All the codeword symbols in polar codes have the same SER under the SC decoder
| Autor: | Li, Guodong, Ye, Min, Hu, Sihuang |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | IEEE Transactions on Communications ( Volume: 71, Issue: 7, July 2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/TCOMM.2023.3265687 |
| Popis: | 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. Comment: We extend the results in the previous version to polar codes over finite fields. Previously, we only proved the results for binary polar codes |
| Databáze: | arXiv |
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