二元偏振核的窗口处理
Window Processing of Binary Polarization Kernels
摘要：
提出了一种基于二进制$2^t\times 2^t$极化核的极化（子）码译码算法。它是基于窗口处理（WP）的方法，利用极化核和Arikan矩阵的线性关系。这种关系使得人们能够通过计算Arikan连续消除（SC）解码器中几条路径的概率来计算内核输入符号概率。在本文中，我们提出了一个改进版本的WP，它具有显着降低的算术复杂度，并在对数似然比（LLR）域操作。该算法识别并重用Arikan SC路径分数计算中出现的常见子表达式。所提出的算法被应用到大小为16和32的核，具有改进的偏振特性。它使极化（子）码与所考虑的内核，同时提供更好的性能和更低的解码复杂度与Arikan内核的极化（子）码相比。
英文摘要：
A decoding algorithm for polar (sub)codes with binary $2^t\times 2^t$ polarization kernels is presented. It is based on the window processing (WP) method, which exploits the linear relationship of the polarization kernels and the Arikan matrix. This relationship enables one to compute the kernel input symbols probabilities by computing the probabilities of several paths in Arikan successive cancellation (SC) decoder. In this paper we propose an improved version of WP, which has significantly lower arithmetic complexity and operates in log-likelihood ratios (LLRs) domain. The algorithm identifies and reuses common subexpressions arising in computation of Arikan SC path scores. The proposed algorithm is applied to kernels of size 16 and 32 with improved polarization properties. It enables polar (sub)codes with the considered kernels to simultaneously provide better performance and lower decoding complexity compared with polar (sub)codes with Arikan kernel.
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