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The problem of recovering heavy components of a high-dimensional vector from compressed data is of great interest in broad applications, such as feature extraction under scarce computing memory and distributed learning under limited bandwidth. Recently, a compression algorithm called count sketch has gained wide popularity to recover heavy components in various fields. In this paper, we carefully analyze count sketch and illustrate that its default recovery method, namely median filtering, has a distinct error pattern of reporting false positives. To counteract this error pattern, we propose a new scheme called zero checking which adopts a two-step recovery approach to improve the probability of detecting false positives. Our proposed technique builds on rigorous error analysis, which enables us to optimize the selection of a key design parameter for maximum performance gain. The empirical results show that our scheme achieves better recovery accuracy than median filtering and requires less samples to accurately recover heavy components. 

Cooperative jamming is deemed as a promising physical layer based approach to secure wireless transmissions in the presence of eavesdroppers. In this paper, we investigate cooperative jamming in a two-tier 5G heterogeneous network (HetNet), where the macro base stations (MBSs) at the macrocell tier are equipped with large-scale antenna arrays to provide space diversity and the local base stations (LBSs) at the local cell tier adopt non-orthogonal multiple access (NOMA) to accommodate dense local users. In the presence of imperfect channel state information, we propose three robust secrecy transmission algorithms that can be applied to various scenarios with different security requirements. The first algorithm employs robust beamforming (RBA) that aims to optimize the secrecy rate of a marco user (MU) in a macrocell. The second algorithm provides robust power allocation (RPA) that can optimize the secrecy rate of a local user (LU) in a local cell. The third algorithm tackles a robust joint optimization (RJO) problem across tiers that seeks the maximum secrecy sum rate of a target MU and a target LU robustly. We employ convex optimization techniques to find feasible solutions to these highly non-convex problems. Numerical results demonstrate that the proposed algorithms are highly effective in improving the secrecy performance of a two-tier HetNet.