We consider polar codes constructed from the $2\times 2$ kernel $\begin{bmatrix} 1 & 0 \\ \alpha & 1 \end{bmatrix}$ over a finite field $\mathbb{F}_{q}$, where $q=p^s$ is a power of a prime number $p$, and $\alpha$ satisfies that $\mathbb{F}_{p}(\alpha) = \mathbb{F}_{q}$. We prove that for any $\mathbb{F}_{q}$-symmetric memoryless channel, any code length, and any code dimension, all the codeword symbols in such polar codes have the same symbol error rate (SER) under the successive cancellation (SC) decoder.

翻译：我们认为,用2美元内核$\ begin{bmatrix} 1 & 0\\\\\ alpha & 1\\ end{ bmatrix} 构建的极地代码是一个有限的字段$\ mathbb{F\\ q}$, 其中$q=p ⁇ $是质数$p$的功率, $\ alpha$满足了$\mathb{F\\\ p} (\ alpha) =\ mathbb{F\\ q}$。 我们证明,对于任何一个 $\ mathb{F\ q} $- tymematricness无记忆通道、 任何代码长度和任何代码维度, 在连续取消( SC) 的解码下, 极代码中的所有代号符号均具有相同的符号错误率(SER) 。