Abstract: A message-passing decoder operates by storing, at a check node, a minimum value, a next-to-minimum value, an edge location of the minimum value, and information regarding the signs of incoming messages. For an edge which is not the location of a previous minimum value, the minimum value and the next-to-minimum value, and the location of the minimum value, are set based on the magnitude of an incoming message. For an edge which is the location of the previous minimum value, the minimum value and the next-to-minimum value are set based on the magnitude of an incoming message, and when the magnitude of the incoming message is at most equal to the previous next-to-minimum value, the location of the minimum value is set to the respective edge, and when the magnitude of the incoming message is greater than the previous next-to-minimum value, the location of the minimum value is approximated.

Abstract: Systems and techniques relating to decoder memory management are described. A described system includes a decoder system configured to perform decoder processes in order to decode signals generated by reading a storage medium, the decoder processes being associated with respective memory thresholds; and a memory structure coupled with the decoder system. The decoder processes use the memory structure in accordance with the respective memory thresholds. The decoder system can be configured to detect whether the memory structure is underutilized by a process of the decoder processes, determine an underutilization amount associated with the process with respect to the memory threshold of the process, identify a target decoder process of the decoder processes, and enable the target decoder process to exceed the memory threshold of the target decoder process based on the underutilization amount. Enabling the target decoder process to exceed can increase decoding performance of the target decoder process.

Abstract: Systems and methods of reading data from a storage device are provided. A first codeword and a second codeword are read from a storage device, where the second codeword is positioned after the first codeword. The first and second codewords are decoded in parallel, and the decoding of the second codeword completes before the decoding of the first codeword completes. The decoded second codeword and a signal indicating whether the decoding of the second codeword is complete are transmitted to control circuitry before the decoding of the first codeword completes.

Abstract: A method for writing data onto a medium on which data are stored in tracks includes encoding the data into at least one codeword, and writing a respective portion of each of the at least one codeword onto respective different tracks on the medium. The writing may include writing a respective portion of each of the at least one codeword onto respective different adjacent tracks on the medium. Another method for reading data includes positioning a plurality of read heads to read codewords that have been written across multiple tracks of a medium. Each read head in the plurality of read heads reads a different portion of the first group of the multiple tracks, and where each different portion of the multiple tracks overlaps at least one other different portion of the multiple tracks. Signals are detected from the plurality of read beads, and the detected signals are decoded.

Abstract: Systems and methods are provided for decoding a codeword using an iterative decoding process. The systems and methods include receiving a codeword comprising a plurality of symbols, and concurrently processing the received codeword with a detector and a decoder based in part on extrinsic information associated with the plurality of symbols to obtain updated extrinsic information. The systems and methods further include modifying the extrinsic information associated with the plurality of symbols based on the updated extrinsic information, and repeating the processing and modifying steps until a stopping criterion is met.

Abstract: A message-passing decoder operates by storing, at a check node, a minimum value, a next-to-minimum value, an edge location of the minimum value, and information regarding the signs of incoming messages. For an edge which is not the location of a previous minimum value, the minimum value and the next-to-minimum value, and the location of the minimum value, are set based on the magnitude of an incoming message. For an edge which is the location of the previous minimum value, the minimum value and the next-to-minimum value are set based on the magnitude of an incoming message, and when the magnitude of the incoming message is at most equal to the previous next-to-minimum value, the location of the minimum value is set to the respective edge, and when the magnitude of the incoming message is greater than the previous next-to-minimum value, the location of the minimum value is approximated.

Abstract: The present disclosure includes apparatus, systems, and techniques relating to noise-predictive detector adaptation. A described technique includes operating a decoder system to decode codewords that are based on a received encoded signal by processing the codewords and exchanging information between path and code decoders, operating the path decoder to use estimation parameters to produce first and second paths based on a codeword of the codewords, operating the code decoder to produce a decoded path based on the codeword; determining a winning path of first and second paths based on whether the decoded path matches the first path or the second path; and updating, based on one or more error terms and the winning path, the estimation parameters to favor selection of the winning path by the path decoder and to disfavor selection of a losing path of the first and second paths by the path decoder.

Abstract: A method for writing data onto a medium on which data are stored in tracks includes encoding the data into at least one codeword, and writing a respective portion of each of the at least one codeword onto respective different tracks on the medium. The writing may include writing a respective portion of each of the at least one codeword onto respective different adjacent tracks on the medium. Another method for reading data includes positioning a plurality of read heads to read codewords that have been written across multiple tracks of a medium. Each read head in the plurality of read heads reads a different portion of the first group of the multiple tracks, and where each different portion of the multiple tracks overlaps at least one other different portion of the multiple tracks. Signals are detected from the plurality of read heads, and the detected signals are decoded.

Abstract: Systems and methods are provided for using a product code having a first dimension and a second dimension to encode data, decode data, or both. An encoding method includes receiving a portion of user data to be written in the first dimension, and computing first parity symbols with respect to the first dimension for the portion of user data. Partial parity symbols with respect to the second dimension are computed for the portion of user data and are used to obtain second parity symbols for the portion of user data. A decoding method includes decoding a first codeword in the first dimension. When the decoding the first codeword in the first dimension is successful, a target syndrome of a second codeword in the second dimension is computed based on a result of the decoding of the first codeword, wherein the first codeword partially overlaps with the second codeword.

