论文标题
提高极性代码的最小距离的预先转换方法
A Pre-Transformation Method to Increase the Minimum Distance of Polar-Like Codes
论文作者
论文摘要
Reed Muller（RM）代码以其良好的最小距离而闻名。可以使用其结构来构建具有良好距离属性的极性代码，从而选择集合作为具有最高锤击权重的极化矩阵的行，而不是最可靠的合成通道。但是，由于其特定结构，RM代码的信息长度选项非常有限。在这项工作中，我们提出了足够的条件，以使某些基本的RM代码至少增加一位，以获得比较低的速率代码相同的预先转换的极性代码，这些证明提供了一种建设性的方法，可以选择划分的三倍，以合并为合并的代码，并遵循构造的图表，并遵循隔离式的零件，它们的构造构成了“零星”的层次构造，它们的层面构成了零星的编码，这些均可构成的行编码的编码编号的编码构成的编码行索引的表示。此外，我们的发现与[2]中介绍的方法相结合，以进一步减少最小重量代码字的数量。数值结果表明，设计的代码在短块长度下执行近似键键结合，并且比具有相同参数的极化调整后的跨跨斜向极性代码更好。
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the highest Hamming weight, instead of the most reliable synthetic channels. However, the information length options of RM codes are quite limited due to their specific structure. In this work, we present sufficient conditions to increase the information length by at least one bit for some underlying RM codes and in order to obtain pre-transformed polar-like codes with the same minimum distance than lower rate codes.The proofs give a constructive method to choose the row triples to be merged together to increase the information length of the code and they follow from partitioning the row indices of the polar encoding matrix with respect to the recursive structure imposed by the binary representation of row indices. Moreover, our findings are combined with the method presented in [2] to further reduce the number of minimum weight codewords. Numerical results show that the designed codes perform close to the meta-converse bound at short blocklengths and better than the polarization-adjusted-convolutional polar codes with the same parameters.
