Abstract: There is provided a method of recursive sequential list decoding of a codeword of a polar code comprising: obtaining an ordered sequence of constituent codes usable for the sequential decoding of the polar code, representable by a layered graph; generating a first candidate codeword (CCW) of a first constituent code, the first CCW being computed from an input model informative of a CCW of a second constituent code, the first constituent code and second constituent code being children of a third constituent code; using the first CCW and the second CCW to compute, by the decoder, a CCW of the third constituent code; using the CCW of the third constituent code to compute a group of symbol likelihoods indicating probabilities of symbols of a fourth (higher-layer) constituent code having been transmitted with a particular symbol value, and using the group of symbol likelihoods to decode the fourth constituent code.

Abstract: There is provided a method of sequential list decoding of an error correction code (ECC) utilizing a decoder comprising a plurality of processors. The method comprises: a) obtaining an ordered sequence of constituent codes usable for the sequential decoding of the ECC; b) executing, by a first processor, a task of decoding a first constituent code, the executing comprising: a. generating decoding candidate words (DCWs) usable to be selected for decoding a subsequent constituent code, each DCW associated with a ranking; b. for the first constituent code, upon occurrence of a sufficiency criterion, and prior to completion of the generating all DCWs and rankings, selecting, in accordance with a selection criterion, at least one DCW; c) executing, by a second processor, a task of decoding a subsequent constituent code, the executing comprising processing data derived from the selected DCWs to generate data usable for decoding a next subsequent constituent code.

Abstract: There is provided a method of obtaining one or more parity symbols (PS) of an encoding of information symbols (IS) according to a linear cyclic code, the method comprising: upon a permutation of information symbols (IS), generating data indicative of parity coefficients of a row of a generator matrix associated with the linear cyclic code, computing, for each given parity coefficient, a first data in accordance with, at least, the given parity coefficient and the first IS; updating, by the processing circuitry, for each given parity coefficient of the one or more parity coefficients, the first data, in accordance with, at least, the given parity coefficient and the respective IS; and upon meeting a parity completion criterion for a given parity coefficient, deriving a parity symbol from the respective first data, thereby obtaining the one or more parity symbols of the codeword of the linear cyclic code.

Abstract: A device, system and method for decoding a product code generated by encoding input data by a plurality of first and second dimension error correction codes. For each of a plurality of first dimension codewords, the first dimension input data codeword may be decoded using a first dimension error correction code and the first dimension codeword may be erased if errors are detected in the decoded first dimension codeword. For each of a plurality of second dimension codewords, the second dimension codeword may be decoded using a second dimension erasure correction code to recover an erasure in the second dimension codeword that was erased in the first dimension decoding.

Abstract: A device, system and method for decoding a product code generated by encoding input data by a plurality of first and second dimension error correction codes. For each of a plurality of first dimension codewords, the first dimension input data codeword may be decoded using a first dimension error correction code and the first dimension codeword may be erased if errors are detected in the decoded first dimension codeword. For each of a plurality of second dimension codewords, the second dimension codeword may be decoded using a second dimension erasure correction code to recover an erasure in the second dimension codeword that was erased in the first dimension decoding.

Abstract: A device system and method is provided for early termination of a decoding process performed at a receiving user device. A user-specific message may be received, from a communication channel shared by multiple user devices. The user-specific message may include an error correction codeword generated by shifting an original codeword by an offset codeword uniquely associated with a target user device. The error correction codeword may be shifted based on an offset codeword uniquely associated with the receiving user device. The received message may begin to be decoded. If the receiving device is the target device, the offsets respectively associated therewith are equal and cancel, and the original message is decoded to completion. If, however, the receiving device is not the target device, the offsets respectively associated therewith are not equal and combine to form an above threshold decoding error and decoding is terminated before completion.

Abstract: A device system and method is provided for early termination of a decoding process performed at a receiving user device. A user-specific message may be received, from a communication channel shared by multiple user devices. The user-specific message may include an error correction codeword generated by shifting an original codeword by an offset codeword uniquely associated with a target user device. The error correction codeword may be shifted based on an offset codeword uniquely associated with the receiving user device. The received message may begin to be decoded. If the receiving device is the target device, the offsets respectively associated therewith are equal and cancel, and the original message is decoded to completion. If, however, the receiving device is not the target device, the offsets respectively associated therewith are not equal and combine to form an above threshold decoding error and decoding is terminated before completion.

Abstract: A device system and method is provided for early termination of a decoding process performed at a receiving user device. A user-specific message may be received, from a communication channel shared by multiple user devices. The user-specific message may include an error correction codeword generated by shifting an original codeword by an offset codeword uniquely associated with a target user device. The error correction codeword may be shifted based on an offset codeword uniquely associated with the receiving user device. The received message may begin to be decoded. If the receiving device is the target device, the offsets respectively associated therewith are equal and cancel, and the original message is decoded to completion. If, however, the receiving device is not the target device, the offsets respectively associated therewith are not equal and combine to form an above threshold decoding error and decoding is terminated before completion.

Abstract: A device, system and method for decoding. A noisy version of an error correction codeword may be received, for example, over a noisy communication channel or retrieved from a memory device (e.g. a flash memory device). One or more symbol probabilities may be transformed, from an initial domain to a transformed domain, the symbol probabilities being one or more individual symbols of the received error correction codeword were transmitted as one or more symbols in candidate transmitted error correction codewords. In the transformed domain, a plurality of the transformed symbol probabilities may be composed to generate a combined coset probability defining the likelihood that the transmitted error correction codeword is associated with the individual symbols belongs to a particular one of a plurality of candidate cosets. A plurality of the coset probabilities for the plurality of respective cosets may be inverse transformed from the transformed domain to the initial domain.