Abstract: A method and apparatus for generating a code having properties specific to its intended use, the method comprising the steps of: selecting a group from a set of groups; selecting a ring from a set of rings; forming a group ring from said select group and selected ring; selecting a generator element from said group ring, wherein said selection is based on the desired properties of the code to be generated; and inputting said selected generator element into a code generation process to obtain a corresponding check element.

Abstract: Circuits perform row-by-row matrix generation for encoding and decoding of data blocks. They perform fast algebraic generation of high performance low density parity check (LDPC) matrices suitable for use in a wide range of error correction coding and decoding (ECC) applications. Circuit operation is based on a mathematical Cyclic Ring method that enables matrices of any size to be generated from a simple set of initial parameters, based on user-defined performance requirements. The main steps for generating a parity check matrix (H) are selection of an RG matrix structure, selection of Group Ring elements, generating the sub matrices for the RG matrix by a row filling scheme, generating the RG matrix by a cyclic arrangement of the sub matrices, and generating the parity-check matrix by deleting suitably chosen columns from the RG matrix to achieve the desired performance and then transposing the matrix.