Abstract: An array f(n) is received for n=1, . . . , N where N is a length of a codeword. An array g(n) is received for n=1, . . . , N where N is a length of a codeword. Input data is encoded to satisfy an MTR constraint and a RLL constraint using the array f(n) and the array g(n).

Abstract: Inter-track interference cancelation is disclosed, including: receiving an input sequence of samples associated with a track on magnetic storage; using a processor to generate inter-track interference (ITI) data associated with a first side track including by performing a correlation between the input sequence of samples and a sequence of data associated with the first side track.

Abstract: It is decided whether to adjust data associated with a decoder. In the event it is decided to adjust the data associated with the decoder, the data is adjusted to obtain adjusted data and decoding is performed on the adjusted data. In the event it is decided to not adjust the data associated with the decoder, decoding is performed on the data associated with the decoder.

Abstract: A codebook which includes a plurality of messages and a plurality of codewords, a specified codeword bit value, and a specified message bit value are obtained. The LLR for bit ci in a codeword is generated, including by: identifying, from the codebook, those codewords where bit ci has the specified codeword bit value; for a message which corresponds to one of the codewords where bit ci has the specified codeword bit value, identifying those bits which have the specified message bit value; and summing one or more LLR values which correspond to those bits, in the message which corresponds to one of the codewords where bit ci has the specified codeword bit value, which have the specified message bit value.

Abstract: An indication of a page type which failed error correction decoding is received. A threshold to adjust is selected from a plurality of thresholds based at least in part on the page type. A third adjusted threshold associated with the page type is generated, including by: determining a first number of flipped bits using a first adjusted threshold associated with the page type, determining a second number of flipped bits using a second adjusted threshold associated with the page type, and generating the third adjusted threshold using the first number of flipped bits and the second number of flipped bits.

Abstract: A first decoder performs decoding on each data set in a first plurality of data sets using a first code; each data set in the first plurality is stored on a different NAND Flash chip. It is determined if the first decoding is successful; if not, a second decoder performs a second decoding on each data set in a second plurality of data sets using a second code; each data set in the second plurality includes at least some data, after the first decoding using the first code, from each data set in the first plurality. The first decoder performs a third decoding on each data set in the first plurality using the first code, where each data set in the first plurality includes at least some data, after the second decoding using the second code, from each data set in the second plurality.

Abstract: Processing a received signal includes receiving a code word that is different from an expected code word, determining, at least in part using a logic circuit, whether the difference between the received code word and the expected code word is acceptable based at least in part on one or more bit differences, and in the event it is determined that the difference is unacceptable, providing an indication of an error.

Abstract: Determining a parameter associated with whether a portion of a storage device is defective is disclosed. Determining comprises: obtaining known data associated with the portion; reading back from the portion to produce a read-back waveform; decoding the read-back waveform, including producing statistical information; and determining a parameter associated with whether the portion is defective based at least in part on the statistical information.

Abstract: Data which is read back from a multi-level storage device is received. For each bin in a set of bins, a portion of reads which fall into that particular bin and which are to be maintained is received. The set of bins is adjusted so that the read-back data, after assignment using the adjusted set of bins, matches the received portions of reads which are to be maintained.

Abstract: For each of a plurality of locations in flash memory, a number of pulses required to change a value stored in that location is obtained. From the plurality of locations, a location to write to is selected using the obtained number of pulses. The selected location is written to.

Abstract: A method for reducing a number of bits for representing a value is disclosed. A first value represented with a first number of bits is transformed to a second value represented with a second number of bits, wherein the first number of bits is greater than the second number of bits. The transformed second value is scaled by a scale factor to a third value. Transforming includes selecting a target window with a width of a third number of bits, wherein the third number of bits is smaller than the first number of bits. Transforming further includes saturating the first value to a most significant bit (MSB) within the selected target window and extracting bits within the selected target window from the saturated value.

