Closed-Form Error Probability of Network-Coded Cooperative Wireless Networks with Channel-Aware Detectors

International audienceIn this paper, we propose a simple analytical methodology to study the performance of multi-source multi-relay cooperative wireless networks with network coding at the relay nodes and Maximum-Likelihood (ML-) optimum channel-aware detectors at the destination. Channel-aware detectors are a broad class of receivers that account for possible decoding errors at the relays, and, thus, are inherently designed to mitigate the effect of erroneous forwarded and network-coded data. In spite of the analytical complexity of the problem at hand, the proposed framework turns out to be simple enough yet accurate and insightful to understand the behavior of the system, and, in particular, to capture advantages and disadvantages of various network codes and the impact of error propagation on their performance. It is shown that, with the help of cooperation, some network codes are inherently more robust to decoding errors at the relays, while others better exploit the inherent spatial diversity and redundancy provided by cooperative networking. Finally, theory and simulation highlight that the relative advantage of a network code with respect to the others might be different with and without decoding errors at the relays

Diversity, Coding, and Multiplexing Trade-Off of Network-Coded Cooperative Wireless Networks

In this paper, we study the performance of network-coded cooperative diversity systems with practical communication constraints. More specifically, we investigate the interplay between diversity, coding, and multiplexing gain when the relay nodes do not act as dedicated repeaters, which only forward data packets transmitted by the sources, but they attempt to pursue their own interest by forwarding packets which contain a network-coded version of received and their own data. We provide a very accurate analysis of the Average Bit Error Probability (ABEP) for two network topologies with three and four nodes, when practical communication constraints, i.e., erroneous decoding at the relays and fading over all the wireless links, are taken into account. Furthermore, diversity and coding gain are studied, and advantages and disadvantages of cooperation and binary Network Coding (NC) are highlighted. Our results show that the throughput increase introduced by NC is offset by a loss of diversity and coding gain. It is shown that there is neither a coding nor a diversity gain for the source node when the relays forward a network-coded version of received and their own data. Compared to other results available in the literature, the conclusion is that binary NC seems to be more useful when the relay nodes act only on behalf of the source nodes, and do not mix their own packets to the received ones. Analytical derivation and findings are substantiated through extensive Monte Carlo simulations.Comment: IEEE International Conference on Communications (ICC), 2012. Accepted for publication and oral presentatio

Error Rate Analysis of GF(q) Network Coded Detect-and-Forward Wireless Relay Networks Using Equivalent Relay Channel Models

This paper investigates simple means of analyzing the error rate performance of a general q-ary Galois Field network coded detect-and-forward cooperative relay network with known relay error statistics at the destination. Equivalent relay channels are used in obtaining an approximate error rate of the relay network, from which the diversity order is found. Error rate analyses using equivalent relay channel models are shown to be closely matched with simulation results. Using the equivalent relay channels, low complexity receivers are developed whose performances are close to that of the optimal maximum likelihood receiver.Comment: 28 pages, 10 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

On the Diversity Order and Coding Gain of Multi-Source Multi-Relay Cooperative Wireless Networks with Binary Network Coding

In this paper, a multi-source multi-relay cooperative wireless network with binary modulation and binary network coding is studied. The system model encompasses: i) a demodulate-and-forward protocol at the relays, where the received packets are forwarded regardless of their reliability; and ii) a maximum-likelihood optimum demodulator at the destination, which accounts for possible demodulations errors at the relays. An asymptotically-tight and closed-form expression of the end-to-end error probability is derived, which clearly showcases diversity order and coding gain of each source. Unlike other papers available in the literature, the proposed framework has three main distinguishable features: i) it is useful for general network topologies and arbitrary binary encoding vectors; ii) it shows how network code and two-hop forwarding protocol affect diversity order and coding gain; and ii) it accounts for realistic fading channels and demodulation errors at the relays. The framework provides three main conclusions: i) each source achieves a diversity order equal to the separation vector of the network code; ii) the coding gain of each source decreases with the number of mixed packets at the relays; and iii) if the destination cannot take into account demodulation errors at the relays, it loses approximately half of the diversity order.Comment: 35 pages, submitted as a Journal Pape

Anti error propagation methods for wireless uplink using network coding

Abstract—Wireless network coding suffers the error propaga-tion issues that may severely degrade the diversity performance. In this work, we develop two power scaling schemes at the relay side and two detection schemes at the receiver side, respectively, to mitigate error propagation in network-coded uplink channel and thus achieve full diversity. For the soft power scaling based link adaptive relaying, we develop a virtual channel model and demonstrate that the relay power should be such to balance the signal-to-noise ratios of the source-relay channel and relay-destination channel. As for the hard power scaling based ON-OFF relaying, we first design a decision rule based on total pairwise error probability, and then simplifies it to the threshold-based relaying strategy. At the receiver side, we show that the weighted minimum distance detection with the weight being determined by the relative link quality of source-relay channel and relay-destination channel can achieve full diversity once the global channel state information is available, otherwise the maximum likelihood detection that explicitly takes into account relay decoding error should be employed to achieve full diversity. I