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.