One example of layer-by-layer error correction can include iteratively error correcting the codeword on a layer-by-layer basis with the first error correction circuit in a first mode and determining on the layer-by-layer basis whether a number of parity errors in a particular layer is less than a threshold number of parity errors. The codeword can be transferred to a second error correction circuit when the number of parity errors is less than the threshold number of parity errors. The codeword can be iteratively error corrected with the first error correction circuit in a second mode when the number of parity errors is at least the threshold number of parity errors. The threshold number of parity errors can be at least partially based on an adjustable code rate of the first error correction circuit or the second error correction circuit.

A decoding method and device are provided. The method includes: decoding grouped original data in parallel by a first decoding unit to obtain grouped decoded data; decoding merged grouped decoded data by a second decoding unit to obtain decoded data; and if the sum of the lengths of the decoded data is an integer multiple of an upper limit of the decoding times of the second decoding unit, updating the first decoding unit and the second decoding unit, and if the sum of the lengths of the decoded data is not an integer multiple of the upper limit of the decoding times of the second decoding unit, updating the second decoding unit to obtain the decoded data again, until the sum of the lengths of the decoded data is equal to a decoding length, and merging the decoded data to serve as a decoding result of the original data.

A memory system includes a non-volatile memory and a memory controller. The memory controller is configured to read a received word from the non-volatile memory, estimate noise by using a plurality of different models for estimating the noise included in the received word to obtain a plurality of noise estimation values, select one noise estimation value from the plurality of noise estimation values, update the received word by using a value obtained by subtracting the selected noise estimation value from the read received word, and decode the updated received word by using a belief-propagation method.

A method for Bose-Chaudhuri-Hocquenghem (BCH) soft error decoding includes receiving a codeword x, wherein the received codeword x has τ=t+r errors for some r≥1; computing a minimal monotone basis {λ.sub.i(x)}.sub.1≤i≤r+1.Math.F[x] of an affine space V={λ(x)∈F[x]:λ(x).Math.S(x)=λ′(x) (mod x.sup.2t), λ(0)=1, deg(λ(x)≤t+r}, wherein λ(x) is an error locator polynomial and S(x) is a syndrome; computing a matrix A≡(λ.sub.j(β.sub.i)).sub.i∈[w],j∈[r+1], wherein W={β.sub.1, . . . , β.sub.w} is a set of weak bits in x; constructing a submatrix of r+1 rows from sub matrices of r+1 rows of the subsets of A such that the last column is a linear combination of the other columns; forming a candidate error locating polynomial using coefficients of the minimal monotone basis that result from the constructed submatrix; performing a fast Chien search to verify the candidate error locating polynomial; and flipping channel hard decision at error locations found in the candidate error locating polynomial.

A decoding method adopting an algorithm with weight-based adjusted parameters and a decoding system are provided. The decoding method is applied to a decoder. M×N low density parity check codes (LDPC codes) having N variable nodes and M check nodes are generated from input signals. In the decoding method, information of the variable nodes and the check nodes is initialized. The information passed from the variable nodes to the check nodes is formed after multiple iterations. After excluding a connection to be calculated, a product of the remaining connections between the variable nodes and the check nodes is calculated. Next, an estimated first minimum or an estimated second minimum can be calculated with multi-dimensional parameters. The information passed from the check nodes to the variable nodes can be updated for making a decision.

A data processing device includes a plurality of variable nodes configured to receive and store a plurality of target bits; a plurality of check nodes each configured to receive stored target bits from one or more corresponding variable nodes of the plurality of variable nodes, check whether received target bits have an error bit, and transmit a check result to the corresponding variable nodes; and a group state value manager configured to determine group state values of variable node groups into which the plurality of variable nodes are grouped.

Disclosed are devices, systems and methods for precoding and decoding polar codes using local feedback are described. One example method for improving an error correction capability of a decoder includes receiving a noisy codeword vector of length n, the codeword having been generated based on a concatenation of a convolutional encoding operation and a polar encoding operation and provided to a communication channel prior to reception by the decoder, performing a successive-cancellation decoding operation on the noisy codeword vector to generate a plurality of polar decoded symbols (n), generating a plurality of information symbols (k) by performing a convolutional decoding operation on the plurality of polar decoded symbols, wherein k/n is a rate of the concatenation of the convolutional encoding operation and the polar encoding operation, and performing a bidirectional communication between the successive-cancellation decoding operation and the convolutional decoding operation.

A method of soft-decision decoding including training a machine learning agent with communication signal training data; providing to the trained machine learning agent a signal that has been received via a communications channel; operating the machine learning agent to determine respective probabilities that the received signal corresponds to each of a plurality of symbols; and, based on the determined probabilities, performing soft decision decoding on the received signal.

A method for Bose-Chaudhuri-Hocquenghem (BCH) soft error decoding includes receiving a codeword x, wherein the received codeword x has τ=t+r errors for some r≥1; computing a minimal monotone basis {λ.sub.i(x)}.sub.1≤i≤r+1.Math.F[x] of an affine space V={λ(x)ϵF[x]: λ(x).Math.S(x)=λ′(x) (mod x.sup.2t), λ(0)=1, deg(λ(x)≤t+r}, wherein λ(x) is an error locator polynomial and S(x) is a syndrome; computing a matrix A≡(λ.sub.jβ.sub.i)).sub.iϵ[W],jϵ[r+1], wherein W={β.sub.i, . . . , β.sub.W} is a set of weak bits in x; constructing a submatrix of r+1 rows from sub matrices of r+1 rows of the subsets of A such that the last column is a linear combination of the other columns; forming a candidate error locating polynomial using coefficients of the minimal monotone basis that result from the constructed submatrix; performing a fast Chien search to verify the candidate error locating polynomial; and flipping channel hard decision at error locations found in the candidate error locating polynomial.

The present invention is directed to communication systems and methods. In a specific embodiment, the present invention provides a receiver that includes an error correction module. A syndrome value, calculated based on received signals, may be used to enable the error correction module. The error correction module includes an error generator, a Nyquist error estimator, and a decoder. The decoder uses error estimation generated by the Nyquist error estimator to correct the decoded data. There are other embodiments as well.