Title: Selective Reverse PAC Coding for Sphere Decoding Show Chinese title

Title: 用于球形解码的选择性反向PAC编码

Abstract: Convolutional precoding in polarization-adjusted convolutional (PAC) codes can reduce the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This can result in improving the error correction performance of (near) maximum likelihood (ML) decoders such as sequential decoders and sphere decoders. However, PAC codes cannot be decoded by sphere decoding. The reason is twofold: 1) Sphere decoding of polar codes is performed from the last bit - due to the lower rectangular shape of the polar transform. Whereas the shape of PAC codes generator matrix is no longer triangular. 2) One may modify the precoding matrix to get a lower-triangular shape. However, this may reduce the minimum distance of the code due to the formation of unwanted cosets. This work proposes a selective convolutional precoding scheme with transposed precoding matrix to reduce the error coefficient while avoiding the reduction in the minimum distance. The numerical results show the improvement of block error rate by 0.2-0.6 dB, depending on the code rate, in medium and high SNR regimes. Show Chinese abstract

Abstract: 在极化调整卷积（PAC）码中的卷积预编码可以减少极化码的最小重量码字数量（也称为错误系数）。这可以导致改进（接近）最大似然（ML）解码器的纠错性能，例如序列解码器和球面解码器。然而，PAC码不能通过球面解码进行解码。原因是多方面的：1）极化码的球面解码是从最后一位开始进行的——由于极化变换的下矩形形状。而PAC码生成矩阵的形状不再是三角形。2）可以修改预编码矩阵以获得下三角形形状。然而，这可能会由于不想要的陪集的形成而减少码的最小距离。这项工作提出了一种选择性卷积预编码方案，使用转置的预编码矩阵，在减少错误系数的同时避免最小距离的减少。数值结果表明，在中等和高信噪比条件下，根据码率的不同，块错误率提高了0.2-0.6 dB。