$\beta$-expansion: A Theoretical Framework for Fast and Recursive Construction of Polar Codes
| Autor: | Yiqun Ge, Rong Li, Ingmar Land, Liu Xiaocheng, Jean-Claude Belfiore, Chen Ying, Ran Zhang, Ganghua Yang, Jun Wang, Gaoning He, Wen Tong |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Computer Science - Information Theory 020302 automobile design & engineering 020206 networking & telecommunications 02 engineering and technology Polarization (waves) Electronic mail symbols.namesake Number theory Additive white Gaussian noise 0203 mechanical engineering 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics Polar Algorithm design Mathematics |
| Zdroj: | GLOBECOM |
| Popis: | In this work, we introduce $\beta$-expansion, a notion borrowed from number theory, as a theoretical framework to study fast construction of polar codes based on a recursive structure of universal partial order (UPO) and polarization weight (PW) algorithm. We show that polar codes can be recursively constructed from UPO by continuously solving several polynomial equations at each recursive step. From these polynomial equations, we can extract an interval for $\beta$, such that ranking the synthetic channels through a closed-form $\beta$-expansion preserves the property of nested frozen sets, which is a desired feature for low-complex construction. In an example of AWGN channels, we show that this interval for $\beta$ converges to a constant close to $1.1892 \approx 2^{1/4}$ when the code block-length trends to infinity. Both asymptotic analysis and simulation results validate our theoretical claims. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|