Abstract: Methods and systems are presented in this disclosure for implementing forward error correction in cloud and data center storage devices based on low-density parity-check (LDPC) channel coding. A forward error correction circuit presented herein includes a first LDPC decoder configured to perform hard-decision LDPC decoding of data read from a storage medium through a first read channel. The forward error correction circuit further includes a hybrid LDPC decoder selectively configurable to perform a selected one of hard-decision LDPC decoding and soft-decision LDPC decoding of data read from the storage medium through a second read channel, wherein, responsive to a control signal generated based, at least in part, on one or more parameters indicative of condition of the storage medium, the hybrid LDPC decoder is switchable between hard-decision LDPC decoding and soft-decision LDPC decoding.

Abstract: A system for providing data encoding includes: an encoder configured to encode message data with an encoding parity-check matrix having a parity part that is in lower-triangular form to generate an encoded message data, the encoded message data being for decoded by a decoder; wherein the encoding parity-check matrix is based on a decoding parity-check matrix that does not comprise any degree-1 node in a parity part of the decoding parity-check matrix; and wherein the system further comprises a non-transitory medium for storing the encoding parity-check matrix, wherein the non-transitory medium is a part of the encoder or is communicatively coupled to the encoder.

Abstract: Methods and circuits are disclosed for forward-error-correction (FEC) decoding. A plurality of symbols are received in an interleaved format of rows and columns of the symbols. A plurality of FEC decoding iterations are performed on the plurality of symbols. Each decoding iteration performs FEC decoding of the rows of the plurality of symbols and performs FEC decoding of the columns of the plurality of symbols. After performing the decoding iterations, rows in error and columns in error of the plurality of symbols are determined. In response to the determined rows in error and the determined columns in error matching a deadlock pattern, symbols at intersections of the determined rows and columns in error are determined. Bits of one or more symbols of the determined symbols are inverted. After the inverting of the bits, one or more of the FEC decoding iterations are performed.

Abstract: A method for matrix expansion is disclosed. In this method, a Progressive Edge Growth (“PEG”) expanding of an H matrix by a coder is used to provide an expanded H matrix. An Approximate Cycle Extrinsic Message Degree (“ACE”) expanding of the expanded H matrix by the coder is used to provide a parity check matrix for a code. The ACE expanding includes initializing a first index to increment in a first range associated with a PEG expansion factor, expanding each non-zero element in the expanded H matrix with a random shifted identity matrix for the first range, initializing a second index to increment in a second range associated with the first index and an ACE expansion factor, and performing an ACE detection for each variable node in the second range for the variable nodes of the parity check matrix. The coder outputs information using the parity check matrix.

Abstract: In one embodiment, a device is provided. The device includes a first formatting circuit configured to add zero padding bits to a received data block. An FEC encoder circuit is coupled to the first formatting circuit and is configured to determine parity bits for the data block at a first code rate. A second formatting circuit is coupled to the FEC encoder circuit and is configured to combine the parity bits with the data block and remove the zero padding bits to provide an FEC coded data block at a second code rate. The second code rate is less than the first code rate.

Abstract: An apparatus is disclosed. In this apparatus, at least one coder block has a parity check matrix. The parity check matrix comprises each element of an H matrix expanded by a Progressive Edge Growth (“PEG”) expansion factor and an Approximate Cycle Extrinsic Message Degree (“ACE”) expansion factor.

Abstract: A first systolic array receives an input set of time division multiplexed matrices from a plurality of channel matrices. In a first mode, the first systolic array performs triangularization on the input matrices, producing a first set of matrices, and in a second mode performs back-substitution on the first set, producing a second set of matrices. In a first mode, a second systolic array performs left multiplication on the second set of matrices with the input set of matrices, producing a third set of matrices. In a second mode, the second systolic array performs cross diagonal transposition on the third set of matrices, producing a fourth set of matrices, and performs right multiplication on the second set of matrices with the fourth set of matrices. The first systolic array switches from the first mode to the second mode after the triangularization, and the second systolic array switches from the first mode to the second mode after the left multiplication.

