Abstract: A system corrects errors in a bit stream. The system includes an encoder and a decoder. The encoder encodes the bit stream using a low density parity check code by inserting parity check bits into the bit stream to generate codewords. The decoder decodes the codewords using parity check equations that are based on the low density parity check code. The parity check bits may comprise no more than four percent of the bits in the codewords of the low density parity check code. The low density parity check code can have a minimum separation of at least 7 between any two ones in each row of a parity-check matrix that is based on the low density parity check code. The encoder and the decoder can be defined in hardware using logic circuits that are interconnected to implement a trellis based on the low density parity check code.

Abstract: Servo patterns for patterned media. The servo pattern includes specification of cylinder/track ID with and without a Gray code. The servo pattern space is minimized by the optimum usage of the islands. This is achieved by island allocation rules to take advantage of non-magnetic island. The island allocation also provides for easier lift-off. Logic is used to encode and decode the Gray code. Further, the Gray code is designed to stabilize the magnetic island/non-magnetic island ratio to allow for easier manufacture.

Abstract: Techniques are provided that generate bit reliabilities for a detected sequence. A detector generates the detected sequence. According to one embodiment, a post-processor finds a first set of combinations of one or more error events in the detected sequence satisfying a complete set or a subset of error correction constraints corresponding to the first bit value, finds a second set of combinations of one or more error events in the detected sequence satisfying a complete set or a subset of error correction constraints corresponding to the second bit value, selects a first most likely combination of one or more events of the first set and a second most likely combination of one or more events of the second set, and generates a bit reliability based on the first and the second most likely values.

Abstract: A detector generates a detected sequence, and a post processor generates probability values that indicate the likelihood of a plurality of error events in the detected sequence. The post processor partitions the values into first and second subsets. The post processor selects a first most likely value from the first subset of the values and a second most likely value from the second subset of the values. The post processor generates a bit reliability based on the first and the second most likely values.

Abstract: A method for adaptively applying an error-correcting code to a storage device is disclosed. A determination is made that a system is in an idle state of input/output requests. First data symbols are copied into a first location within a buffer. First data symbol errors corrected using a first error-correcting code. Second data symbols including corrected bits are written in a second location on the recording media with a second error-correcting code. An error number for the second data symbols in the second location is determined. If the error number is below a first threshold error number, the first data symbols are deleted. If the error number is above the first threshold error number, the second data symbols are deleted.

Abstract: Techniques are provided for identifying the servo sectors in a track on a data storage device. A data storage device identifies the servo sectors in a track by reading distributed index bits from multiple servo sectors in a track. The data storage device analyzes only one index bit from each servo sector to identify the index of a track. In some embodiments, the index of a track can be identified after examining the index bits stored in a particular number of consecutive servo sectors, even in the presence of errors. The index bits in each track can have an error tolerance with a minimum Hamming distance greater than one. In other embodiments, a data storage device compares a sliding window of the index bits read from the servo sectors to all possible N-bit vectors that exist within a pattern of the index bits stored on a track.

Abstract: Servo patterns for patterned media. The servo pattern includes specification of cylinder/track ID with and without a Gray code. The servo pattern space is minimized by the optimum usage of the islands. This is achieved by island allocation rules to take advantage of non-magnetic island. The island allocation also provides for easier lift-off. Logic is used to encode and decode the Gray code. Further, the Gray code is designed to stabilize the magnetic island/non-magnetic island ratio to allow for easier manufacture.

Abstract: Servo patterns for patterned media. The servo pattern includes specification of cylinder/track ID with and without a Gray code. The servo pattern space is minimized by the optimum usage of the islands. This is achieved by island allocation rules to take advantage of non-magnetic island. The island allocation also provides for easier lift-off. Logic is used to encode and decode the Gray code. Further, the Gray code is designed to stabilize the magnetic island/non-magnetic island ratio to allow for easier manufacture.

Abstract: Techniques are provided for reducing error propagation in encoded data using Fibonacci modulation codes. The Fibonacci modulation codes have a Fibonacci base with a variable span that limits error propagation. Some of the elements in the Fibonacci base have a larger span than limited span elements in the base. Errors occurring in bit positions of an encoded sequence that correspond to the limited span elements do not propagate to adjacent bytes in the decoded sequence. The Fibonacci modulation codes can also have a relatively high code rate.

Abstract: Flash memory devices and associated methods are described for controlling data errors in the devices through various forms of decoding, error correction, and wear concentration. To this end, a flash memory device may be partitioned into a plurality of sectors. Data may then be received from, for example, a host processor for storage within the flash memory device. Storage durations of the data are then estimated and the data is stored in the data sectors based on those estimated storage durations.

