Error correction circuit

Claim 2

An error correction circuit for detecting and correcting a plurality of errors in codewords made up of k data and n-k inspection symbols in the playback data from a recorded medium each symbol made up of m binary bits of information using a Reed-Solomon code for error detection and correction so that the error location polynomial σ(x)=x e +σ 1 x -1 + . . . +σ e where e is the number of errors and the coefficients σ 1 to σ e of the error location polynomial σ(x) are related to the error syndromes S i generated by the error correction circuit by the equation: S.sub.i+e +σ.sub.1 S.sub.i+e-1 + . . . σ.sub.e-1 S.sub.i+1 +σ.sub.3 S.sub.i =0 where the syndromes S i+e to S i are field elements α i of the Galois field GF(2 m ), the error correction circuit comprising: means for generating syndromes S 0 , S 1 , S 2 and S 3 from the codewords; means for effecting the following three calculations on the basis of the syndromes S 0 , S 1 , S 2 and S 3 generated by said syndrome generating means: S.sub.2 S.sub.0 +S.sub.1.sup.2 =r.sub.3 S.sub.3 S.sub.0 +S.sub.1 S.sub.2 =r.sub.2 S.sub.3 S.sub.1 +S.sub.2.sup.2 =r.sub.1 where r 3 , r 2 and r 1 represent the values of the respective calculations; means for judging whether the condition r 3 ≠0 or r 3 =0; a first processing means for finding error locations by determining the roots of the following equation as the error location polynomial, when the condition r 3 ≠0 is confirmed in said judging means: r.sub.3 x.sup.2 +r.sub.2 x+r.sub.1 =0 where x represents the error locations; and a second processing means for finding error location by determining the root of the following equation as the error location polynomial, when the condition r 3 =0 is confirmed in said judging means under the condition of r 2 =0: S.sub.1 +S.sub.0 x=0.

Claim 3

An error correction circuit for detecting and correcting a plurality of errors in codewords made up of k data and n-k inspection symbols in the playback data from a recorded medium each symbol made up of m binary bits of information using a Reed-Solomon code for error detection and correction so that the error location polynomial σ(x)=x e +σ 1 x e-1 + . . . +σ e where e is the number of errors and the coefficients σ 1 to σ e of the error location polynomial σ(x) are related to the error syndromes S i generated by the error correction circuit by the equation: S.sub.i+e +σ.sub.1 S.sub.i+e-1 + . . . σ.sub.e-1 S.sub.i+1 +σ.sub.e S.sub.i =0 where the syndromes S i+e to S i are field elements α i of the Galois field GF(2 m ), the error correction circuit comprising: means for generating syndromes S 0 , S 1 , S 2 and S 3 from the codewords; first and second means for holding the syndromes S 1 and S 0 , means for effecting the following three calculations of the basis of the syndromes S 0 , S 1 , S 2 and S 3 generated by said syndrome generating means: S.sub.2 S.sub.0 +S.sub.1.sup.2 =r.sub.3 S.sub.3 S.sub.0 +S.sub.1 S.sub.2 =r.sub.2 S.sub.3 S.sub.1 +S.sub.2.sup.2 =r.sub.1 where r 3 , r 2 and r 1 represent the values of the respective calculations; third means for holding the value r 3 ; means for judging whether the condition r 3 ≠0 or r 3 =0; control means for replacing, when the condition r 3 ≠0 is determined by said judging means, the syndromes S 1 and S 0 with the values r 1 and r 2 in said first and second holding means; and processing means for finding error locations by determining the roots of the following equations as the error locations polynomials: r.sub.3 x.sup.2 +r.sub.2 x+r.sub.1 =0 or S.sub.1 +S.sub.0 x=0 where x represents the error locations, said processing means being adapted to add a value obtained through adding the content of said first holding means, the syndrome S 1 or the value r 1 , to the content of said second holding means, the syndrome S 0 or the value r 2 , after the content of said second holding means has been multiplied by an element α of said Galois field GF(2 m ), to a value obtained from said third holding means after the content of said third holding means has been multiplied by the element α 2 , whereby each element α obtained when the output from said processing means is reduced to zero is used as an error location.

Claim 4

An error correction circuit for detecting and correcting a plurality of errors in codewords made up of k data and n-k inspection symbols in the playback data from a recorded medium each symbol made up of m binary bits of information using a Reed-Solomon code for error detection and correction so that the error location polynomial σ(x)=x e +σ 1 x e-1 + . . . +σ e where e is the number of errors and the coefficients σ 1 to σ e of the error location polynomial σ(x) are related to the error syndromes S i generated by the error correction circuit by the equation: S.sub.i+e +σ.sub.1 S.sub.i+e-1 + . . . σ.sub.e-1 S.sub.i+1 +σ.sub.e S.sub.i =0 where the syndromes S i+e to S i are field elements α i of the Galois field GF(2 m ), the error correction circuit comprising: means for generating syndromes S 0 , S 1 , S 2 and S 3 from the codewords; first and second means for holding the syndromes S 1 and S 0 , means for effecting the following three calculations of the basis of the syndromes S 0 , S 1 , S 2 and S 3 generated by said syndrome generating means: S.sub.2 S.sub.0 +S.sub.1.sup.2 =r.sub.3 S.sub.3 S.sub.0 +S.sub.1 S.sub.2 =r.sub.2 S.sub.3 S.sub.1 +S.sub.2.sup.2 =r.sub.1 where r 3 , r 2 and r 1 represent the values of the respective calculations; third means for holding the value r 3 ; means for judging whether the condition r 3 ≠0 or r 3 =0; control means for replacing, when the condition r 3 ≠0 is determined by said judging means, the syndromes S 1 and S 0 with the values r 1 and r 2 in said first and second holding means; and processing means for finding error locations by determining the roots of the following equations as the error locations polynomials: r.sub.3 x.sup.2 +r.sub.2 x+r.sub.1 =0 or S.sub.1 +S.sub.0 x=0 where x represents the error locations, said processing means being adapted to add a value obtained through adding the content of said first holding means, the syndrome S 1 or the value r 1 , to the content of said second holding means, the syndrome S 0 or the value r 2 , after the content of said second holding means has been multiplied by an element α of said Galois field GF(2 m ), to a value obtained from said third holding means after the content of said third holding means has been multiplied by the element α 2 , whereby each element α obtained when the output from said processing means is reduced to zero is used as an error location.