Distributed MAC Protocol Supporting Physical-Layer Network Coding

Physical-layer network coding (PNC) is a promising approach for wireless networks. It allows nodes to transmit simultaneously. Due to the difficulties of scheduling simultaneous transmissions, existing works on PNC are based on simplified medium access control (MAC) protocols, which are not applicable to general multi-hop wireless networks, to the best of our knowledge. In this paper, we propose a distributed MAC protocol that supports PNC in multi-hop wireless networks. The proposed MAC protocol is based on the carrier sense multiple access (CSMA) strategy and can be regarded as an extension to the IEEE 802.11 MAC protocol. In the proposed protocol, each node collects information on the queue status of its neighboring nodes. When a node finds that there is an opportunity for some of its neighbors to perform PNC, it notifies its corresponding neighboring nodes and initiates the process of packet exchange using PNC, with the node itself as a relay. During the packet exchange process, the relay also works as a coordinator which coordinates the transmission of source nodes. Meanwhile, the proposed protocol is compatible with conventional network coding and conventional transmission schemes. Simulation results show that the proposed protocol is advantageous in various scenarios of wireless applications.Comment: Final versio

Constellation Mapping for Physical-Layer Network Coding with M-QAM Modulation

The denoise-and-forward (DNF) method of physical-layer network coding (PNC) is a promising approach for wireless relaying networks. In this paper, we consider DNF-based PNC with M-ary quadrature amplitude modulation (M-QAM) and propose a mapping scheme that maps the superposed M-QAM signal to coded symbols. The mapping scheme supports both square and non-square M-QAM modulations, with various original constellation mappings (e.g. binary-coded or Gray-coded). Subsequently, we evaluate the symbol error rate and bit error rate (BER) of M-QAM modulated PNC that uses the proposed mapping scheme. Afterwards, as an application, a rate adaptation scheme for the DNF method of PNC is proposed. Simulation results show that the rate-adaptive PNC is advantageous in various scenarios.Comment: Final version at IEEE GLOBECOM 201

A New Specific Property of Schweizer-Sklard Operators

A new specific property of Schweizer-Sklard operators is discovered that Schweizer-Sklard operations are continued fuzzy operators. The relation between Schweizer-Sklard operators and other Fuzzy operators is analysis. The conclusion that Schweizer-Sklard operations could partly replace other fuzzy operations most in use is given. At the same time the relation between Schweizer-Sklard operations and Zadeh operations as well as probability operators is given

Study on Linear Correlation Coefficient and Nonlinear Correlation Coefficient in Mathematical Statistics

In the two-dimensional or multidimensional experimental data in the traditional statistics, there is usually a linear relationship, or a similar linear relationship between independent variables and the dependent variable. Commonly the linear correlation coefficient is used to measure the degree of linear between the independent variables and the dependent variable. However, for the two-dimensional or multidimensional experimental data, there may be a simple linear relationship between independent variables and the dependent variable, or a simple non-linear relationship, or both linear and non-linear relationship. Article [1] found that the traditional correlation coefficient (linear correlation coefficient) r is only suitable for simple linear relationship. On the basis of article [1], this article discusses the linear correlation coefficient r, analyzes nonlinear correlation coefficient rnl, and gives a new definition of the correlation coefficient R. The new correlation coefficient R can not only describe the case of a simple linear relationship, but also describe the case of a simple nonlinear relationship and the case of both simple linear relationship and nonlinear relationship. That is to say, the new correlation coefficient R can describe the internal law of any experimental data