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: Method and apparatus for signal processing to minimize the peak to average power ratio of an Orthogonal Frequency Division Multiplexing (“OFDM”) or Orthogonal Frequency Division Multiple Access (“OFDMA”) signal with bounded error vector magnitude for an integrated circuit are described. An Active Constellation Extension (“ACE”) iteration, using a constellation points adjustment module, is performed. Symbols outside of a bounded region after the ACE iteration are identified. The bounded region is determined responsive to an error vector magnitude target. The symbols identified are translated to the bounded region.

Abstract: Approaches for Cholesky decomposition of a matrix are described. A first circuit is configured to generate an inverse square root of an input value. A second circuit is configured to generate a product of a value output by the first circuit and provided at a first input and a value provided at a second input. A third circuit is configured to generate a difference between a value provided at the first input and a value provided at the second input of the third circuit. The first input of the third circuit is coupled to the output of the second circuit. A control circuit is configured to iteratively distribute a plurality of values of the matrix and the outputs of the first, second, and third circuits to the inputs of the first, second, and third circuits such that the Cholesky decomposition of the matrix is output by the third circuit.

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 embodiment of a method for decoding is disclosed. For this embodiment of the method, a decoder is limited to a set number of iterations for a decoding sequence. The set number of iterations is selected to be less than an optimal number of iterations for an optimal bit error rate (“BER”) resulting in a BER penalty. Inner loop decoding operations are performed within the decoder for the set number of iterations. Reliability information is output from the decoder to a data slicer. A symbol stream is output from the data slicer responsive to the reliability information.

Abstract: Methods for matrix processing and devices therefor are described. A systolic array in an integrated circuit is coupled to receive a first matrix as input; and is capable of operating in two modes, namely a triangularization mode and a back-substitution mode. The systolic array, when in a triangularization mode, is coupled to triangularize the first matrix to provide a second matrix. When in a back-substitution mode, the systolic array is coupled to invert the second matrix.

Abstract: Nulling a cell of a complex matrix is described. A complex matrix and a modified Givens rotation matrix are obtained for multiplication by a processing unit, such as a systolic array or a CPU, for example, for the nulling of the cell to provide a modified form of the complex matrix. The modified Givens rotation matrix includes complex numbers c*, c, ?s, and s*, wherein the complex number s* is the complex conjugate of the complex number s, and wherein the complex number c* is the complex conjugate of the complex number c. The complex numbers c and s are associated with complex numbers of the complex matrix including the cell to be nulled. The modified form is then output by the processing unit. The modified Givens rotation matrix may be implemented as a systolic array or otherwise used for processing complex numbers or matrices.

Abstract: A decoder, such as for example an MMSE MIMO decoder, and a method for decoding are described. An input channel matrix is obtained, and an extended channel matrix of the input channel matrix is generated. The extended channel matrix is triangularized to provide a triangularized matrix, and the triangularized matrix is inverted to provide an inverted triangular matrix. A left matrix multiplication result matrix associated with multiplication of the input channel matrix and the inverted triangular matrix is generated, and a weight matrix from the left matrix multiplication result matrix and the inverted triangular matrix is generated. A received symbols matrix is obtained, and a weighted estimation is generated and output using the weight matrix and the received symbols matrix to provide an estimate of a transmit symbols matrix for output of estimated data symbols.

Abstract: An embodiment of a method for decoding is disclosed. For this embodiment of the method, a decoder is limited to a set number of iterations for a decoding sequence. The set number of iterations is selected to be less than an optimal number of iterations for an optimal bit error rate (“BER”) resulting in a BER penalty. Inner loop decoding operations are performed within the decoder for the set number of iterations. Reliability information is output from the decoder to a data slicer. A symbol stream is output from the data slicer responsive to the reliability information.

Abstract: A systolic array for Cholesky decomposition of an N×N matrix is described. A plurality of processing cells, including a corner cell, N?1 boundary cells, and (N2?3N+2)/2 internal cells, are arranged into N?1 rows and N columns of processing cells. Each row of processing cells is configured to calculate elements of a respective column of a lower triangular output matrix. Each processing cell of each row is configured to determine a value of a respective element of the lower triangular output matrix using a value of an element calculated in a previous processing cell of the row.

Abstract: In an embodiment of an equalizer, a demodulator for MMSE-SIC receives a symbol vector to provide first information. A decoder receives the first information to provide second information to the demodulator. The decoder iteratively processes the first information to provide the second information. The demodulator and decoder are coupled in a loop for feeding back the second information for iteratively refining the first information. A detection-cancellation block of the demodulator receives the symbol vector to provide an equalized vector. A channel pre-processor block of the demodulator receives an initial vector output of the detection-cancellation block for the symbol vector for a demodulating-decoding iterative sequence to provide a weight vector. The channel pre-processor block provides an approximation using a fixed matrix to generate the weight vector. The detection-cancellation block receives the weight vector for equalization of the symbol vector in order to provide the equalized vector.

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: A method, machine-readable medium, and systolic array for left matrix multiplication of a first matrix and a second matrix are described. The first matrix is a triangular matrix, and a cross-diagonal transpose of the first matrix is loaded into a triangular array of cells in an integrated circuit. A cross-diagonal transpose of the second matrix is input into the triangular array of cells for multiplication with the cross-diagonal transpose of the first matrix to produce an interim result. The interim result is cross-diagonally transposed to provide a left matrix multiplication result, which is stored or otherwise output.