基于下三角H矩阵的LDLC整形研究

Shaping method for low-density lattice codes based on lower triangular matrix

针对低密度格码(LDLC)编码后不能适应在功率限制的加性高斯白噪声(AWGN)信道上传输的问题,研究了编码前的整形问题。构造了一种特殊结构的下三角H矩阵,并结合超立方整形和系统整形方案,分析并仿真了整形前后格点的变化及取得的整形增益。结果显示:整形后的码字沿格的Voronoi域均匀分布,并当码长为10000、误码率为10-5时,可得到1.31 dB的整形增益,相对于传统的整形技术提高了0.31 dB。通过整形,有效地产生了功率受限的格点。

To solve the problem that Low Density Lattice Codes （LDLC） cannot be used on the constrained power communication Additive White Gaussian Noise （AWGN） channel, the shaping methods were studied. In this paper, a lower triangular Hmatrix with a special structure was constructed first, together with the hypercube and systematic shaping method, and then the average power was fixed, the position change of lattice point before and after the shaping process, and its corresponding shaping gain were analyzed. The simulation results show that the codeword is uniformly distributed within the Voronoi regions of the lattice after shaping, and these shaping methods can achieve a shaping gain of 1.31dB when Symbol Error Rate （SER） 10 -5 and code length 10000 which improves 0.31dB compared with the traditional shaping technique. Power limited lattice points were generated efficiently after shaping.