论文标题
选择性反向PAC编码用于球体解码
Selective Reverse PAC Coding for Sphere Decoding
论文作者
论文摘要
极化调整后的卷积（PAC）代码中的卷积预编码可以减少极性代码的最小重量代码字（又称误差系数）的数量。这可能导致改善（接近）最大似然（ML）解码器（例如顺序解码器和球形解码器）的误差校正性能。但是，PAC代码不能通过球体解码来解码。原因是双重的：1）极性代码的球形解码是从最后一个位执行的 - 由于极性变换的矩形较低。而PAC代码的形状发电机矩阵不再是三角形。 2）可以修改预编码矩阵以获得较低三角形的形状。但是，由于不需要的coset形成，这可能会降低代码的最小距离。这项工作提出了一种具有转置预编码矩阵的选择性卷积预编码方案，以减少误差系数，同时避免最小距离的降低。数值结果表明，根据中等和高SNR制度，取决于代码速率，块错误率提高了0.2-0.6 dB。
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.
