AN ENCODING SCHEME, AND A DECODING SCHEME USING A SERIES OF LDPC CODES BASED ON FINITE INVERSIVE SPACES

摘要

There is disclosed a method of creating an LDPC code that is defined by a parity-check matrix H. The parity-check matrix H is derived from a (0,l)-geometry which is induced by a finite inversive space. This inversive space has an order q where every circle in the inversive space contains exactly q + 1 points, q is preferably even, and most preferably equal to 2. Where the inversive space has a dimension n. Where the (0,l)-geometry is formed as a derived geometric structure based on pencils of degree m ≤ n in the inversive space. The method includes construction of a binary K by N matrix H labelled by K circles and N pencils of the inversive space, wherein the (i, j)-entry of the matrix is 1 if circle i belongs to pencil j, and 0 otherwise. If the degree of the pencil is given by 2 then the parity-check matrix H needs to be transposed, i.e. Hτ is used instead of H. A method of transmitting a message, a coder, a decoder and a data transmission system using such codes are also disclosed.