Blockchain-based voting, including liquid voting, has been extensively studied in recent years. However, it remains challenging to implement liquid voting on blockchain using Ethereum smart contract. The challenge comes from the gas limit, which is that the number of instructions for processing a ballot cannot exceed a certain amount. This restricts the application scenario with respect to algorithms whose time complexity is linear to the number of voters, i.e., O(n). As the blockchain technology can well share and reuse the resources, we study a model of liquid voting on blockchain and propose a fast algorithm, named Flash, to eliminate the restriction. The key idea behind our algorithm is to shift some on-chain process to off-chain. In detail, we first construct a Merkle tree off-chain which contains all voters' properties. Second, we use Merkle proof and interval tree to process each ballot with O(log n) on-chain time complexity. Theoretically, the algorithm can support up to 21000 voters with respect to the current gas limit on Ethereum. Experimentally, the result implies that the consumed gas fee remains at a very low level when the number of voters increases. This means our algorithm makes liquid voting on blockchain practical even for massive voters.

In this paper, we propose an improved weighted least square (IWLS) method to estimate and compensate phase variations utilizing pilots, for Orthogonal Frequency Division Multiplexing (OFDM) based very high throughput wireless local area networks (WLANs). The remaining phase is composed of the common phase error (CPE) and the sampling time offset (STO). For IWLS, the CPE maximum likelihood (ML) estimation is proposed to improve the CPE estimation accuracy, while the STO fitting is proposed to enhance the estimation of STO. With these two mechanisms, IWLS can improve phase estimation performance. Simulation results show that, compared to weighted least square (WLS) scheme, a better pocket error rate (PER) is achieved by using the proposed method, but with a comparable complexity.

In this letter, an angle adjustment method is proposed to improve the accuracy of the sampling frequency offset (SFO) estimation for the very high throughput wireless local area networks (WLANs). This angle adjustment can work together with existing least square (LS) and weighted least square (WLS) to achieve better system performance. Simulation results show that, the angle adjustment can help LS and WLS to get better pocket error rate (PER).