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.

Systems and methods are provided for decoding data read from non-volatile storage devices. A method that may include decoding a first codeword read from a storage location of a non-volatile storage device using a first decoder without soft information, determining that the first decoder has failed to decode the first codeword, decoding the first codeword using a second decoder without soft information, determining that the second decoder has succeeded in decoding the first codeword, generating soft information associated with the storage location using decoding information generated by the second decoder and decoding a subsequent codeword from the storage location using the soft information associated with the storage location. The second decoder may be more powerful than the first decoder.

A flash memory system may include a flash memory and a circuit for decoding a result of a read operation on the flash memory using a first codeword. The circuit may be configured to generate an estimated codeword based on a result of hard decoding the first codeword and a result of hard decoding a second codeword. The circuit may be further configured to generate soft information based on the hard decoding result of the first codeword and the estimated codeword. The circuit may be further configured to decode the result of the read operation on the flash memory using the soft information.

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.

Systems and methods are provided for decoding data read from non-volatile storage devices. A method may comprise receiving a chunk of data read from a physical location of a non-volatile storage device and searching a memory for soft information associated with the physical location using a unique identifier associated with the physical location. The soft information may be generated from one or more previous decoding processes on previous data from the physical location. The method may further comprise retrieving the soft information identified by the unique identifier associated with the physical location from the memory, decoding the chunk of data with the soft information indicating reliability of bits in the chunk of data and updating the soft information with decoding information generated during the decoding.

Systems and methods are provided for decoding data read from non-volatile storage devices. A method may comprise receiving a chunk of data read from a physical location of a non-volatile storage device and searching a memory for soft information associated with the physical location using a unique identifier associated with the physical location. The soft information may be generated from one or more previous decoding processes on previous data from the physical location. The method may further comprise retrieving the soft information identified by the unique identifier associated with the physical location from the memory, decoding the chunk of data with the soft information indicating reliability of bits in the chunk of data and updating the soft information with decoding information generated during the decoding.

A method and an apparatus for decoding polar codes, the method comprising: determining a starting level for processing an overflow according to a number of encoded bits of a received polar encoded codeword, an input bit-width, and an internal bit-width of a decoder; multiplying an output Log-Likelihood Ratio (LLR) value and two input LLR values of the G function by a first coefficient and a second coefficient respectively; and finally, the LLR values corresponding to the received codeword are decoded to obtain decoded bits.

A method of operating a first communication node includes receiving a communication at the first communication node from a second communication node, wherein the communication includes information bits in a plurality of information bit positions, determining, by the first communication node, a subset of the information bit positions of the communication that are punctured wherein the determining is performed based on detected or decoded control information, and responsive to determining the subset, reducing, by the first communication node, magnitudes of information bits in the subset of the information bit positions that are punctured.

A method of operating a first communication node includes receiving a communication at the first communication node from a second communication node, wherein the communication includes information bits in a plurality of information bit positions, determining, by the first communication node, a subset of the information bit positions of the communication that are punctured wherein the determining is performed based on detected or decoded control information, and responsive to determining the subset, reducing, by the first communication node, magnitudes of information bits in the subset of the information bit positions that are punctured.