Abstract: A method for detecting a defect in a portion of a storage device is disclosed. Reference data and data read from the portion are compared to determine a number of error bits and a number of error symbols. An error ratio is computed, wherein the error ratio comprises a ratio of the number of error bits to the number of error symbols. A defect is detected based on whether the error ratio exceeds a threshold. In some embodiments, the reference data and the read data are compared to determine an error vector, wherein a bit in the error vector with a value one indicates a bit error in the read data. For each of a plurality of windows of the error vector, a corresponding number of error bits is determined. A defect is detected based on whether any of the numbers of error bits exceeds a threshold.

Abstract: Decoding associated with a second error correction code and a first error correction code is performed. Ns first and second-corrected segments of data, first sets of parity information, and second sets of parity information are intersegment interleaved to obtain intersegment interleaved data, where the Ns segments of data, the Ns first sets of parity information, and the Ns second sets of parity information have had decoding associated with the first and the second error correction code performed on them (Ns is the number of segments interleaved together). Decoding associated with a third error correction code is performed on the intersegment interleaved data and interleaved parity information to obtain at least third-corrected interleaved data. The third-corrected interleaved data is de-interleaved.

Abstract: Accessing data at a memory is described. A request associated with a read or write operation is received, wherein the request includes a logical address associated with the memory. A physical address is generated based at least in part on the logical address. A block of data at the memory that includes data associated with the physical address is determined. Data at the determined block of data and a corresponding set of ECC from the memory are accessed. Whether the accessed data can be decoded based at least in part on the corresponding set of ECC is determined.

Abstract: A system for decoding data is disclosed. The system includes: an input interface configured to receive data associated with encoded data; a first decoder configured to decode a first subset of the encoded data to obtain a first portion of decoded data; a second decoder configured to decode a second subset of the encoded data to obtain a second portion of the decoded data, wherein the second portion includes decoded data not included in the first portion; and an output interface configured to output the decoded data.

Abstract: Second interleaved data is de-interleaved using a second interleaving mapping to obtain encoded data. The second interleaved data includes a copy of constrained data in the same sequence and having the same values as the constrained data. Also, the portion of the second interleaved data that includes the copy of the constrained data satisfies a modulation constraint associated with limiting a number of consecutive events to a maximum number of consecutive events. The encoded data is decoded to obtain first interleaved data and the first interleaved data is de-interleaved using a first interleaving mapping to obtain the constrained data, a copy of which is included in the second interleaved data, where the constrained data satisfies the modulation constraint.

Abstract: A plurality of interpolated samples is generated. Using a plurality of soft-decision detectors, error correction decoding is performed on the plurality of interpolated samples in order to obtain a plurality of decisions. From the plurality of decisions, one is selected by determining which of the plurality of soft-decision detectors are able to come to a decision during error correction decoding. It is determined whether a majority of the detectors that are able to come to a decision come to a same decision. If not, a decision associated with a greatest reliability is selected from the decision detectors that are able to come to a decision.

Abstract: f(x(sk?1, sk))=A(sk?1)+B(sk) is calculated for nm2 pairs of consecutive state variables {sk?1, sk} using A(sk)=minsk?1,x{A(sk?1)+?(xk=x)} and B(sk)=minsk+1,x{B(sk+1)+?(xk+1=x, sk+1)}, where ?(xk=x) is a metric associated with a branch xk=x connecting consecutive state variables sk?1 and sk. The nm lowest values are selected from the nm2 calculated values of f(x(sk?1, sk))=A(sk?1)+B(sk) and log likelihood ratios (LLRs) are set to those lowest f(x(sk?1, sk)) values. The nm values of x that correspond to the nm lowest values are determined.

Abstract: A data signal is sampled by generating a read enable signal at a first semiconductor device which is intended for a second semiconductor device. A read enable signal with at least some I/O pad delay included is obtained, including by passing the read enable signal intended for the second semiconductor device at least partially through an input/output (I/O) pad on the first semiconductor device. At the first semiconductor device, a data signal from the second semiconductor is sampled using the read enable signal with at least some I/O pad delay included.

Abstract: A number of pulses to modify information stored in a given location in a plurality of locations is obtained for each of the plurality of locations in flash memory. A location having the largest number of pulses is selecting from the plurality of locations. The selected location is written to.