Capacity-Approaching Polar Codes with Long Codewords and Successive Cancellation Decoding Based on Improved Gaussian Approximation

Hideki Ochiai, Patrick Mitran, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish (US)
Article number9220133
Pages (from-to)31-43
Number of pages13
JournalIEEE Transactions on Communications
Issue number1
StatePublished - Jan 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


  • Block error rate
  • Gaussian approximation
  • code construction
  • density evolution
  • polar codes


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