Abstract: A first systolic array receives an input set of time division multiplexed matrices from a plurality of channel matrices. In a first mode, the first systolic array performs triangularization on the input matrices, producing a first set of matrices, and in a second mode performs back-substitution on the first set, producing a second set of matrices. In a first mode, a second systolic array performs left multiplication on the second set of matrices with the input set of matrices, producing a third set of matrices. In a second mode, the second systolic array performs cross diagonal transposition on the third set of matrices, producing a fourth set of matrices, and performs right multiplication on the second set of matrices with the fourth set of matrices. The first systolic array switches from the first mode to the second mode after the triangularization, and the second systolic array switches from the first mode to the second mode after the left multiplication.

Abstract: A decoding circuit is disclosed that includes a decoding pipeline configured to receive a data block that includes a plurality of data symbols, encoded with a Reed-Solomon (RS) FEC coding thereafter further encoded by a second FEC coding. The data block also includes a first and second sets of FEC datagrams for correcting received words of the plurality of data symbols encoded with the RS FEC coding and second FEC coding, respectively. Each decoding stage of the pipeline is configured to decode the plurality of data symbols using the first and second sets of FEC datagrams. A post-processing circuit connected to an output of the pipelines is configured to perform bitwise RS decoding of ones of the plurality of data symbols in error.

Abstract: In one embodiment, a circuit for FEC decoding includes first and second syndrome calculation circuits, configured to calculate FEC syndromes for rows and columns of symbols in a de-interleaved format, respectively. A decoding circuit is configured to arrange the symbols into windows. Each window includes a plurality of sequential rows and sequential columns of the symbols in the de-interleaved format. The decoding circuit is configured to place N of the windows in a group and perform M decoding iterations of the windows in the group. In each decoding iteration, the decoding circuit performs FEC decoding of rows of each of the windows in the group followed by FEC decoding of columns of each of the windows in the group.

Abstract: In one embodiment, a Chien search circuit includes a plurality of evaluation circuits, each configured to sequentially evaluate possible roots ?i in a respective subset of possible roots of an error location polynomial (?(x)). Each evaluation circuit includes a respective sub-circuit for each of a plurality of coefficients ?i (0?i?T) of the error location polynomial ?(x) having T+1 coefficients. Each sub-circuit is configured to calculate one term of the error location polynomial for each possible root ?i in the respective subset of possible roots. Each evaluation circuit is configured to evaluate the error location polynomial for each possible root in the respective subset of possible roots, as a sum of the terms calculated by the plurality of sub-circuits.

Abstract: In one embodiment, a block code decoder is provided. The block code decoder includes a first decoder configured to decode Bose-Chaudhuri-Hochquenghem (“BCH”) coded data packets and a second decoder configured to receive and decode Reed-Solomon (“RS”) encoded data from the first decoder. The first decoder includes a first buffer configured to receive BCH encoded data and one or more BCH decoder circuits coupled to the first buffer. Each BCH decoder circuit decodes a plurality of BCH encoded bits in parallel. A second buffer is arranged to store the decoded BCH data. The second decoder includes a third buffer, arranged to receive the RS encoded data from the first decoder, one or more RS decoder circuits configured to decode a plurality of RS encoded bits in parallel, and a fourth buffer arranged to store RS payload data decoded by the RS decoder circuits.

Abstract: A first systolic array receives an input set of time division multiplexed matrices from a plurality of channel matrices. In a first mode, the first systolic array performs triangularization on the input matrices, producing a first set of matrices, and in a second mode performs back-substitution on the first set, producing a second set of matrices. In a first mode, a second systolic array performs left multiplication on the second set of matrices with the input set of matrices, producing a third set of matrices. In a second mode, the second systolic array performs cross diagonal transposition on the third set of matrices, producing a fourth set of matrices, and performs right multiplication on the second set of matrices with the fourth set of matrices. The first systolic array switches from the first mode to the second mode after the triangularization, and the second systolic array switches from the first mode to the second mode after the left multiplication.

