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Investigation of Polarization Weight -an Efficient Construction for Polar Codes

Polarization weight (PW) is a novel construction method for polar codes, which results in universal reliability ordering efficiently and yields imilar performance as other channel dependent construction methods. In this paper, we interpret PW method or algorithm from a rate allocation perspective of channel polarization to show its effectiveness. Take the AWGN channel as an example, we show that the rate allocation for information bits by PW method coincides with the capacities of channel polarization. Furthermore, some properties of PW algorithm, including the universal and fractal of the reliability ordering, are illustrated, which facilitate the implementation in practice. Comprehensive simulation results with various code rates, code lengths and list sizes are also shown to validate the effectiveness of PW method.