Embodiments of the invention provide a check node processing unit implemented in a decoder for decoding a signal, the check node processing unit being configured to receive at least three input messages and to generate at least one output message, wherein the check node processing unit comprises: a syndrome calculator (31) configured to determine a set of syndromes from said at least three input messages using at least two elementary check node processors (311), each syndrome comprising a symbol, a reliability metric associated with said symbol, and a binary vector; a decorrelation unit (33) configured to determine, in association with at least an output message, a set of candidate components from said set of syndromes, each candidate component comprising a symbol and a reliability metric associated with said symbol, said set of candidate components comprising one or more pairs of components comprising a same symbol; and a selection unit (35) configured to determine at least an output message by selecting components comprising distinct symbols from the set of candidate components associated with said at least an output message.

Embodiments of the invention provide a device for determining a coded modulation scheme, said coded modulation scheme being defined by at least one non-binary error correcting code containing at least one non-binary parity-check equation, a modulation scheme, and a modulation mapping, wherein the device comprises: a calculation unit (31) configured to determine one or more candidate modulation mappings and one or more candidate parity-check equations defining said at least one non-binary error correcting code, each set of a candidate modulation mapping and at least one candidate parity-check equation providing codeword vectors and being associated with one or more metrics, each metric being defined by a number of distinct pairs of codeword vectors having an Euclidean distance of a defined value; and a selection unit (35) configured to select one candidate modulation mapping and at least one candidate parity-check equation according to an optimization criterion applied to said one or more metrics.

An operation method of a memory controller includes: reading a second data from memory cells when a hard decision error correction decoding operation based on a first data read from the memory cells fails; calculating a LLR of each bit-data included in the first data by using the first and second data; and performing a soft decision error correction decoding operation based on the LLR, wherein the memory cells include a first and second memory cell, wherein the first data includes first-bit-data read from the first and second memory cell, wherein the second data includes second-bit-data read from the first and second memory cell, wherein the LLR is a LLR of the first-bit-data read from the first memory cell calculated based on the first bit and a second bit read from the first memory cell and a first bit and a second bit read from the second memory cell.

A method and data storage system receives a confidence vector for a non-binary symbol value read from a memory cell of a non-volatile memory device, where the confidence vector includes a first plurality of confidence values and transforms the first plurality of confidence values into a first plurality of likelihood values using a forward tensor-product transform. A respective binary message passing decoding operation is performed with each of the first plurality of likelihood values to generate a second plurality of likelihood values, and the second plurality of likelihood values are transformed into a second plurality of confidence values of the confidence vector using a reverse tensor-product transform.

A data storage system and method are provided for storing data in non-volatile memory devices. Binary data is received for storage in a non-volatile memory device. The binary data is converted into non-binary data comprising base-X values, where X is an integer greater than two. The non-binary data is encoded to generate a codeword and the codeword is written to a wordline of the non-volatile memory device.

A device includes a memory configured to store syndromes, a first data processing unit coupled to the memory, and a second data processing unit coupled to the memory. The first data processing unit is configured to process a first value corresponding to a first symbol of data to be decoded. The second data processing unit is configured to process a second value corresponding to a second symbol of the data. Syndrome aggregation circuitry is coupled to the first data processing unit and to the second data processing unit. The syndrome aggregation circuitry is configured to combine syndrome change decisions of the first data processing unit and the second data processing unit.

An operation method of a LPC decoder includes: initializing variable nodes of a Tanner graph representing a parity check matrix; performing a check node update to check nodes of the Tanner graph based on variable node values of the variable nodes; performing a variable node update when there are USC nodes among the updated check nodes as a result of the check node update; and repeating the performing of the check node update and the variable node update when there are USC nodes as the result of the check node update, wherein the performing of the variable node update includes: selecting among the variable nodes a predetermined number of variable nodes having a USC value greater than a threshold; and flipping the variable node values of the selected variable nodes, and wherein the USC value is a number of the USC nodes linked to one of the variable nodes.

A memory system includes a non-volatile memory. A coding unit generates a codeword by performing coding of a graph code using a graph. A side of the graph is associated with a block that is a part of user data and that has one or more symbols at which component codes intersect one another. A control unit stores the codeword in the non-volatile memory. Error correction is performed on the user data in accordance with the codeword.

An embodiment of an electronic apparatus comprises one or more substrates, and logic coupled to the one or more substrates, the logic to detect unreliable messages between check nodes and variable nodes in association with an error correction operation, determine respective degrees of unreliability for the unreliable messages, and reduce an influence of the unreliable messages on the error correction operation, as compared to an influence of reliable messages between the check nodes and the variables nodes, based on the determined respective degrees of unreliability. Other embodiments are disclosed and claimed.

A system and method for memory error detection and recovery in a decoding system in CXL components is presented. The method includes receiving, into a first decoder within the decoding system, a memory transfer block (MTB) having data and parity information, and having a vertical portion and a horizontal portion, performing error detection and correction on the vertical portion of the MTB using binary hamming code logic within the first decoder; and upon performing error detection and correction in the first decoder, then forwarding MTB to a second decoder, and performing error detection and correction, via the second decoder, on the horizontal portion of the MTB using a non-binary hamming code logic within the second decoder such that the first and second decoders perform the error detection and correction on the vertical and horizontal portions of the MTB in a serial manner.