on GF (2 Furthermore, it is possible to add the additional information of k The present invention is applicable not only to a magnetic disk apparatus but also to an optical recording and reproducing apparatus, and an optical magnetic recording and reproducing apparatus. Patent Citations
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