Wireless network coding for multiple unicast transmissions

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2014
Aktaş, Tuğcan
In this work, firstly we propose a practical and effective cooperative communication technique based on network coding (NC) in order to mitigate the detrimental consequences of fading in wireless channels. We base our formulation on multiple unicast transmissions which is the natural way of communication in many modern wireless networks. The proposed technique utilizes spatial diversity through cooperation between overhearing nodes which carry out distributed encoding operations dictated by the generator matrices of chosen linear block codes. In order to exemplify the technique, we make use of greedy codes over the binary field and adapt a Time Division Multiple Access (TDMA) type use of the channel. We show that arbitrary diversity orders can be flexibly assigned to the nodes according to the separation vector corresponding to the generator matrix. In addition to the optimal detection rule for deciding on the information symbols transmitted in the network, we present a novel network decoder which relies on the sum-product (SP) algorithm running on a Tanner graph that is constructed for the underlying distributed block code. This network decoder is shown to be both advantageous in terms of its low-complexity and its performance which is very close to that of the optimal one. We further show asymptotic superiority of NC over a plain Automatic Repeat-reQuest (ARQ) method that utilizes the wireless channel in a repetitive manner without NC and present related rate-diversity trade-off curves. In the second part, we derive approximate average bit-error-rate (BER) expressions for the proposed network coded system. In order to reach these expressions, we initially consider the cooperative systems' instantaneous BER values that are commonly composed of Q-functions of more than one variable. For evaluating the expectation integrals involving these Q-functions easily, we investigate the convergence characteristics of the \textit{sampling property} for integrand functions and generalize this property to arbitrary functions of multiple variables. Then, we adapt the equivalent channel approach to the network coded scenario for ease of analysis and propose a corresponding suboptimal network decoder based on the Cooperative-Maximal Ratio Combining (C-MRC) method. Finally, by combining the sampling property, equivalent channel assumption and C-MRC technique, we reach closed form average BER expressions. Through simulations, the agreement of the obtained closed form expressions with the performance of the proposed network coded system is demonstrated in a wide SNR range. As one of the initial studies from the communication theory window in the field of NC, the proposed system model and the analysis techniques are expected to serve as the building blocks for the design and the performance analysis of general network coded systems with larger number of nodes and practical considerations like channel coding, resource reuse, channel estimation, multi-user interference management, etc.

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Citation Formats
T. Aktaş, “Wireless network coding for multiple unicast transmissions,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.