Network Codes Based on Symmetric Matrices

Network Codes Based on Symmetric Matrices

Edidiong Anselm Attang (Illinois Institute of Technology, Department of Electrical and Computer Engineering, Chicago, IL, USA), Yuteng Wu (Illinois Institute of Technology, Department of Electrical and Computer Engineering, Chicago, IL, USA), Mandana Norouzi (Illinois Institute of Technology, Department of Electrical and Computer Engineering, Chicago, IL, USA) and Guillermo E. Atkin (Illinois Institute of Technology, Department of Electrical and Computer Engineering, Chicago, IL, USA)
Copyright: © 2016 |Pages: 14
DOI: 10.4018/IJHCR.2016100101
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The key challenges of future wireless communication are improving data rate and quality of service. However, the challenges posed by having a large number of users such as power control, frequency synchronization and independently faded channels scales with the number of users. Cooperative communications is a candidate technology for high data rate and multi-user communications. In this paper, a new design of distributed network codes is introduced. These network codes are based on algebraic constructions in finite fields. Finite fields have an attractive feature of constraining transmit signal energy and is resilient to fading channels. The codes have high diversity and scale up with an arbitrary number of users. The codes are an alternative to Generalized Dynamic Network Codes without a restriction on the field size. Results are compared to theoretical evaluations and systems with similar configurations.
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The proliferation of communication devices coupled with the exponential demands for high data rates motivates multiuser communications. For multiuser communications, wireless technology is the most active technology that will drive solutions for high data rates. However, wireless technologies are encumbered with problems of which random channel fading is dominant. Given this, there are considerable research aimed at providing resiliency by deploying intelligent wireless networks (Giannakis et. al, 2000) (Liu, 2000). A key aspect is the development of signal processing and receiver techniques that provides optimum capacity for the large number of users. Since the multiuser access will support high data rates without requiring the need for increased bandwidth, a blend of signal processing with physical layer techniques will drive capacity demands while countering the effects of fading. A metric capturing the system/receiver performance is diversity (Diggavi & Tse, 2005). Diversity can either be a function of the signal to noise ratio, number of times a signal is transmitted. In CDMA systems, diversity is represented by length of orthogonal spreading sequences (Hochwald, Marzetta, & Papadias, 2001). In pure fading systems, diversity is given as a function of the Signal to Noise Ratio (SNR) (Diggavi & Tse, 2005; Xiao & Skoglund, 2005).

A major driver for countering the effects of fading is cooperative diversity. This is the process of using alternate transmission paths under the assumption that all the signal paths to the destination fade independently. Cooperative diversity will have a wide range of applications such as vehicle-to-vehicle communications and wireless sensor networks (Dohler & Li, 2010). Wireless sensor networks are increasingly deployed for numerous purposes such as data logging, crime control, unsupervised monitoring of environmental conditions such as humidity. The communicating nodes are highly dependent on limited battery power. A major design criterion in sensor network deployment is optimizing the networks lifetime without degrading communication between sensor nodes. Therefore, limiting transmission power save battery life and coverage is a predominant problem. Therefore, cooperative techniques are beneficial to close up coverage gaps which helps in preserving network integrity (Dohler & Li, 2010). Cooperative diversity makes use of various cooperative relay strategies to achieve spatial diversity gains. For a properly designed system, the diversity can scale up to the number of nodes known as a full diversity system (Wang, Cano, Giannakis, & Laneman, 2007). Therefore, the performance will depend on the number of cooperative relay nodes, the operations at each node and the channel model in operation. There are numerous references on cooperative communications (Lozana, Heath, & Andrews, 2013; Laneman, Tse, & Wornell, 2004).

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