1 research outputs found
Capacity-Approaching Polar Codes with Long Codewords and Successive Cancellation Decoding Based on Improved Gaussian Approximation
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 has proven that polar
codes with low-complexity SC decoder 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 , we explicitly demonstrate that various
code-rate polar codes with long codeword and capacity approaching behavior can
be easily designed.Comment: Accepted for IEEE Transactions on Communication