Disclosed herein are a system, non-transitory computer-readable medium, and method for encoding and decoding information on a data bearing medium. A message comprising a bit string is read. A plurality of substrings in the message may be associated with a phase invariant codeword.

According to one embodiment, a magnetic recording and reproducing device includes an output driver, a magnetic head, and a magnetic recording medium. The output driver outputs a recording signal corresponding to input information. The magnetic head includes a coil. A recording current includes the recording signal flows in the coil. Information corresponding to the input information is recorded in the magnetic recording medium. The input information includes first, second, and third information combinations. The first information combination includes first to fourth information. The second information combination includes fifth to eighth information. The third information combination includes ninth to twelfth information. The recording signal changes to an eleventh recording current to correspond to the eleventh information. The recording signal changes to a third recording current to correspond to the third information. An absolute value of the eleventh recording current is greater than an absolute value of the third recording current.

A storage device includes read circuitry having a read head having a detector that outputs signals representing data from a first track and an adjacent track. The read head is subject to off-track excursions during which the read head detects signals from both the first track and an adjacent track. Data on each track includes a preamble including a repeating pattern. The repeating pattern in any first track is orthogonal to the repeating pattern in any track adjacent to the first track. The read circuitry also includes respective Discrete Fourier Transform circuits to identify components in the signals corresponding to respective frequencies characteristic of the repeating pattern on the first track and the repeating pattern on the second track, and computation circuitry to determine from the components a ratio by which the read head is off-track. Corresponding methods are provided for operating such a storage device and for reading data.

A storage device includes a recording medium, a first memory storing first data read from the recording medium, and a controller. The controller searches for read target data in the first data by executing a parity check on second data that is in the first data and starts at a first position, while executing the parity check, determining whether or not an interruption condition is satisfied, storing the second data in a second memory when the parity check completes without the interruption condition being satisfied and a result of a completed parity check satisfies a first condition, and executing a parity check on third data that is in the first data and starts at a second position, responsive to the interruption condition being satisfied and responsive to the result of the completed parity check not satisfying the first condition.

According to one embodiment, there is provided a storage device including a controller circuit and a storage medium. The controller circuit includes a first conversion circuit and a second conversion circuit. The first conversion circuit converts data into M-ary symbols where M is an integer of 3 or more. The second conversion circuit converts respective ones of the converted n samples of M-ary symbols into signals with L-patterned pulse width where n is an integer of 2 or more. The storage medium stores the converted n samples of signals with L-patterned pulse width. The controller circuit further includes an equalization circuit that equalizes signals read from the storage medium into the n samples of M-ary symbols.

According to one embodiment, there is provided a storage device including a controller circuit and a storage medium. The controller circuit includes a first conversion circuit and a second conversion circuit. The first conversion circuit converts data into M-ary symbols where M is an integer of 3 or more. The second conversion circuit converts respective ones of the converted n samples of M-ary symbols into signals with L-patterned pulse width where n is an integer of 2 or more. The storage medium stores the converted n samples of signals with L-patterned pulse width. The controller circuit further includes an equalization circuit that equalizes signals read from the storage medium into the n samples of M-ary symbols.

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.

A storage device includes read circuitry having a read head having a detector that outputs signals representing data from a first track and an adjacent track. The read head is subject to off-track excursions during which the read head detects signals from both the first track and an adjacent track. Data on each track includes a preamble including a repeating pattern. The repeating pattern in any first track is orthogonal to the repeating pattern in any track adjacent to the first track. The read circuitry also includes respective Discrete Fourier Transform circuits to identify components in the signals corresponding to respective frequencies characteristic of the repeating pattern on the first track and the repeating pattern on the second track, and computation circuitry to determine from the components a ratio by which the read head is off-track. Corresponding methods are provided for operating such a storage device and for reading data.

As disclosed herein a method for encoding information on tape using write offset gaps. The method includes receiving a request to write a dataset on a tape medium using a plurality of head groups, and identifying information to be encoded when writing the dataset. The method further includes determining a head group offset pattern that encodes the information, and writing the dataset using the head group offset pattern. Also disclosed herein is a method for decoding information on tape using write offset gaps. The method includes reading a dataset from a tape medium using a plurality of head groups, and determining a head group offset pattern used to read the dataset. The method further includes decoding information encoded in the head group offset pattern to provide decoded information. A computer program product corresponding to the above method is also disclosed herein.

A method, apparatus, and system are provided for implementing an enhanced modulation code for hard disk drives (HDDs). A modulation code directly uses Bit Error Rate (BER) information for different user patterns to construct a coded word minimizing possible error rate. The modulation code has a flexible code rate that simplifies code optimization relative to Coded Bit Density (CBD), signal to noise ratio (SNR) and noise color.