A Nearly Optimal Method of Polar Code Constructions for the AWGN Channel

Polar code is a kind of capacity-approaching code with explicit structure as part of the next generation wireless communication standard. The performance of the polar code is directly determined by the construction method, in which there are three important parameters: code rate
$(R)$
, block-length
$(N)$
, and designSNR (
DSNR
). It is very difficult to obtain an optimal construction because all these three parameters should be optimized in a recursive structure model. In this article, an efficient method, which constructs the desired optimal polar code by simultaneously selecting the three parameters in terms of the error probability, is presented. In the proposed construction, a dimensionality reduction search method is used to solve a fore mentioned optimization problem and to find the relation between the performance of polar code and design parameters. At the same time, the optimal parameters
$N$
and
$R$
can be obtained under any
DSNR
by taking the average group accuracy rate as the evaluation criterion. Through this method, the appropriate solution of three parameters in the construction of the polar code can be determined according to the required error probability. The proposed construction method is verified by numerical simulation, and the optimal performance to
$N$
,
$R $
and
DSNR
is compared and discussed.