A syndrome calculation circuit receives input data r(x) including data and a parity bit and having a code length n of (2.sup.m-1) bits at maximum which is represented by a Galois field GF(2.sup.m), and performs syndrome calculation so as to meet

s≡α.sup.i+α.sup.j

z≡(α.sup.i+β).sup.−1+β.sup.−1+(α.sup.j+β).sup.−1+β.sup.1   (A)

thereby calculating syndromes s and z. An error position polynomial coefficient calculation circuit calculates the coefficient of an error position polynomial to obtain s×z by multiplying s and z by one multiplier. After that, 2-bit error data positions i and j are specified. Errors at the error data positions i and j of the input data are corrected.

An error correction device according to the technical idea of the present disclosure includes a syndrome generation circuit configured to receive data and generate a plurality of syndromes for the data, a partial coefficient generation circuit configured to generate partial coefficient information on a part of a coefficient of an error location polynomial by using the data while the plurality of syndromes are generated, an error location determination circuit configured to determine the coefficient of the error location polynomial based on the plurality of syndromes and the partial coefficient information, and obtain a location of an error in the data by using the error location polynomial, and an error correction circuit configured to correct the error in the data according to the location of the error.

A method includes, storing a set of valid codewords including: a first valid functional codeword representing a functional state of a controller subsystem; a first valid fault codeword representing a fault state of the controller subsystem and characterized by a minimum hamming distance from the first valid functional codeword; a second valid functional codeword representing a functional state of a controller; and a second valid fault codeword representing a fault state of the controller; in response to detecting functional operation of the controller subsystem, storing the first valid functional codeword in a first memory; in response to detecting a match between contents of the first memory and the first valid functional codeword, outputting the second valid functional codeword; in response to detecting a mismatch between contents of the first memory and every codeword in the first set of valid codewords, outputting the second valid fault codeword.

The disclosed invention provides system and method for multi-path mesh network communications. The network system utilizes multiple communication paths and linearly encoded and disassembled packets through mathematical coding techniques that respectively travel the communication paths. The system includes an encoder, a transmitter, a decoder and a receiver. The encoder receives data from an external source and linearly encodes and simultaneously disassembles the data to generate copackets. None of the individual copackets contain decodable information of the data. The transmitter is coupled to the multiple communication paths and respectively transmits the copackets through different communication paths. The receiver receives the copackets transmitted through the communication paths. The decoder decodes available copackets and reassembles the data from the available copackets if a number of the available copackets are no less than a mathematically calculated number. The reassembled data has the complete information of the data originally transmitted.

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.

The disclosed invention provides system and method for multi-path mesh network communications. The network system utilizes multiple communication paths and linearly encoded and disassembled packets through mathematical coding techniques that respectively travel the communication paths. The system includes an encoder, a transmitter, a decoder and a receiver. The encoder receives data from an external source and linearly encodes and simultaneously disassembles the data to generate copackets. None of the individual copackets contain decodable information of the data. The transmitter is coupled to the multiple communication paths and respectively transmits the copackets through different communication paths. The receiver receives the copackets transmitted through the communication paths. The decoder decodes available copackets and reassembles the data from the available copackets if a number of the available copackets are no less than a mathematically calculated number. The reassembled data has the complete information of the data originally transmitted.

A method includes, storing a set of valid codewords including: a first valid functional codeword representing a functional timeout state of a second controller; a first valid fault codeword representing a fault timeout state of the second controller and characterized by a minimum hamming distance from the first valid functional codeword; a second valid functional codeword representing a functional state of a system; and a second valid fault codeword representing a fault state of the system; in response to detecting receipt of a safety message from the second controller within a predefined time quantum, storing the first valid functional codeword in a first memory; in response to detecting a match between contents of the first memory and the first valid functional codeword, outputting the second valid functional codeword; in response to detecting a mismatch between contents of the first memory and every codeword in the first set of valid codewords, outputting the second valid fault codeword.

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.

The disclosed invention provides system and method for multi-path mesh network communications. The network system utilizes multiple communication paths and linearly encoded and disassembled packets through mathematical coding techniques that respectively travel the communication paths. The system includes an encoder, a transmitter, a decoder and a receiver. The encoder receives data from an external source and linearly encodes and simultaneously disassembles the data to generate copackets. None of the individual copackets contain decodable information of the data. The transmitter is coupled to the multiple communication paths and respectively transmits the copackets through different communication paths. The receiver receives the copackets transmitted through the communication paths. The decoder decodes available copackets and reassembles the data from the available copackets if a number of the available copackets are no less than a mathematically calculated number. The reassembled data has the complete information of the data originally transmitted.

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.