Fast Construction of Polar Codes.
arXiv: Information Theory(2016)
摘要
The construction of polar codes for channels other than BECs requires sorting of all bit channels and then selecting the best $K$ of them for a block length $N=2^n$. The sorting algorithms, be it density evolution or Tal-Vardyu0027s algorithm, typically require intense computations. In this paper, two types of partial orders (PO) of polar codes are incorporated in the construction process to decrease the required computations. Three sets, corresponding to the good bit channels ($mathcal{I}$), the frozen bit channels ($mathcal{F}$), and the undetermined bit channels ($mathcal{U}$), are selected by applying PO relations. A new process, called Dimension Reduction (DR), is proposed in this paper to further reduce the size of $mathcal{U}$. Our studies show that for $N=10$ and the code rate $R=0.5$ (being the worst code rate), incorporating PO relations alone can determine 50% of the bit channels ($|mathcal{I}| + |mathcal{F}| approx N/2$), resulting in only 50% of the sorting calculations. With our proposed DR, this number of the determined bit channels goes up to 75%, which brings a significant reduction of computations in the construction of polar codes.
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