All the codeword symbols in polar codes have the same SER under the SC decoder

Abstract

We consider polar codes constructed from the $2\times 2$ kernel $\left[\begin{array}{cc}1& 0\\ \alpha & 1\end{array}\right]$ 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.

We extend the results in the previous version to polar codes over finite fields. Previously, we only proved the results for binary polar codes

References in corpus (2)

• Algebraic Properties of Polar Codes From a New Polynomial Formalism
• Flexible and Low-Complexity Encoding and Decoding of Systematic Polar Codes