期刊
IEEE TRANSACTIONS ON COMMUNICATIONS
卷 69, 期 1, 页码 31-43出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCOMM.2020.3030057
关键词
Block error rate; code construction; density evolution; Gaussian approximation; polar codes
资金
- Japan Society for the Promotion of Science (JSPS) [JP16KK0145]
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- U.S. National Science Foundation [CCF-1908308]
This paper focuses on an improved Gaussian approximation (GA) based construction of polar codes with successive cancellation (SC) decoding over an additive white Gaussian noise (AWGN) channel. By analyzing the asymptotic behavior of the nonlinear function, the proposed improved GA approach makes an accurate trace of mean LLR evolution feasible. Through numerical analysis and simulations with code lengths up to N=2(18), it is explicitly demonstrated that various code-rate polar codes with long codewords and capacity approaching behavior can be easily designed.
This paper focuses on an improved Gaussian approximation (GA) based construction of polar codes with successive cancellation (SC) decoding over an additive white Gaussian noise (AWGN) channel. Arikan proved that polar codes with low-complexity SC decoding can approach the channel capacity of an arbitrary symmetric binary-input discrete memoryless channel, provided that the code length is chosen large enough. Nevertheless, how to construct such codes over an AWGN channel with low computational effort has been an open problem. Compared to density evolution, the GA is known as a low complexity yet powerful technique that traces the evolution of the mean log likelihood ratio (LLR) value by iterating a nonlinear function. Therefore, its high-precision numerical evaluation is critical as the code length increases. In this work, by analyzing the asymptotic behavior of this nonlinear function, we propose an improved GA approach that makes an accurate trace of mean LLR evolution feasible. With this improved GA, through numerical analysis and simulations with code lengths up to N=2(18), we explicitly demonstrate that various code-rate polar codes with long codeword and capacity approaching behavior can be easily designed.
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