An operating method of a low density parity check (LDPC) decoder, the operating method includes: initially updating codewords to variable nodes; determining an update order in which a plurality of variable node groups are updated, which is determined based on reliability of each of the variable node groups; executing local iterations including update of check nodes associated with a select variable node group among the variable node groups and update of the select variable node group based on the updated check nodes until all the variable node groups are updated based on the update order; performing syndrome check to determine whether LDPC decoding is successful, based on an operation of the updated variable nodes and a parity check matrix.

The present disclosure includes apparatuses and methods related to stopping criteria for layered iterative error correction. A number of methods can include receiving a codeword with an error correction circuit, iteratively error correcting the codeword with the error correction circuit including parity checking the codeword on a layer-by-layer basis and updating the codeword after each layer. Methods can include stopping the iterative error correction in response to a parity check being correct for a particular layer.

Provided is an optical transmission/reception device including an error correction decoding unit (36) for decoding a received sequence encoded with an LDPC code, in which the error correction decoding unit (36) is configured to perform decoding processing using a parity check matrix (70) of a spatially-coupled LDPC code, which includes a plurality of parity check sub-matrices (71) combined with each other, in which the decoding processing is windowed decoding processing that uses a window (80) over one or more parity check sub-matrices (71), and in which a window size of the window (80) and a decoding iteration count due to throughput and requested correction performance are variable and input from a control circuit (12) connected to the error correction decoding device (36).

An operating method of a low density parity check (LDPC) decoder, the operating method includes: initially updating codewords to variable nodes; determining an update order in which a plurality of variable node groups are updated, which is determined based on reliability of each of the variable node groups; executing local iterations including update of check nodes associated with a select variable node group among the variable node groups and update of the select variable node group based on the updated check nodes until all the variable node groups are updated based on the update order; performing syndrome check to determine whether LDPC decoding is successful, based on an operation of the updated variable nodes and a parity check matrix.

Provided herein is an error correction decoder and a memory system having the same. The error correction decoder includes a memory configured to store a hard decision value of a variable node. The decoder further includes a flipping function value generator configured to generate, in an i-th iteration, a first value based on a number of unsatisfied check nodes (UCNs) corresponding to the variable node, and to generate a flipping function value as (i) a difference between the first value and an offset value or (ii) a set value, wherein i is a non-negative integer. The decoder also includes a comparator configured to output, in the i-th iteration, a first signal indicating whether to flip or not flip the hard decision value of the variable node in the memory based on comparing the flipping function value to a flipping threshold value.

A computer-implemented method includes encoding an array of (p−1)×k symbols of data into a p×(k+r) array. The method includes p is a prime number, r≥1, and k≤p. The method includes each column in the p×(k+r) array has an even parity and symbol i in column r+j, for 0≤i≤p−1 and 0≤j≤r−1, is the XOR of symbols in a line of slope j taken with a toroidal topology modulo p in the k columns starting in symbol i of column 0.

A memory controller performs an error recovery operation. The controller performs a read operation on a select block using a select read level; decodes data associated with the read operation to generate a syndrome value; determines whether to stop, before a maximum number of iterations, the read operation and the decoding at the select read level, using the syndrome value; when it is determined to stop the read operation and the decoding at the select read level, selects a next read level in a sequence of read levels; and uses the next read level for a subsequent read operation.

The present disclosure includes apparatuses and methods related to stopping criteria for layered iterative error correction. A number of methods can include receiving a codeword with an error correction circuit, iteratively error correcting the codeword with the error correction circuit including parity checking the codeword on a layer-by-layer basis and updating the codeword after each layer. Methods can include stopping the iterative error correction in response to a parity check being correct for a particular layer.

Techniques are described herein to terminate a list decoding operation before its completion based on performing one or more error check processes. A transmitted codeword encoded using a polar code may include one or more error check vectors interspersed with one or more information vectors. Upon receiving the codeword, a decoder may perform a list decoding operation on the received codeword. Upon decoding one of the error check vectors, the decoder may determine whether at least one candidate path used in the successive cancellation list decoding operation passes an error check process based on the error check vector. If no candidate paths satisfy the error check process, the decoder may terminate the list decoding operation. In some examples, the decoder may recheck whether candidate paths satisfy the error check operation at intermediate positions between error check vectors. Such rechecking may occur while decoding information vectors.

Memory controllers, decoders and methods execute a hybrid decoding scheme. An initial iteration of decoding of a codeword is performed using a bit-flipping (BF) decoder or a min-sum (MS) decoder depending on whether or not an unsatisfied check (USC) count of the codeword is less than a threshold. For this initial iteration, the BF decoder is used when the USC count is less than the threshold, and MS decoder when the USC count is greater than or equal to the threshold. When decoding of the codeword is initially performed with the BF decoder, decoding continues with the BF decoder until a first set of conditions is satisfied or the codeword is successfully decoded. When decoding of the codeword is performed with the MS decoder, decoding continues with the MS decoder until a second set of conditions is satisfied.