Load thresholds for cuckoo hashing with double hashing

In k-ary cuckoo hashing, each of cn objects is associated with k random buckets in a hash table of size n. An l-orientation is an assignment of objects to associated buckets such that each bucket receives at most l objects. Several works have determined load thresholds c^* = c^*(k,l) for k-ary cuckoo hashing; that is, for c c^* no l-orientation exists with high probability. A natural variant of k-ary cuckoo hashing utilizes double hashing, where, when the buckets are numbered 0,1,...,n-1, the k choices of random buckets form an arithmetic progression modulo n. Double hashing simplifies implementation and requires less randomness, and it has been shown that double hashing has the same behavior as fully random hashing in several other data structures that similarly use multiple hashes for each object. Interestingly, previous work has come close to but has not fully shown that the load threshold for k-ary cuckoo hashing is the same when using double hashing as when using fully random hashing. Specifically, previous work has shown that the thresholds for both settings coincide, except that for double hashing it was possible that o(n) objects would have been left unplaced. Here we close this open question by showing the thresholds are indeed the same, by providing a combinatorial argument that reconciles this stubborn difference

Event-based security control for discrete-time stochastic systems

This study is concerned with the event-based security control problem for a class of discrete-time stochastic systems with multiplicative noises subject to both randomly occurring denial-of-service (DoS) attacks and randomly occurring deception attacks. An event-triggered mechanism is adopted with hope to reduce the communication burden, where the measurement signal is transmitted only when a certain triggering condition is violated. A novel attack model is proposed to reflect the randomly occurring behaviours of the DoS attacks as well as the deception attacks within a unified framework via two sets of Bernoulli distributed white sequences with known conditional probabilities. A new concept of mean-square security domain is put forward to quantify the security degree. The authors aim to design an output feedback controller such that the closed-loop system achieves the desired security. By using the stochastic analysis techniques, some sufficient conditions are established to guarantee the desired security requirement and the control gain is obtained by solving some linear matrix inequalities with nonlinear constraints. A simulation example is utilised to illustrate the usefulness of the proposed controller design scheme.This work was supported in part by Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61573246 and 61374039, the Shanghai Rising-Star Programme of China under Grant 16QA1403000, the Program for Capability Construction of Shanghai Provincial Universities under Grant 15550502500 and the Alexander von Humboldt Foundation of Germany

Multi-cell massive MIMO network optimization towards power consumption in suburban scenarios

In this paper, we propose a simulation-based method to design low power multi-cell multi-user massive MIMO network by optimizing the positions of the base stations. Two realistic outdoor suburban areas have been considered in Ghent, Belgium (Europe) and Kinshasa, the Democratic Republic of Congo (Africa), in which the power consumption, the energy efficiency, the network capacity and the multiplexing gain are investigated and compared with LTE networks. The results of the simulations demonstrated that massive MIMO networks provide better performance in the crowded scenario where user's mobility is relatively low. A massive MIMO BS consumes 5-8 times less power than the LTE networks, with a pilot reuse pattern of 3 that helps obtaining a good tradeoff between the higher bit rate requested and the low power requirements in cellular environment