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 method includes communicating data in a channel. Received symbols for the data correspond to points of a received symbol space respectively. First and second dimensions of the received symbol space correspond to a real part and an imaginary part of the received symbols respectively. A first received symbol for the data is obtained. A first region of the received symbol space for the first received symbol is determined. A first regression model associated with the first region and a first bit of the first received symbol is retrieved from a storage. The first regression model includes a plurality of regressors. A first log-likelihood ratio (LLR) for the first bit of the first received symbol is estimated using the first regression model.

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: 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: An encoder module includes P/L parity shift registers that are sequentially coupled, wherein an input of a first parity shift register of the parity shift registers is coupled to the input of the encoder module, an output of the last parity shift register of the parity shift registers is coupled to the output of the encoder module, each of the parity shift registers being configured to store L parity digits. The encoder module also includes a feedback circuit comprising P/L parity generation modules, wherein each of the parity generation modules is coupled to an output of a corresponding one of the parity shift registers by a switch and also coupled to the input of the first parity shift register, wherein each of the parity generation modules is configured to generate L parity digits for transmission to the input of the first parity shift register when its corresponding switch is closed.

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: An encoder module includes P/L parity shift registers that are sequentially coupled, wherein an input of a first parity shift register of the parity shift registers is coupled to the input of the encoder module, an output of the last parity shift register of the parity shift registers is coupled to the output of the encoder module, each of the parity shift registers being configured to store L parity digits. The encoder module also includes a feedback circuit comprising P/L parity generation modules, wherein each of the parity generation modules is coupled to an output of a corresponding one of the parity shift registers by a switch and also coupled to the input of the first parity shift register, wherein each of the parity generation modules is configured to generate L parity digits for transmission to the input of the first parity shift register when its corresponding switch is closed.

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 pipeline Fast Fourier Transform (“FFT”) architecture for a programmable device is described. A first Radix-2 butterfly stage is coupled to receive a first input, configured to provide a first output responsive thereto, and configured to truncate at least one Least Significant Bit of the first output. A delay and swap stage is coupled to receive the first output and configured to provide a second output. A second Radix-2 butterfly stage is coupled to receive the second output and a second input, configured to provide a third output responsive thereto, and configured to truncate at least one Most Significant Bit of the third output. The first Radix-2 butterfly stage and the second Radix-2 butterfly stage are implemented in digital signal processing slices of a programmable device.

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 method of accessing a memory of a trellis decoder. The method comprises the steps of writing a first block of data associated with a trellis function to a first memory block; writing a second block of data associated with the trellis function to a second memory block; simultaneously writing a third block of data to a third memory block and reading the second block of data from the second memory block to generate training data; and simultaneously reading data to be decoded from the first memory block and writing a fourth block of data to the first memory block and generating training data associated with the third block of data. A circuit for accessing a memory of a trellis decoder is also described.

Abstract: A method of buffering data in a circuit processing data in both a natural address order and a modified address order is described. The method comprises the steps of storing a first block of data according to a first addressing order of a natural address order or a modified address order; reading the first block of data stored in a buffer according to the other addressing order of the natural address order and the modified address order; and simultaneously writing a second block of data to the buffer in the other addressing order while reading the first block of data stored in a buffer according to the other addressing order.

Abstract: Each array in a sequence of arrays is reordered. A first port receives in a first serial order a number of values in each array in the sequence and a second port transmits the values in a different second serial order. For each value in each array in the sequence, the address generator generates an address within a range of zero through one less than the number of values in the array. For each address from the generator, the memory performs an access to a location corresponding to the address in the memory. The access for each address includes a read from the location before a write to the location. For each array in the sequence, the writes for the addresses serially write the values of the array in the first serial order and the reads for the addresses serially read the values in the second serial order.

Abstract: Various approaches for performing a fast-Fourier transform (FFT) of N input data elements using a radix K decomposition of the FFT are disclosed (K>=2, and N>=8). In one approach, N/K input data elements are written to respective ones of K addressable memories, and N/K*logK N passes are performed on the input data. Each pass includes reading K data elements in parallel from the K addressable memories using the respectively generated addresses, the K data elements being in a first order corresponding to the respective memories; permuting the first order of K data elements into a second order of K data elements; performing a radix K calculation on the second order of K data elements, resulting in corresponding result data elements in the second order; permuting the second order of K result data elements into the first order; and writing the K result data elements in parallel to the corresponding K addressable memories using the respective addresses.

Abstract: Crest factor reduction in a multiband transmitter is described. Component signals (xi[n]) are respectively obtained from constituent signals. The component signals (xi[n]) are respectively associated with sub-bands. A superposed signal associated with the component signals (xi[n]) is clipped to obtain a clipping noise error signal. The clipping noise error signal is applied to the component signals (xi[n]) using a least squares estimation to project clipping noise error onto the sub-bands.