Parity-check and G-matrix based intelligent early stopping criterion for belief propagation decoder for polar codes

The error correction performance of Belief Propagation(BP)decoding for polar codes is satisfactory compared with the Successive Cancellation(SC)decoding.Nevertheless,it has to complete a fixed number of iterations,which results in high computational complexity.This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding.This paper proposes a hybrid technique that combines the“paritycheck”with the“G-matrix”to reduce the computational complexity of BP decoder for polar codes.The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process,which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding.We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance.Moreover,mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated.The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding.Simulation results show that the proposed hybrid technique reduces the iterations by about 90%of BP decoding in a high Signal-to-Noise Ratio(SNR)(i.e.,3.5~4 dB),and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.

MoS2 nanorods with inner caves through synchronous encapsulation of sulfur for high performance Li–S cathodes

Lithium–sulfur(Li–S)batteries have become one of the most promising candidates for next-generation batteries owing to their high specific capacity,low cost,and environment-friendliness.Many efforts have been made to mitigate the"shuttle effect"through physical adsorption and chemical bonding.MoS2 has been proposed as a cathode material to provide effective anchoring sites for lithium polysulfides(Li PSs),but is still limited by its layer structure.Herein,we designed novel MoS2 nanorods with inner caves based on our previous work,and performed synchronous encapsulation of sulfur during the synthesis process.The outer MoS2 tubular shells physically inhibit the outward diffusion of polysulfide species while the inner particles chemically anchor the polysulfides to prevent shuttling.As the cathode matrix in Li–S batteries,the electrochemical results deliver a high initial discharge capacity of 1213 mAhg^-1 for sulfur at 0.1 C.After cycling at 1 C for 300 cycles,the cells exhibit a capacity decay of only 0.076%per cycle and high average coulombic efficiency over 95%.The tubular MoS2 structure is an innovative and appealing design,which could be regarded as a prospective substrate for the improved performance of Li–S batteries.