A low density parity check (LDPC) encoder, an LDPC decoder, and an LDPC encoding method are disclosed. The LDPC encoder includes first memory, second memory, and a processor. The first memory stores an LDPC codeword. The second memory is initialized to 0. The processor generates the LDPC codeword by performing accumulation with respect to the second memory using information bits. The accumulation is performed at parity bit addresses that are updated using a sequence corresponding to a parity check matrix (PCM).

Secure distributed storage and transmission of electronic content is provided over at least one communication network. At least one data file is received and parsed into a plurality of segments, wherein each one of the segments has a respective size. Thereafter, each of the plurality of segments is divided into a plurality of slices, wherein each one of the slices has a respective size. A plurality of data chunks are encoded, each data chunk comprising a portion of at least two of the slices, wherein no portion comprises an entire slice. The data chunks are packaged with at least metadata, and each of the packages is assigned to respective remote storage nodes. Each of the packages is transmitted to the respectively assigned remote storage node.

Techniques for performing forward error correction of data to be transmitted over an optical communications channel. The techniques include: receiving data bits; organizing the data bits into an arrangement having a plurality of blocks organized into rows and columns and into a plurality of strands including a first strand of blocks that includes a back portion comprising a first row of the plurality of blocks, and a front portion comprising blocks from at least two different columns in at least two different rows other than the first row of blocks; and encoding at least some of the data bits in the arrangement using a first error correcting code at least in part by generating first parity bits by applying the first error correcting code to first data bits in the front portion of the first strands and second data bits in the back portion of the first strand.

A method, apparatus, and system for deinterleaving data.

A low density parity check (LDPC) encoder, an LDPC decoder, and an LDPC encoding method are disclosed. The LDPC encoder includes first memory, second memory, and a processor. The first memory stores an LDPC codeword. The second memory is initialized to 0. The processor generates the LDPC codeword by performing accumulation with respect to the second memory using information bits. The accumulation is performed at parity bit addresses that are updated using a sequence corresponding to a parity check matrix (PCM).

Systems may include a memory storage suitable for storing data, an encoder suitable for encoding data into codewords arranged in an array of a number of rows and a number of columns, and a decoder suitable for receiving the encoded codewords, decoding the encoded codewords, and detecting miscorrections in the decoding.

Bit-flip coding uses a bit-flip encoder to flip bits in a redundancy-intersecting vector of a binary array having n rows and n columns until Hamming weights of the binary array are within a predetermined range of n divided by two. Information bits of an input data word to the bit-flip coding apparatus are stored in locations within the binary array that are not occupied by n redundancy bits of a redundancy vector.

Techniques for performing forward error correction of data to be transmitted over an optical communications channel. The techniques include: receiving data bits; organizing the data bits into an arrangement having a plurality of blocks organized into rows and columns and into a plurality of strands including a first strand of blocks that includes a back portion comprising a first row of the plurality of blocks, and a front portion comprising blocks from at least two different columns in at least two different rows other than the first row of blocks; and encoding at least some of the data bits in the arrangement using a first error correcting code at least in part by generating first parity bits by applying the first error correcting code to first data bits in the front portion of the first strands and second data bits in the back portion of the first strand.

A first set of data is encoded using a first code to obtain a first-code codeword which includes the first set of data and first-code parity information. The first set of data is stored on a plurality of drives, wherein the first set of data is distributed amongst the plurality of drives. A second set of data is encoded using a second code to obtain a second-code codeword which includes the second set of data and second-code parity information. The second-code codeword is stored on the plurality of drives, wherein the second set of data and second-code parity information are distributed amongst the plurality of drives.

Techniques for performing forward error correction of data to be transmitted over an optical communications channel. The techniques include: receiving data bits; organizing the data bits into an arrangement having a plurality of blocks organized into rows and columns and into a plurality of strands including a first strand of blocks that includes a back portion comprising a first row of the plurality of blocks, and a front portion comprising blocks from at least two different columns in at least two different rows other than the first row of blocks; and encoding at least some of the data bits in the arrangement using a first error correcting code at least in part by generating first parity bits by applying the first error correcting code to first data bits in the front portion of the first strands and second data bits in the back portion of the first strand.