Abstract: A system corrects errors in a bit stream. The system includes an encoder and a decoder. The encoder encodes the bit stream using a low density parity check code by inserting parity check bits into the bit stream to generate codewords. The decoder decodes the codewords using parity check equations that are based on the low density parity check code. The parity check bits may comprise no more than four percent of the bits in the codewords of the low density parity check code. The low density parity check code can have a minimum separation of at least 7 between any two ones in each row of a parity-check matrix that is based on the low density parity check code. The encoder and the decoder can be defined in hardware using logic circuits that are interconnected to implement a trellis based on the low density parity check code.

Abstract: An error correction encoder inserts redundant parity information into a data stream to improve system reliability. The encoder can generate the redundant parity information using a composite code. Dummy bits are inserted into the data stream in locations reserved for parity information generated by subsequent encoding. The error correction code can have a uniform or a non-uniform span. The span corresponds to consecutive channel bits that are within a single block of a smaller parity code that is used to form a composite code. The span lengths can be variant across the whole codeword by inserting dummy bits in less than all of the spans.

Abstract: A magnetic disk for a hard disk drive comprising a distributed track identifier is described. The disk includes a first portion of a track identifier physically located at a first location on a disk sector and a second portion of the track identifier physically located at a second location on the disk sector wherein the first portion and the second portion of the track identifier are discontinuous on the sector.

Abstract: Geometrically-dependent error rates are used to identify sectors for XORing data in a RAID system for parity purposes in such a way that the probability of failure of any particular group is minimized.

Abstract: Techniques are provided that generate bit reliabilities for a detected sequence. A detector generates the detected sequence. According to one embodiment, a post-processor finds a first set of combinations of one or more error events in the detected sequence satisfying a complete set or a subset of error correction constraints corresponding to the first bit value, finds a second set of combinations of one or more error events in the detected sequence satisfying a complete set or a subset of error correction constraints corresponding to the second bit value, selects a first most likely combination of one or more events of the first set and a second most likely combination of one or more events of the second set, and generates a bit reliability based on the first and the second most likely values.

Abstract: A detector generates a detected sequence, and a post processor generates probability values that indicate the likelihood of a plurality of error events in the detected sequence. The post processor partitions the values into first and second subsets. The post processor selects a first most likely value from the first subset of the values and a second most likely value from the second subset of the values. The post processor generates a bit reliability based on the first and the second most likely values.

Abstract: Techniques are provided for identifying the servo sectors in a track on a data storage device. A data storage device identifies the servo sectors in a track by reading distributed index bits from multiple servo sectors in a track. The data storage device analyzes only one index bit from each servo sector to identify the index of a track. In some embodiments, the index of a track can be identified after examining the index bits stored in a particular number of consecutive servo sectors, even in the presence of errors. The index bits in each track can have an error tolerance with a minimum Hamming distance greater than one. In other embodiments, a data storage device compares a sliding window of the index bits read from the servo sectors to all possible N-bit vectors that exist within a pattern of the index bits stored on a track.

Abstract: Bit and byte synchronization for sampling and decoding a data string is provided a single data field u. The data string x has pre-pended to it a short string of 1s (ones), followed by u to yield a string y= . . . 1111, u, x. The string is pre-coded by convolution with 1/(1?D2). PRML-sampling of y starts at an initial phase, and vectors are obtained from that string by sampling at pre-selected phases following the initial sampling point. The vectors of y are compared with vectors corresponding to PRML samples of an initial set of bits in u obtained at predetermined phases. The pair of y, u vectors exhibiting the minimum Euclidian distance yields a sampling correction value by which the initial sampling phase is corrected and a new initial sampling point preceding x is determined. Here, bit and byte synchronization have been achieved and sampling of x proceeds at the corrected phase, from the new initial sampling point.

Abstract: Servo patterns for patterned media. The servo pattern includes specification of cylinder/track ID with and without a Gray code. The servo pattern space is minimized by the optimum usage of the islands. This is achieved by island allocation rules to take advantage of non-magnetic island. The island allocation also provides for easier lift-off. Logic is used to encode and decode the Gray code. Further, the Gray code is designed to stabilize the magnetic island/non-magnetic island ratio to allow for easier manufacture.

Abstract: Techniques are provided for reducing error propagation in encoded data using Fibonacci modulation codes. The Fibonacci modulation codes have a Fibonacci base with a variable span that limits error propagation. Some of the elements in the Fibonacci base have a larger span than limited span elements in the base. Errors occurring in bit positions of an encoded sequence that correspond to the limited span elements do not propagate to adjacent bytes in the decoded sequence. The Fibonacci modulation codes can also have a relatively high code rate.