Abstract: Apparatuses and methods associated with instant syndrome computation in a layered LDPC decoder are described. In one embodiment an apparatus includes a first hardware layer configured to compute a first group of syndrome values from one or more bit values in the codeword and a second hardware layer configured to compute a second group of syndrome values from one or more bit values in the codeword. The apparatus also includes a first physical memory associated with the first hardware layer and configured to store the first group of syndrome values until the syndrome values change due to a change in a codeword bit value. The apparatus also includes a second physical memory associated with the second hardware layer and configured to store the second group of syndrome values until the syndrome values change due to a change in a codeword bit value.

Abstract: Systems and methods are provided for decoding a codeword using an iterative decoding process. The systems and methods include receiving a codeword comprising a plurality of symbols, and concurrently processing the received codeword with a detector and a decoder based in part on extrinsic information associated with the plurality of symbols to obtain updated extrinsic information. The systems and methods further include modifying the extrinsic information associated with the plurality of symbols based on the updated extrinsic information, and repeating the processing and modifying steps until a stopping criterion is met.

Abstract: A method for writing data onto a medium on which data are stored in tracks includes encoding the data into at least one codeword, and writing a respective portion of each of the at least one codeword onto respective different tracks on the medium. The writing may include writing a respective portion of each of the at least one codeword onto respective different adjacent tracks on the medium. Another method for reading data includes positioning a plurality of read heads to read codewords that have been written across multiple tracks of a medium. Each read head in the plurality of read heads reads a different portion of the first group of the multiple tracks, and where each different portion of the multiple tracks overlaps at least one other different portion of the multiple tracks. Signals are detected from the plurality of read heads, and the detected signals are decoded.

Abstract: Methods and systems are provided for encoding and/or decoding data based on a constrained code and an error correction code (ECC). The data is encoded to generate combined LDPC-constrained codewords that may substantially satisfy both an ECC structure condition and a constrained code condition. A first plurality of sequences may be generated from input data to satisfy the constrained code condition. The first plurality of sequences may then be mapped to a second plurality of sequences that satisfies the ECC condition while preserving the constrained code condition.

Abstract: The present disclosure includes apparatus, systems, and techniques relating to noise-predictive detector adaptation. A described technique includes operating a decoder to decode a received encoded signal based on estimation parameters to produce paths including a first path and a second path, the second path being an alternate to the first path, determining a decoded path based on at least a portion of the paths, determining a winning path of the first path and the second path based on whether the decoded path matches the first path or the second path, and updating the estimation parameters based on one or more error terms and the winning path to favor selection of the winning path by the decoder and to disfavor selection of a losing path of the first and second paths by the decoder in a subsequent iteration.

Abstract: Methods and systems are disclosed herein for generating parity information for using information in a low-density parity check (LDPC) encoder. A quasi-cyclic LDPC generator matrix K can be generated based on the non-invertible parity-check matrix H. Parity information can be generated by the LDPC encoder based at least in part on the user information, the non-invertible parity check matrix H, and the quasi-cyclic LDPC generator matrix K.

Abstract: Systems and methods are provided for using a product code having a first dimension and a second dimension to encode data, decode data, or both. An encoding method includes receiving a portion of user data to be written in the first dimension, and computing first parity symbols with respect to the first dimension for the portion of user data. Partial parity symbols with respect to the second dimension are computed for the portion of user data and are used to obtain second parity symbols for the portion of user data. A decoding method includes decoding a first codeword in the first dimension. When the decoding the first codeword in the first dimension is successful, a target syndrome of a second codeword in the second dimension is computed based on a result of the decoding of the first codeword, wherein the first codeword partially overlaps with the second codeword.

Abstract: Systems and methods are provided for encoding information using a code specified by a target Markov distribution. The systems and methods include selecting a set of parameters comprising a block length, a plurality of weight metrics, and a threshold, and estimating a Markov distribution associated with the selected set of parameters from a plurality of data blocks defined by the selected parameters. The systems and methods further include modifying the set of parameters based on the estimated Markov distribution, and encoding the information using the modified set of parameters.

Abstract: Systems and methods are provided for decoding data stored on a storage device. A decoding method is described for retrieving data from the storage device, wherein the retrieved data are encoded using a product code having a first dimension and a second dimension. The decoding method includes processing at least one codeword from the first dimension to form detector soft information, decoding the at least one codeword from the first dimension based on the detector soft information to form a first decoder soft information, and decoding at least one codeword from the second dimension based on the first decoder soft information to form a second decoder soft information.

Abstract: Systems, methods, and other embodiments associated with an iterative decoder logic. In one embodiment, the iterative decoder logic is configured to decode data. The iterative decoder logic includes a detector configured to generate code words from the data and identify short code words. A short code word has a length less than a length of a full code word. The iterative decoder logic also includes a decoder having a shortening support module and a decoder core. The shortening support module appends at least one dummy value to at least one short code word to convert the at least one short code word to a full code word. The decoder core decodes the converted full code word to generate a decoded converted full code word. The decoder transmits the decoded converted full code word without the at least one dummy variable.

Abstract: In iterative decoding, a data recovery scheme corrects for corrupted or defective data by determining reliability metrics for blocks of decoded data. Block or windowed detectors generate block reliability metrics for data blocks (rather than individual bits) of decoded data using soft information from the regular decoding mode or from new iterative decoding iterations performed during error recovery mode. An error recovery system triggers corrective decoding of selected data blocks based on the block reliability metrics, by for example, comparing the block reliability metrics to a threshold or by selecting an adjustable number of the least reliable data blocks.