An error correction block generated by performing error correction coding to the user data is divided into b number of sectors (b: a natural number), each sector having a number of bits (a: a natural number), the sector is divided into c number of sub-sectors (c: a natural number) and bits are distributed to each of the c number of sub-sectors, arrangement order of the bits is randomized for each sub-sector to which the bits are distributed, the c number of sub-sectors in which the arrangement order of the bits is randomized are combined to generate an interleaved sector, the interleaved sector is divided into c/d (d: a natural number, cd, and c>d) and e number of divided interleaved sectors (e: a natural number, eb, and b>e) are combined to generate a pre-modulation block, which is modulated by a modulation rule.

An error correction block generated by performing error correction coding to the user data is divided into b number of sectors (b: a natural number), each sector having a number of bits (a: a natural number), the sector is divided into c number of sub-sectors (c: a natural number) and bits are distributed to each of the c number of sub-sectors, arrangement order of the bits is randomized for each sub-sector to which the bits are distributed, the c number of sub-sectors in which the arrangement order of the bits is randomized are combined to generate an interleaved sector, the interleaved sector is divided into c/d (d: a natural number, cd, and c>d) and e number of divided interleaved sectors (e: a natural number, eb, and b>e) are combined to generate a pre-modulation block, which is modulated by a modulation rule.

The present disclosure describes aspects of codeword interleaving over magnetic media surfaces. In some aspects, segments of a codeword are spread or interleaved across multiple surfaces of magnetic storage media. Data for one or more codewords may be received by a read/write channel and, for each codeword, a respective index is selected, received, or generated. The index may indicate which sector partitions of the multiple surfaces that segments of one of the codewords are to be written. The data of the codewords can be segmented and then arranged in an interleaver based on the respective index to which the codeword corresponds. The codeword segments are written from the interleaver to sectors of the multiple surfaces of the magnetic media. By so doing, codewords may be spread across multiple surfaces, such that a loss of a portion of a segment track does not prevent readback and decoding of the codewords.

A two-dimensional interleaving method is provided. The two-dimensional interleaving method includes dividing a first page having N.sup.2N.sup.2 pixels, N being a natural number, into a plurality of blocks, wherein each of the plurality of blocks includes NN pixels, rearranging each of the plurality of the blocks of the first page into a second page, wherein each of two index located at same position in two adjacent block of the first page, respectively, is rearranged to have at least a dispersion distance D in the second page, and relocating an index pixel located at same position of each of the plurality of the blocks of the first page into a k-th block of the second page.

In one embodiment, a system includes a data processing unit configured to read encoded data from a magnetic tape medium. The data processing unit is also configured to decode a plurality of codeword interleaves (CWIs) from the encoded data, each CWI being a row in a sub data set logically organized into a two-dimensional array. The array includes a predetermined number of rows and columns of predetermined lengths. The data processing unit is also configured to determine an address for a first-written CWI without successfully decoding a corresponding codeword interleave designation (CWID) from the encoded data, each CWID specifying an address for a corresponding CWI. Also, each CWID is calculated as a function of a logical track number and a CWI set number.

In one embodiment, a system includes a data processing unit configured to read encoded data from a magnetic tape medium. The data processing unit is also configured to decode a plurality of codeword interleaves (CWIs) from the encoded data, each CWI being a row in a sub data set logically organized into a two-dimensional array. The array includes a predetermined number of rows and columns of predetermined lengths. The data processing unit is also configured to determine an address for a first-written CWI without successfully decoding a corresponding codeword interleave designation (CWID) from the encoded data, each CWID specifying an address for a corresponding CWI. Also, each CWID is calculated as a function of a logical track number and a CWI set number.

A two-dimensional interleaving method is provided. The two-dimensional interleaving method includes dividing a first page having N.sup.2N.sup.2 pixels, N being a natural number, into a plurality of blocks, wherein each of the plurality of blocks includes NN pixels, rearranging each of the plurality of the blocks of the first page into a second page, wherein each of two index located at same position in two adjacent block of the first page, respectively, is rearranged to have at least a dispersion distance D in the second page, and relocating an index pixel located at same position of each of the plurality of the blocks of the first page into a k-th block of the second page.

In one embodiment, a computer program product for providing header protection in magnetic tape recording includes a computer readable storage medium having program instructions embodied therewith, the program instructions readable by a processor to cause the processor to: calculate or obtain, by the processor, codeword interleave designation (CWID) parity for all CWIDs in a codeword interleave (CWI) set header, the CWID parity including error correction coding (ECC) parity, and store, by the processor, the CWID parity to a magnetic tape in one or more fields which are repeated for each CWI header in the CWI set header without using reserved bits in the CWI set header to store the CWID parity. Other systems and methods for providing header protection in magnetic tape recording are described in more embodiments.

A method for decoding a headerized sub data set (SDS) according to one embodiment includes decoding a header from a headerized SDS to obtain a SDS. C1 and C2 decoding are performed on the SDS in a number of iterations based on a number of interleaves in each row of the SDS. A number of columns of the SDS are overwritten with successfully decoded C2 codewords. A number of rows of the SDS are overwritten with successfully decoded C1 codewords. A number of C1 and/or C2 codewords of the SDS are erased. Remaining rows and/or columns of the SDS are maintained as uncorrected. The SDS is output when all rows of the SDS include only C1 codewords and all columns of the SDS include only C2 codewords.