Abstract: Multiple input multiple output (MIMO) receiver circuitry is described. In one circuit, input circuitry provides a matrix of unresolved symbols received from a plurality of receive antennas. Channel estimation circuitry constructs a plurality of channel matrices including at least two channel matrices corresponding first and second subcarriers, respectively. A preprocessing circuit receives input from the plurality of channel matrices and interleaves retrieved input into an input matrix. A first systolic array includes boundary cells and internal cells. The boundary cells and internal cells are configured to perform triangulation and back-substitution on the input matrix to produce an output matrix. A second systolic array performs right and left multiplication operations and cross-diagonal transpose on the output matrix to produce a weighted matrix.

Abstract: In one embodiment, a circuit for matrix decomposition is provided. The circuit includes an input circuit for receiving a first matrix. A permutation circuit is coupled to the input circuit and configured to interchange columns of the first matrix according to a selected permutation to produce a second matrix. A systolic array is coupled to the permutation circuit and configured to perform QR decomposition of the second matrix to produce a third matrix and a fourth matrix. A reverse permutation circuit is coupled to the systolic array and configured to interchange rows of the third matrix according to an inverse of the selected permutation to produce a first factor matrix and interchange rows of the fourth matrix according to the inverse of the selected permutation to produce a second factor matrix.

Abstract: A first systolic array receives an input set of time division multiplexed matrices from a plurality of channel matrices. In a first mode, the first systolic array performs triangularization on the input matrices, producing a first set of matrices, and in a second mode performs back-substitution on the first set, producing a second set of matrices. In a first mode, a second systolic array performs left multiplication on the second set of matrices with the input set of matrices, producing a third set of matrices. In a second mode, the second systolic array performs cross diagonal transposition on the third set of matrices, producing a fourth set of matrices, and performs right multiplication on the second set of matrices with the fourth set of matrices. The first systolic array switches from the first mode to the second mode after the triangularization, and the second systolic array switches from the first mode to the second mode after the left multiplication.

Abstract: A digital communication system includes a generator for generating a plurality of pulse trains, each having a different timing, and pre-compensation circuitry for synchronizing the plurality of pulse trains to a timing signal. The system also includes comparison circuitry for simultaneously comparing a received burst code signal to each of the plurality of pulse trains, where the burst code signal is synchronized to the timing signal, and a detector for detecting which of the pulse trains is a closest temporal match to the burst code signal. The pre-compensation circuitry operates to reduce acquisition time and keep PN code uncertainties within the range of the comparison circuitry.

Abstract: A method and apparatus for performing a recursion process on a data block for error correction. The disclosure describes concurrently operating pipelined sub-processes that decode the data block with error correction. The pipelined sub-processes are implemented as sub-circuits of an integrated circuit. The output data from each sub-process is stored for input by a subsequent sub-process of the pipelined sub-processes.

Abstract: Method and apparatus are described for determining when a convolution decoder is out of synchronization. Normalizations from a convolutional decoder are counted to provide a normalization count, and errors from the convolutional decoder are counted to provide an error count. One of the normalization count and the error count is compared to a first threshold associated with the selected one of the normalization count and the error count. The other of the normalization count and the error count is compared to a second threshold in response to meeting the first threshold, such as bit errors per X normalizations or normalizations per Y bit errors. From this latter comparison, an indicator is generated as to whether the convolutional decoder is synchronized or not.

Abstract: Method and apparatus for concatenated and interleaved turbo product code (TPC) encoding and decoding are described. Described are series concatenated and interleaved TPC encoders and decoders. One or more combinations of these encoders and decoders may be combined to provide a coder/decoder (CODEC). Such a CODEC may be used for communicating information between a computer and a network via a data channel.