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To remove the restriction on code length of polar codes, this paper proposes a construction scheme, called stepwise polar codes, which can generate arbitrary-length polar codes. The stepwise polar codes are generated by sub-polar codes with different code lengths. To improve coding performance, sub-polar codes are united by polarization effect priority algorithm, which can reduce the number of incompletely polarized channels. Then, the construction method of the generator matrix of the stepwise polar code is presented. Furthermore, we prove that the proposed scheme has lower decoding complexity than punctured, multi-kernel polar codes. Simulation results show that the proposed method can achieve similar decoding performance compared with the conventional punctured polar codes, rate-compatible punctured polar code, PC-short and asymmetric polar codes (APC) when code length N=48 and 72, respectively.

Alzheimer’s disease (AD) is a progressive neurodegenerative disorder and is clinically characterized by the impairment of memory and cognition. Accumulation of β-amyloid (Aβ) in the brain is considered as a key process in the development of AD because it impairs the synapses’ function to impair memory formation. Recent research studies have indicated that a group of edible plant-derived Thymelaeaceaecompounds known as coumarin may exert particularly powerful actions on alleviating learning and memory impairment. 7,8-Dithydroxycoumarin (7,8-DHC), a bioactive component of coumarin derived from Thymelaeaceae, showed its function in neuroprotection before. In this study, we found that 7,8-DHC was able to mitigate Aβ accumulation via reducing the level of BACE1 and increasing the level of ADAM17 and ADAM10. More importantly, we found that 7,8-DHC could mitigate memory impairment, promote the dendrite branch density, and increase synaptic protein expression via activating PI3K-Akt-CREB-BDNF signaling. Hence, these results suggested that 7,8-DHC represented a novel bioactive therapeutic agent in mitigating Aβ deposition and synaptic loss in the process of treating AD.