The authors prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space.Then a direct proof of the iteration formulae for the Masl...The authors prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space.Then a direct proof of the iteration formulae for the Maslov-type indices of symplectic paths is given.展开更多
The state-of-the-art soft-output decoder of polar codes is the soft cancellation(SCAN) decoding algorithm, which performs well at the cost of plentiful computations. Based on the SCAN decoding algorithm, a modified me...The state-of-the-art soft-output decoder of polar codes is the soft cancellation(SCAN) decoding algorithm, which performs well at the cost of plentiful computations. Based on the SCAN decoding algorithm, a modified method with revised iterative formula is proposed, marked modified min-sum SCAN(MMS-SCAN). The proposed algorithm simplifies the update formula of nodes and reduces the complexity of iterative decoding process by the piecewise approximation function. Meanwhile, the bit error rate(BER) of the proposed method can approach the performance of original SCAN decoding method without performance loss. The simulation reveals that the MMS-SCAN decoding algorithm can achieve the effect that the BER curve almost coincides with the original SCAN decoding curve.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11221091,11471169)the Key Laboratory of Pure Mathematics and Combinatorics,the Ministry of Education of China
文摘The authors prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space.Then a direct proof of the iteration formulae for the Maslov-type indices of symplectic paths is given.
基金supported by the Program of Introducing Talents of Dis-Cipline to Universities(B08038)the Open Fund Project of the Key Laboratory of the Space Information Application Technology of China Electronic Technology Group Corporation(XX17629X009)
文摘The state-of-the-art soft-output decoder of polar codes is the soft cancellation(SCAN) decoding algorithm, which performs well at the cost of plentiful computations. Based on the SCAN decoding algorithm, a modified method with revised iterative formula is proposed, marked modified min-sum SCAN(MMS-SCAN). The proposed algorithm simplifies the update formula of nodes and reduces the complexity of iterative decoding process by the piecewise approximation function. Meanwhile, the bit error rate(BER) of the proposed method can approach the performance of original SCAN decoding method without performance loss. The simulation reveals that the MMS-SCAN decoding algorithm can achieve the effect that the BER curve almost coincides with the original SCAN decoding curve.
