A bit interleaving method involves applying a bit permutation process to a QC LDPC codeword made up of N cyclic blocks each including Q bits, and dividing the codeword, after the bit permutation process, into a plurality of constellation words each made up of M bits, the codeword being divided into N/M sections, each constellation word being associated with one of the N/M sections, and the bit permutation process being performed such that each of the constellation words includes one bit from each of M different cyclic blocks associated with a given section.

A decoder includes circuitry and multiple Variable-Node Circuits (VNCs). The VNCs individually hold one or more variables of an Error Correction Code (ECC) that is representable by a plurality of check equations defined over the variables. The circuitry is configured to receive a code word including variables having m-bit values that was encoded using the ECC, to further receive reliability levels assigned respectively to the variables, to decode the code word by applying to the code word a sequence of iterations, including deciding in a given iteration whether a given VNC is to be processed or skipped in that iteration, depending on the reliability levels assigned to the variables of the given VNC, and, when the given VNC is selected for processing, to make a decision whether or not to update one or more of the variables of the given VNC, and to apply the decision by the given VNC.

A bit interleaving method applying a bit permutation process to a QC LDPC codeword made up of N cyclic blocks of Q bits each, dividing the processed codeword into constellation words of M bits each, and applying an intra-cyclic-block permutation process to the cyclic blocks, where the codeword is divided into FN/M folding sections of M/F cyclic blocks each and the constellation words are each associated with one of the folding sections, and the bit permutation process is applied such that the constellation words are each made up of F bits from each of M/F different cyclic blocks in the associated section, after the permutation process.

A bit interleaving method involves applying a bit permutation process to a QC LDPC codeword made up of N cyclic blocks each including Q bits, and dividing the codeword, after the bit permutation process, into a plurality of constellation words each made up of M bits, the codeword being divided into N/M sections, each constellation word being associated with one of the N/M sections, and the bit permutation process being performed such that each of the constellation words includes one bit from each of M different cyclic blocks associated with a given section.

Provided is a low density parity check (LDPC) decoder. An LDPC decoder according to an embodiment of the inventive concept includes a variable node calculator for adding an input log-likelihood ratio (LLR) to message information of a check node to output the added values, a check node calculator for extracting signs of the output values of the variable node calculator, determining a minimum value of the output values, and calculating a correction term for the output values by using a binary logarithm to transmit to the variable node calculator, a hard decision block for determining bit values of the output values of the variable node calculator, and a parity check block for performing a parity check operation for determining validity of the bit value.

A pipeline decoding system for performing pipelined decoding of a codeword characterized by one or more parity checks may include a first pipeline stage circuit configured to process a first parity set composed of one or more first parity checks of the codeword and to process a second parity set composed of one or more second parity checks of the codeword, a second pipeline stage circuit configured to generate one or more codeword update messages for the second parity set based on a first estimate of the codeword, and a third pipeline stage circuit configured to update the first estimate of the codeword with one or more codeword update messages for the first parity set to obtain a second estimate of the codeword.

A bit interleaving method applying a bit permutation process to a QC LDPC codeword made up of N cyclic blocks of Q bits each, dividing the processed codeword into constellation words of M bits each, and applying an intra-cyclic-block permutation process to the cyclic blocks, where the codeword is divided into FN/M folding sections of M/F cyclic blocks each and the constellation words are each associated with one of the folding sections, and the bit permutation process is applied such that the constellation words are each made up of F bits from each of M/F different cyclic blocks in the associated section, after the permutation process.

A bit interleaving method involves applying a bit permutation process to a QC LDPC codeword made up of N cyclic blocks each including Q bits, and dividing the codeword, after the bit permutation process, into a plurality of constellation words each imade up of M bits, the codeword being divided into N/M sections, each constellation word being associated with one of the N/M sections, and the bit permutation process being performed such that each of the constellation words includes one bit from each of M different cyclic blocks associated with a given section.

Provided is a method of scheduling a parity check matrix, the method performed by a low-density parity-check (LDPC) decoder, the method including checking at least one non-zero elemental variable node in the parity check matrix, identifying a first index of a row of the parity check matrix in the at least one non-zero elemental variable node, extracting a column in which the at least one non-zero elemental variable node is positionable from the parity check matrix using the first index, and mapping the at least one non-zero elemental variable node to the extracted column based on an arrangement, and identifying a second index of the column of the parity check matrix through the mapped at least one non-zero elemental variable node.

A method of processing data received over a channel includes receiving data representing probabilities associated with a plurality of variables and receiving a parity check matrix associated with a factor graph which includes variable nodes and check nodes connected by edges. After each exchange of messages between the variable nodes and check nodes, messages are calculated based on messages received at the variable nodes and permuted messages to be sent from the variable nodes in the next iteration are calculated by applying a permutation to the calculated messages. The permutation is of a set of permutations which map each codeword of the set of codewords onto a different codeword of the set of codewords. Soft values associated to variable nodes can be accumulated over two iterations of the message exchange processing.