To cope with the issue of determining cyclic shift coefficients of the quasi-cyclic sub-matrix in the Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes

a method was presented based on the arithmetic progression to compute the cyclic shift coefficients.By this method

a class of girth eight QC-LDPC codes for any column weight is obtained

and the cyclic shift coefficients can be expressed in simple analytic expressions to reduce required memory usage.Meanwhile

the encoding complexity is linearly proportional to code length due to the lower triangular parity matrix.The simulation result shows that column weight and girth have important influences on code performance.Furthermore

over an Additive White Gauss Noise (AWGN) channel and under the Belief Propagation (BP) decoding algorithm

the simulation results represent that bit error rate of the proposed QC-LDPC codes is no less than the LDPC codes in IEEE 802.11n and 802.16e with short code length

and is close to the LDPC codes in DVB-S2 with long code length.Moreover

the study result also confirms that the proposed algorithm has high flexibility with respect to the design of code length and rate.