任意列重大围长QC-LDPC码的确定性构造

针对准循环低密度奇偶校验（Quasi-Cyclic Low-Density Parity-Check，QC-LDPC）码中准循环基矩阵的移位系数确定问题，提出基于等差数列的确定方法.该方法构造的校验矩阵围长为8，列重可任意选取，移位系数由简单的数学表达式确定，编码复杂度与码长呈线性关系，节省了编解码存储空间.研究结果表明，列重和围长是影响码字性能的重要因素.在加性高斯白噪声（Additive White Gauss Noise，AWGN）信道和置信传播（Belief Propagation，BP）译码算法下，该方法构造的码字在短码时可以获得与IEEE 802.11n、802.16e码相一致的性能，在长码时误比特率性能接近DVB-S2码.同时表明该方法对码长和码率参数的设计具有较好的灵活性.

Deterministic Construction of QC-LD PC Codes for Any Column Weight with a Large Girth

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 com-pute 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.Mean-while,the encoding complexity is linearly proportional to code length due to the lower triangular parity matrix.The simula-tion result shows that column weight and girth have important influences on code performance.Furthermore,over an Addi-tive White Gauss Noise (AWGN)channel and under the Belief Propagation (BP)decoding algorithm,the simulation re-sults 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.