Arikan’s polar codes are capable of approaching Shannon’s capacity at a low encoding and decoding complexity, while conveniently supporting rate adaptation. By virtue of these attractive features, polar codes have found their way into the 5G New Radio (NR). Hence, in this paper we provide a comprehensive survey of polar codes, highlighting the major milestones achieved in the last decade. Furthermore, we also provide tutorial insights into the operation of the polar encoder, decoders as well as their code construction methods. We also extend our discussions to quantum polar codes with an emphasis on the underlying quantum-to-classical isomorphism and the syndrome-based quantum polar decoders.

中文翻译：

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极性代码及其量子域对应物

Arikan 的极化码能够以较低的编码和解码复杂度接近香农的容量，同时方便地支持速率自适应。凭借这些吸引人的特性，极化码已进入 5G 新无线电 (NR)。因此，在本文中，我们对极坐标代码进行了全面调查，重点介绍了过去十年中取得的主要里程碑。此外，我们还提供有关 polar 编码器、解码器及其代码构造方法的操作的教程见解。我们还将讨论扩展到量子极坐标代码，重点是潜在的量子到经典同构和基于综合症的量子极坐标解码器。