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Abstract-In this paper, we contribute to the theoretical understanding, the design, and the performance evaluation of multi-source multi-relay network-coded cooperative diversity protocols. These protocols are useful to counteract the spectral inefficiency of repetition-based cooperation. We provide a general analytical framework for analysis and design of wireless networks using the Demodulate-and-Forward (DemF) protocol with binary Network Coding (NC) at the relays and Cooperative Maximal Ratio Combining (C-MRC) at the destination. Our system model encompasses an arbitrary number of relays which offer two cooperation levels: i) full-cooperative relays, which postpone the transmission of their own data frames to help the transmission of the sources via DemF relaying and binary NC; and ii) partial-cooperative relays, which exploit NC to transmit their own data frames along with the packets received from the sources. The relays can apply NC on different subsets of sources, which is shown to provide the sources with unequal diversity orders. Guidelines to choose the packets to be combined, i.e., the network code, to achieve the desired diversity order are given. Our study shows that partial-cooperative relays provide no contribution to the diversity order of the sources. Theoretical findings and design guidelines are validated through extensive Monte Carlo simulations.

Abstract-In this paper, we propose Unequal Error Protection (UEP) coding theory as a viable and flexible method for the design of network codes for multi-source multi-relay cooperative networks. As opposed to state-of-the-art solutions available for improving the diversity gain of cooperative networks, it is shown that the proposed method allows us to assign each source node the desired diversity gain, according to, e.g., the requested Qualityof-Service (QoS) or power constraints. The diversity advantage of the UEP-based network code design over conventional relay-only and XOR-only solutions is shown for the canonical two-source two-relay network. Furthermore, Maximum-Likelihood (ML-) optimum channel-aware receivers for multi-source multi-relay cooperative networks are developed, and their Average Bit Error Probability (ABEP) and achievable diversity over fading channels analytically studied. It is shown that only a cross-layer (joint) implementation of de-modulation and network-decoding allows the destination to fully exploit the diversity inherently provided by the distributed network code. Finally, analytical derivations and findings are substantiated via Monte Carlo simulations.

In this paper, we propose a simple analytical methodology to study the performance of multi-source multirelay cooperative wireless networks with network coding at the relay nodes and Maximum-Likelihood (ML-) optimum channelaware 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.

Since the pioneering research work of Ahlswede et al. in 2000, Network Coding (NC) has rapidly emerged as a major research area in electrical engineering and computer science due to its wide applicability to communication through real networks. The many contributions available in the literature to date, ranging from pure theoretical studies on fundamental limits to practical experimentations in real-world environments, offer a clear evidence that the shift in paradigm envisaged by NC might revolutionize the way we manage, operate, and understand the organization of networks. NC allows intermediate nodes of communication networks to combine the information received from multiple links for subsequent transmissions, and offer a powerful and efficient generalization to network information delivery via routing, where network nodes simply store and forward data, and processing is only accomplished at the end nodes. In this paper, we have a twofold objective: i) first, we summarize fundamental information-theoretic results, which, since their publication, have been representing the foundation for all subsequent research in this field, and ii) then, we introduce and summarize the latest results related to the analysis, design, and optimization of the so-called network error correction coding problem, which is instrumental for the effective use of NC over lossy, e.g., wireless, networks.