Message length adaptive LDPC codes
LDPC codes achieve better performance and lower decoding complexity than turbo codes, with a major drawback of high encoding complexity. The encoder generator matrix is derived from the inverse of portion of parity check matrix. If the message length is changed, the structure of parity check matrix is modified and hence, the generator matrix must be re-computed. This increases the encoding complexity as the computation of matrix inverse is time and resource consuming operation. In this paper, we consider the encoding problem for LDPC codes as the complexity of encoding is essentially quadratic with respect to the block length. Using an efficient encoding method proposed by Richardson and Urbanke, we propose a systematic procedure to construct parity check matrix and generator matrix such that with change in message length, the re-computation for constructing generator matrix is avoided. The presented design uses fixed sub-matrices to construct a semi-random parity check matrix. The resultant design will reduce the pre-computation time of converting parity check matrix to generator matrix. The reported encoder reduces encoding time without the loss of coding gain and Bit Error Rate (BER) performance.
error correction coding low-density parity check codes permutation matrix