Abstract: A method and apparatus for decoding a linear block encoded string of information bits comprising: converting the string into a plurality of codewords. Performing hard and soft decisions on each codeword to generate a hard and soft decision vector. Computing the syndrome and finding the location of the two minimum values by Galois Field Arithmetic. Designating these values LOW1 and LOW2 and xoring with a Nc1, thus generating Nc2. Swapping Nc1 with Nc2 and determining the lowest soft decision value, Min1 and a next lowest value, Min2. The two bit locations creating Min1 are designated as MinA and MinB. MinA being replaced with Min2 minus the value MinA. MinB being replaced with Min2 minus the value at MinB. Generating an output codeword by subtracting Min1 from all other bit locations values and 2's complementing all soft values with 0 in their location. Creating the new soft value vector.

Abstract: A hyper encoder module encodes a block of data having a plurality of sub-blocks. Each sub-block includes a plurality of systematic block code codewords. A parity sub-block is added to the block. The parity sub-block is a first sub-block rotated by a predetermined number of bits. Each subsequent sub-block in the n-dimensional block is rotated by an appropriate number of bits and bit-wise XORed. An encoder method and apparatus which includes the hyper encoder module receives the block of data. A row of the block is immediately output and encoded by a first module according to a first encoding scheme. A column is encoded by a second module according to a second encoding scheme. A second set of encoded data is generated, iteratively updated and output by the second module. The hyper encoder module hyper-diagonally encodes the information bits as described above and then output.

Abstract: A method and apparatus for decoding a linear block encoded string of information bits comprising: converting the string into a plurality of codewords. Performing hard and soft decisions on each codeword to generate a hard and soft decision vector. Computing the syndrome and finding the location of the two minimum values by Galois Field Arithmetic. Designating these values LOW1 and LOW2 and xoring with a Nc1, thus generating Nc2. Swapping Nc1 with Nc2 and determining the lowest soft decision value, Min1 and a next lowest value, Min2. The two bit locations creating Min1 are designated as MinA and MinB. MinA being replaced with Min2 minus the value MinA. MinB being replaced with Min2 minus the value at MinB. Generating an output codeword by subtracting Min1 from all other bit locations values and 2's complementing all soft values with 0 in their location. Creating the new soft value vector.

Abstract: A method and apparatus for decoding a linear block encoded string of information bits comprising: converting the string into a plurality of codewords. Performing hard and soft decisions on each codeword to generate a hard and soft decision vector. Computing the syndrome and finding the location of the two minimum values by Galois Field Arithmetic. Designating these values LOW1 and LOW2 and xoring with a Nc1, thus generating Nc2. Swapping Nc1 with Nc2 and determining the lowest soft decision value, Min1 and a next lowest value, Min2. The two bit locations creating Min1 are designated as MinA and MinB. MinA being replaced with Min2 minus the value MinA. MinB being replaced with Min2 minus the value at MinB. Generating an output codeword by subtracting Min1 from all other bit locations values and 2's complementing all soft values with 0 in their location. Creating the new soft value vector. Some embodiments include a system and method that organizes an encoded codeword.

Abstract: A method and apparatus for decoding a linear block encoded string of information bits comprising: converting the string into a plurality of codewords. Performing hard and soft decisions on each codeword to generate a hard and soft decision vector. Computing the syndrome and finding the location of the two minimum values by Galois Field Arithmetic. Designating these values LOW1 and LOW2 and xoring with a Nc1, thus generating Nc2. Swapping Nc1 with Nc2 and determining the lowest soft decision value, Min1 and a next lowest value, Min2. The two bit locations creating Min1 are designated as MinA and MinB. MinA being replaced with Min2 minus the value MinA. MinB being replaced with Min2 minus the value at MinB. Generating an output codeword by subtracting Min1 from all other bit locations values and 2's complementing all soft values with 0 in their location. Creating the new soft value vector.

Abstract: A method and apparatus for decoding a linear block encoded string of information bits comprising: converting the string into a plurality of codewords. Performing hard and soft decisions on each codeword to generate a hard and soft decision vector. Computing the syndrome and finding the location of the two minimum values by Galois Field Arithmetic. Designating these values LOW1 and LOW2 and xoring with a Nc1, thus generating Nc2. Swapping Nc1 with Nc2 and determining the lowest soft decision value, Min1 and a next lowest value, Min2. The two bit locations creating Min1 are designated as MinA and MinB. MinA being replaced with Min2 minus the value MinA. MinB being replaced with Min2 minus the value at MinB. Generating an output codeword by subtracting Min1 from all other bit locations values and 2's complementing all soft values with 0 in their location. Creating the new soft value vector.

Abstract: A method and apparatus for decoding a linear block encoded string of information bits comprising: converting the string into a plurality of codewords. Performing hard and soft decisions on each codeword to generate a hard and soft decision vector. Computing the syndrome and finding the location of the two minimum values by Galois Field Arithmetic. Designating these values LOW1 and LOW2 and xoring with a Nc1, thus generating Nc2. Swapping Nc1 with Nc2 and determining the lowest soft decision value, Min1 and a next lowest value, Min2. The two bit locations creating Min1 are designated as MinA and MinB. MinA being replaced with Min2 minus the value MinA. MinB being replaced with Min2 minus the value at MinB. Generating an output codeword by subtracting Min1 from all other bit locations values and 2's complementing all soft values with 0 in their location. Creating the new soft value vector.

Abstract: A hyper encoder module encodes a block of data having a plurality of sub-blocks. Each sub-block includes a plurality of systematic block code codewords. A parity sub-block is added to the block. The parity sub-block is a first sub-block rotated by a predetermined number of bits. Each subsequent sub-block in the n-dimensional block is rotated by an appropriate number of bits and bit-wise XORed. An encoder method and apparatus which includes the hyper encoder module receives the block of data. A row of the block is immediately output and encoded by a first module according to a first encoding scheme. A column is encoded by a second module according to a second encoding scheme. A second set of encoded data is generated, iteratively updated and output by the second module. The hyper encoder module hyper-diagonally encodes the information bits as described above and then output.