A LDPC decoder includes: a coded information receiving circuit, configured to receive coded information and initialize bit information of a variable node; a check node processing circuit, configured to receive first reliability information, and perform check node processing and output second reliability information; a variable node processing circuit, configured to receive the second reliability information, and perform variable node processing to update the bit information of the variable node; a decoding decision circuit, configured to perform a decoding decision for the bit information of the variable node; and a scaling circuit configured to scale the first reliability information transmitted, the second reliability information and the bit information of the variable node.

Some embodiments are directed to a method for controlling a check node of a NB-LDPC decoder. The check node receives d.sub.c input lists U.sub.i and delivers and delivers d.sub.c output lists V.sub.i, with i[1 . . . d.sub.c]. Each input list and output list includes n.sub.m elements and each element of the input or output lists includes a reliability value associated to a symbol of a Galois Field GF(q) with q>n.sub.m. The input elements and output elements are sorted according to the reliability values in the lists. The method is a syndrome-based method. The syndromes are sums of d.sub.c elements of input lists U.sub.i. The method includes a step of syndrome calculation, a step of decorrelation and a step for generating the output list.

An apparatus includes a first single-port memory, a second single-port memory, and one or more control circuits in communication with the first single-port memory and in communication with the second single-port memory. The one or more control circuits are configured to initiate a read of stored data on a clock cycle from a physical location of the stored data in the first or second single-port memory and to initiate a write of fresh data on the clock cycle to whichever of the first single-port memory or the second single-port memory does not contain the physical location of the stored data.

A bit determining method, a memory control circuit unit and a memory storage device are provided. The method includes: reading a first storage state of a first memory cell to obtain a first value of a first significant bit; reading the first storage state of the first memory cell to obtain at least one second value of at least one second significant bit; performing a first decoding operation according to the at least one second value to obtain at least one third value of the decoded second significant bit; determining whether the first significant bit is a special bit according to the first storage state and a second storage state corresponding to the at least one third value; and if the first significant bit is the special bit, performing a corresponding decoding operation.

A decoding method for a low density parity check (LDPC) code includes: updating a first check node, among a plurality of check nodes, by receiving, by the first check node, a bit decision and an associated first reliability value from each of a subset of variable nodes including a first variable node among a plurality of variable nodes, calculating a syndrome value and a second reliability value of the first check node based on the received bit decisions and first reliability values, and outputting the calculated syndrome value and second reliability value of the first check node to a variable node of the plurality of variable nodes but not of the subset of variable nodes; and updating the first variable node by receiving, by the first variable node, a syndrome value and a second reliability value of a second check node among the plurality of check nodes, and updating the first reliability value of the first variable node based on the syndrome value and the second reliability value of the second check node.

Systems, methods, and apparatus are provided for iteratively decoding a codeword. Once a codeword is received, the codeword is processed to generate an incremental hard decision value and a log likelihood ratio amplitude value. These values are generated by processing the codeword using a soft output Viterbi algorithm. A faulty symbol in the codeword is identified. A complete hard decision value is generated using the incremental hard decision value. The LLR amplitude value and complete hard decision value corresponding to the identified faulty symbol are selectively provided to a decoder and the decoder uses these values to decode the codeword.

A data storage device is disclosed comprising a head actuated over a disk comprising a data track having at least a first data segment and a second data segment. A first plurality of codewords are generated, and a first parity sector is generated over the first plurality of codewords. The first plurality of codewords and the first parity sector are written to the first data segment. A second plurality of codewords are generated, and a second parity sector is generated over the second plurality of codewords. The second plurality of codewords and the second parity sector are written to the second data segment. During a read operation the data segments of the data track are processed sequentially to decode the codewords using a low density parity check (LDPC) decoder, wherein the reliability metrics of un-converged codewords are stored in a codeword buffer and updated using the respective parity sector.

A method employed in a low-density parity-check code decoder includes: receiving a specific data portion of a first codeword; calculating a flipping function value of the specific data portion of the first codeword according to the specific data portion by using checking equations of a parity check matrix to calculate checking values of the specific data portion; and determining whether to flip the specific data portion of the first codeword by comparing the flipping function value with a flipping threshold which has been calculated based on a plurality of flipping function values of a plurality of previous data portions earlier than the specific data portion.

Certain aspects of the present disclosure generally relate to methods and apparatus for decoding low density parity check (LDPC) codes, and more particularly to an efficient list decoder for list decoding low density parity check (LDPC) codes.

Devices, systems, and methods for reducing a latency of a decoder in a non-volatile memory are described. An example method includes receiving a noisy codeword that is based on a transmitted codeword generated from a low-density parity-check (LDPC) code, the LDPC code having an associated parity matrix comprising a plurality of columns of circulant matrices, performing a sorting operation that sorts the plurality of columns of circulant matrices in a descending order of a first quality metric to generate a plurality of sorted columns of circulant matrices, the first quality metric indicative of a number of errors in a corresponding column of circulant matrices, and iteratively processing the plurality of sorted columns of circulant matrices to determine a candidate version of the transmitted codeword.