关于极化码的缩放：II。非极化通道的行为
On the scaling of Polar Codes: II. The behavior of un-polarized channels
摘要：
我们提供了对应于极化码和二进制擦除信道上的传输的Bhattacharyya过程的逃逸率的上界和下界。更准确地说，我们限制了其Bhattacharyya常数落在固定间隔$[a,b]$中的子信道的数量的指数。在数学上，这可以被表述为限制$\lim_{n \to \infty} \frac{1}{n} \ln \mathbb{P}(Z_n \in [a,b])$，其中$Z_n$是巴塔查里亚过程。量$\mathbb{P}(Z_n \in [a,b])$表示在时间$n$仍然未极化的子信道的分数。
英文摘要：
We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes and transmission over the the binary erasure channel. More precisely, we bound the exponent of the number of sub-channels whose Bhattacharyya constant falls in a fixed interval $[a,b]$. Mathematically this can be stated as bounding the limit $\lim_{n \to \infty} \frac{1}{n} \ln \mathbb{P}(Z_n \in [a,b])$, where $Z_n$ is the Bhattacharyya process. The quantity $\mathbb{P}(Z_n \in [a,b])$ represents the fraction of sub-channels that are still un-polarized at time $n$.
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