A method of decoding a received message includes: determining a weighting vector corresponding to at least one bit of the received message according to a syndrome and a parity check matrix; determining a bit state of the bit according to a bit value of the bit; changing the bit state according to the weighting vector and a flipping threshold, wherein a change range of the bit state is variable; and flipping the bit according to the bit state.

A syndrome calculation circuit includes a matrix product calculation circuit. The matrix product calculation circuit is configured to generate syndrome bits in a composite field by calculating a matrix product of input data bits and a first arithmetic matrix. The first arithmetic matrix is a matrix product of a basis conversion matrix for converting a data string from a Galois field to the composite field and a second arithmetic matrix, which is at least a part of a parity check matrix.

A method and apparatus for decoding syndromes of a quantum error correction code is disclosed. The method includes the steps of receiving syndrome data for a plurality of quantum error correction rounds performed on a plurality of qubits; identifying a plurality of first blocks within the syndrome data, wherein each first block has a respective first central block surrounded by one or more respective first buffer blocks; decoding each first block to obtain a first committed correction for each respective first central block; identifying a plurality of second blocks within the syndrome data, wherein each second block comprises at least part of at least one first buffer block; and decoding each second block to obtain a second committed correction for each second block. An apparatus including a plurality of block decoders and a process manager is disclosed.

The present invention is directed to data communication systems and methods thereof. According to various embodiments, the present invention provides a communication with a reconfigurable forward-error-correction (FEC) module. The FEC module processes data received from two or more communication lanes, and depending on the mode of operation, the FEC module can combine data from the two or more communication lanes and perform error correction on the combined data, or the FEC module can processes data from the two communications lanes separately and perform error correction independently for the each of the data communication lanes. There are other embodiments as well.

Methods, systems, and devices for managing error control information using a register are described. A memory device may store, at a register, an indication of whether the memory device has detected an error included in or otherwise associated with data requested from a host device. The memory device may determine to store the indication based on whether a communication protocol is enabled or disabled, and whether an error control configuration is enabled or disabled. The host device may request information from the register of the memory device, and the memory device may output the indication of whether the error was detected in response to the request.

A memory system according to an embodiment includes a nonvolatile memory and a memory controller. The nonvolatile memory stores data encoded by using an error correcting code for correcting n-bit errors(n is an integer of 3 or more) or less. The memory controller reads a received word from the nonvolatile memory, calculates a syndrome by using the read received word, estimates the number of bit errors by using the syndrome. When the number of bit errors is 2 or 3, the memory controller calculates an inverse element of a value calculated based on the syndrome, executes, by using the inverse element, variable transformation on a variable of an error locator polynomial corresponding to the number of bit errors and calculation of a root of a transformed polynomial obtained by transforming the error locator polynomial according to the variable transformation, executes variable inverse transformation on the root of the transformed polynomial to obtain the root of the error locator polynomial, and corrects the error in the error location corresponding to the root of the error locator polynomial.

A Reed-Solomon encoder that supports multiple code words is provided. The encoder circuit may include partial syndrome calculation circuitry, three matrix multiplication circuits, and two adder circuits. The partial syndrome calculation circuitry may receive a message and generate partial syndromes. The first matrix multiplication circuit may multiply a lower portion of the partial syndromes by a small Lagrange matrix to produce a small parity symbol vector. The second matrix multiplication circuit may multiply the small parity symbol vector by a Vandermonde matrix to produce a product vector. The first adder circuit may add the product vector to an upper portion of the partial syndromes to produce a sum vector. The third matrix multiplication circuit may multiply the sum vector by a large Lagrange matrix to produce a large product vector. The large product vector may be selectively combined with the small parity symbol vector to generate final parity check symbols.

An apparatus for correcting at least one bit error within a coded bit sequence includes an error syndrome generator and a bit error corrector. The error syndrome generator determines the error syndrome of a coded bit sequence derived by a multiplication of a check matrix with a coded bit sequence.

An apparatus includes an interface, main and secondary processing modules, and circuitry. The interface is configured to receive input data to be processed in accordance with a GLDPC code defined by a parity-check-matrix including multiple sub-matrices, each sub-matrix including a main diagonal and one or more secondary diagonals, and each of the main and secondary diagonals includes N respective block matrices. The main processing module is configured to calculate N first partial syndromes based on the input data and on the block matrices of the main diagonals. The secondary processing module is configured to calculate N second partial syndromes based on the input data and on the block matrices of the secondary diagonals. The circuitry is configured to produce N syndromes by respectively combining the N first partial syndromes with the N second partial syndromes, and to encode or decode the input data, based on the N syndromes.

The present embodiments relate to Reed-Solomon encoding, and to circuitry for performing such encoding, particularly in an integrated circuit. A Reed-Solomon encoder circuit may receive a message with data symbols and compute a partial syndrome vector by multiplying the data symbols with a first matrix. The Reed-Solomon encoder circuit may further compute parity check symbols by solving a system of linear equations that includes the partial syndrome vector and a second matrix. As an example, the second matrix may be decomposed into a lower triangular matrix and an upper triangular matrix, and the parity check symbols may be computed by performing a forward substitution and a backward substitution using the lower and upper triangular matrices. The Reed-Solomon encoder circuit may generate a Reed-Solomon code word by combining the data symbols and the parity check symbols, and provide the Reed-Solomon code word at an output port.