Abstract: A method (and system) of finding byte synchronization over random data, which includes selecting a synchronization symbol maximizing the Hamming distance when slid over itself, and appending the synchronization symbol to random data.

Abstract: A soft error correction algebraic decoder and an associated method use erasure reliability numbers to derive error locations and values. More specifically, symbol reliability numbers from a maximum likelihood (ML) decoder as well as a parity check success/failure from inner modulation code symbols are combined by a Reed-Solomon decoder in an iterative manner, such that the ratio of erasures to errors is maximized. The soft error correction (ECC) algebraic decoder and associated method decode Reed Solomon codes using a binary code and detector side information. The Reed Solomon codes are optimally suited for use on erasure channels. A threshold adjustment algorithm qualifies candidate erasures based on a detector error filter output as well as modulation code constraint success/failure information, in particular parity check or failure as current modulation codes in disk drive applications use parity checks. This algorithm creates fixed erasure inputs to the Reed Solomon decoder.

Abstract: A method (and system) of finding byte synchronization over random data, which includes selecting a synchronization symbol maximizing the Hamming distance when slided over itself, and appending the synchronization symbol to random data.

Abstract: A method and apparatus for ensuring the integrity of data that can detect errors that remain when the data correction scheme fails to correct at least some of the errors, or has added additional errors. Reed-Solomon check symbols are used for error correction and cyclic redundancy check symbols are used to detect the remaining errors. The roots of the generator polynomials used to generate the Reed-Solomon check symbols and the cyclic redundancy check symbols meet a selected subset of a plurality of conditions. The roots are further selected so that the necessary exponentiation may be performed by a combination of exponentiations by powers of two and multiplications. The Reed-Solomon check symbols are generated based on the data portion of the data block. A deterministically altered data stream is generated based on the data portion of the data block and the cyclic redundancy check symbols are generated based on the deterministically altered data stream.

Abstract: A method and apparatus for ensuring the integrity of data that can detect errors that remain when the data correction scheme fails to correct at least some of the errors, or has added additional errors. Reed-Solomon check symbols are used for error correction and cyclic redundancy check symbols are used to detect the remaining errors. The roots of the generator polynomials used to generate the Reed-Solomon check symbols and the cyclic redundancy check symbols meet a selected subset of a plurality of conditions. The roots are further selected so that the necessary exponentiation may be performed by a combination of exponentiations by powers of two and multiplications. The Reed-Solomon check symbols are generated based on the data portion of the data block. A deterministically altered data stream is generated based on the data portion of the data block and the cyclic redundancy check symbols are generated based on the deterministically altered data stream.

Abstract: Systematic and noise-induced errors, as detected in words extracted from corresponding locations in a m .times. n word organized memory array, are distinguished as to their source and are corrected by using the conjunction of a nonzero error checking syndrome and the a'priori location defects status as indexed by the location address of the extracted words from an external table memory.

Abstract: A system for correcting two .[.tracks.]. .Iadd.bytes .Iaddend.in error in .Iadd.each code word of .Iaddend.a .[.multi-track.]. .Iadd.multi-code word .Iaddend.data arrangement is provided. The message data Z.sub.1, Z.sub.2, . . . Z.sub.k is encoded by adding two check bytes C.sub.1 and C.sub.2 thereto which are generated from the message data which is arranged in blocks of k bytes, where each byte has f bits of data, .[.arranged in a cross track direction.]. where f = b .times. m and m and b are integers >1 and k is an integer 2<k<2.sup.b. The check bytes are generated in accordance with the equations:C.sub.1 =Z.sub.1 .sym.Z.sub.2 .sym.Z.sub.3 . . . .sym.Z.sub.kandC.sub.2 =T.sup..lambda.Z.sub.1 .sym.T.sup.2 .sup..lambda. Z.sub.2 .sym. . . . .sym.T.sup.k.sup..lambda. Z.sub.kwhere T is the companion matrix of a binary primitive polynomial g(x) of degree f and .lambda. is an integer given by the expression:t(2.sup.f -1)/(2.sup.b -1)in which t is any positive integer prime to 2.sup.b -1.