Multi-kernel polar codes have recently received considerable attention since they can provide more flexible code lengths than do the original ones. The construction process of them can be simplified by obtaining the Bhattacharyya parameter bounds of the kernels employed. However, there has been currently no generic method for seeking such bounds. In this paper, therefore, we focus on the upper Bhattacharyya parameter bounds of the standard binary polar code kernels with an arbitrary dimension of \(l\ge 2\). A calculation process composing of four steps, the common column binary tree construction for the channel inputs, the common factor extraction, the calculation feasibility testing, and the upper bound calculation based on pattern matching, is formulated with a computational complexity of \(O(2^l)\). It is theoretically proved that the upper bounds obtained by the proposed method are tight, which can lay the foundation to compare the reliability of the synthesized channels in polar codes.

最近，多内核极地代码受到了广泛的关注，因为它们可以提供比原始代码更灵活的代码长度。通过获取所用内核的Bhattacharyya参数范围，可以简化它们的构造过程。但是，目前还没有通用的方法来寻找这样的界限。因此，在本文中，我们关注具有任意尺寸\（l \ ge 2 \）的标准二进制极性码内核的Bhattacharyya参数上限。计算过程由四个步骤组成：计算通道输入的公共列二叉树结构，公共因子提取，计算可行性测试以及基于模式匹配的上限计算，计算复杂度为\（O（2 ^ l）\）。从理论上证明了该方法所获得的上限是紧密的，这可以为比较极性码中合成信道的可靠性奠定基础。