A memory system includes a memory controller. The memory controller executes first calculation of obtaining a first degree to k-th degree error locator polynomials (1≤k<t) by using a syndrome, determines whether error locations can be calculated by the error locator polynomials up to the k-th degree, obtains an initial value of a parameter to be used for second calculation of obtaining error locator polynomials up to t-th degree when it is determined that the error locations cannot be calculated, executes the second calculation using the initial value, calculates the error locations by using an error locator polynomial determined to be able to calculate the error locations among the first degree to k-th degree error locator polynomials or by using error locator polynomials obtained in the second calculation, and corrects errors in the calculated error locations.

A method for error correction comprises receiving data at a first device, and decoding, by decoder circuitry of the first device, the data. Decoding the data comprises determining a first error location within the data, and determining a first error magnitude within the data in parallel with determining the first error location. Decoding the data further comprises performing error correction to generate the decoded data based on the first error location and the first error magnitude. The method further comprises transmitting the decoded data to a second device.

A system comprises a forward error correction decoder comprising syndrome computation circuitry, key-equation solver circuitry, and search and evaluator circuitry. The syndrome computation circuitry may comprise a plurality of syndrome compute units connected in parallel. The syndrome computation circuitry may be dynamically configurable to vary a quantity of the syndrome compute units used for processing of a codeword based on conditions of a channel over which the codeword was received. The syndrome computation circuitry may be operable to use a first quantity of the syndrome compute units for processing of a first codeword received over the channel when the channel is characterized by a first bit error rate and a second quantity of the syndrome compute units for processing of a second codeword received over the channel when the channel is characterized by a second bit error rate.

A Reed-Solomon decoder circuit includes: a syndrome calculator circuit to compute syndrome values for a first codeword and a second codeword sequentially supplied to the syndrome calculator circuit, where last symbols of the first codeword overlap with first symbols of the second codeword during an overlap clock cycle between: a first plurality of non-overlap clock cycles during which the first codeword is supplied to the syndrome calculator circuit; and a second plurality of non-overlap clock cycles during which the second codeword is supplied to the syndrome calculator circuit; an error locator and error evaluator polynomial calculator circuit; an error location and error value calculator circuit; an error counter; and an error corrector circuit to correct the errors in the first codeword and the second codeword based on error counts and the error magnitudes computed by an error evaluator circuit.

A multi-port, multi-mode Reed Solomon (RS) forward error correction system includes a plurality of data in lines, each associated with a data port. The system includes a syndrome block (SDM) that has a plurality of syndrome slices and a SDM switching logic. An input of a SDM slice couples with a data in line from the plurality of data in lines. The switching logic couples with an interface port width (IFW) line a mode line. The IFW line identifies a number of data in lines tied together and the mode line to identify a RS mode. A reformulated inversionless Berlekamp-Massey (RiBM) block has a plurality of RiBM slices and a RiBM switching logic. A Chien Forney (ChFr) block has a plurality of ChFr slices. An error evaluation magnitude (ErEval) block has a plurality of ErEval slices. A plurality of adders couple with an output of a corresponding ErEval slice.

An ECC decoder includes a syndrome calculation block, a fast path controller, a KES block, a CSEE block, an UED, and a multiplexer. The KES block includes a plurality of KES-stages to calculate and output an error location/magnitude polynomial of a syndrome outputted from the syndrome calculation block. Each of a second to last KES-stages of the plurality of KES-stages receives the error location/magnitude polynomial from the previous KES-stage to output an error location/magnitude polynomial generated by an additional calculating operation. The additionally calculated error location/magnitude polynomial is not transmitted to the next KES-stage but directly outputted when an error location and an error magnitude are identified by the additionally calculated error location/magnitude polynomial.

A memory system includes a memory controller. The memory controller executes first calculation of obtaining a first degree to k-th degree error locator polynomials (1≤k<t) by using a syndrome, determines whether error locations can be calculated by the error locator polynomials up to the k-th degree, obtains an initial value of a parameter to be used for second calculation of obtaining error locator polynomials up to t-th degree when it is determined that the error locations cannot be calculated, executes the second calculation using the initial value, calculates the error locations by using an error locator polynomial determined to be able to calculate the error locations among the first degree to k-th degree error locator polynomials or by using error locator polynomials obtained in the second calculation, and corrects errors in the calculated error locations.

Provided is a memory system comprising a plurality of memory components; and a controller in communication with the plurality of memory components and configured to perform error correction code (ECC) decoding on a received word read from the plurality of memory components. The ECC decoding is configured to (i) detect one or more random errors in a portion of the received word, the portion corresponding to one of the components within the plurality, and (ii) correct the detected random errors; and when the correcting of the detected random errors fails, iteratively marking symbols in the remaining portions of the received word as erasures.

A multi-port, multi-mode Reed Solomon (RS) forward error correction system includes a plurality of data in lines, each associated with a data port. The system includes a syndrome block (SDM) that has a plurality of syndrome slices and a SDM switching logic. An input of a SDM slice couples with a data in line from the plurality of data in lines. The switching logic couples with an interface port width (IFW) line a mode line. The IFW line identifies a number of data in lines tied together and the mode line to identify a RS mode. A reformulated inversionless Berlekamp-Massey (RiBM) block has a plurality of RiBM slices and a RiBM switching logic. A Chien Forney (ChFr) block has a plurality of ChFr slices. An error evaluation magnitude (ErEval) block has a plurality of ErEval slices. A plurality of adders couple with an output of a corresponding ErEval slice.

An error correction code (ECC) decoder includes a syndrome calculation block and a path controller. The syndrome calculation block is configured to perform a syndrome calculation for generating a syndrome from a codeword. The path controller is configured to output data transmitted through first to third paths. The first path is a path for transmitting the codeword to the path controller when no error is detected. The second path includes a single-error decoding logic circuit, and the single-error decoding logic circuit corrects a single error of the codeword to transmit the corrected codeword to the path controller through the second path. The third path includes a multi-error decoding logic circuit, and the multi-error decoding logic circuit corrects at least two errors of the codeword to transmit the corrected codeword to the path controller.