Efficient Encoder Design of the Q-LDPC Codes

This paper have developed farther the method of constructing sparse parity-check matrix (H-matrix) with determinate systemic structure as well as designing practice recursive encoding algorithm of the low-density parity-check (LDPC) codes. It discovers that the LDPC codes based on the circulant-shifted permutation Q-matrix created by N-queens searching algorithm perform better than them based on permutation identity matrix when H^d -matrix in H =[ H^p H^d] was constructed by using circulant-shifted permutation Q-matrix and identity matrix, respectively. It presents a simple and efficient algorithm of constructing H^d matrix without 4-cycle and 6-cycle. The presented LDPC encoders require O(M) operation (M is check-bit size). They are rate-compatible and length- compatible encoders that can cover a very wide range of rate from 0.1 to 0.9 and length including any positive integer from 20 to infinity except prime number and multiple prime numbers. The presented LDPC codes with moderate length and 1/2 rate can achieve reliable performance - 10^-5~10^-6 bit error rate (BER) - on an additive white Gaussian noise (AWGN) channel with signal-to-noise ratio (SNR) E_b/N_o about 1.42 dB¹.