We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place 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 limn→8 1overn ln ℙ(Zn ∈ [a, b]), where Zn is the Bhattacharyya process. The quantity ℙ(Zn ∈ [a, b]) represents the fraction of sub-channels that are still un-polarized at time n.
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机译：我们提供了Bhattacharyya进程的逃逸率的上限和下限，与通过二进制擦除通道进行传输的极地代码相对应。更准确地说，我们限制了其Bhattacharyya常数处于固定间隔[a，b]的子通道数的指数。从数学上讲，这可以说是限制极限lim n→8 1overn lnℙ（Zn∈[a，b]），其中Z n 是Bhattacharyya过程。 ℙ（Zn∈[a，b]）表示在时间n仍未极化的子信道部分。
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