Systematic modification of parity-check matrices for efficient encoding of LDPC codes

An algorithm for efficient encoding of LDPC codes is presented that does not impose any restrictions on the construction of the parity-check matrices. The algorithm modifies the parity check matrix, without changing the subspace spanned by its rows, by removing linear dependent rows and adding a small number of new rows such that the graph-based message-passing encoder will not get stuck in a stopping set. The added rows are designed by a new algorithm which is based on the notion of the "key set". The encoder exploits the sparseness of the parity-check matrix, and the encoding complexity grows almost linear with the blocksize, because the number of added rows, which may not be sparse, is relatively small.