论文标题
构建和解码的有限级量化程序
Finite-Level Quantization Procedures for Construction and Decoding of Polar Codes
论文作者
论文摘要
我们考虑有限级，对称量化程序，用于构建和解码极地代码。一般而言，在量化存在下是否发生极化。 Hassani和Urbanke表明，简单的三级量化程序极化，他们提出了一种计算方法，以获得可实现率的下限。我们找到了一种改进的可实现率的计算方法，以及上述简单情况下块误差概率的确切渐近行为。然后，我们证明某些D级量化方案两极分化，并在可实现的速率上产生下限。此外，我们表明，广泛的量化程序会导致极化现象的较弱形式。
We consider finite-level, symmetric quantization procedures for construction and decoding of polar codes. Whether polarization occurs in the presence of quantization is not known in general. Hassani and Urbanke have shown that a simple three-level quantization procedure polarizes and they have proposed a calculation method to obtain a lower bound for achievable rates. We find an improved calculation method for achievable rates and also the exact asymptotic behavior of the block error probability under the aforementioned simple case. We then prove that certain D-level quantization schemes polarize and give a lower bound on achievable rates. Furthermore, we show that a broad class of quantization procedures result in a weaker form of the polarization phenomenon.
