Network coding design for multi-source multi-relay cooperative wireless networks

Network coding designs over GF(q) spans an extensive range of research directions covering a wide range of applications. Galois field used for network coding should be a function of the total number of nodes in the networks. Thus, the larger the number of sources and relays the larger the Galois field, while keeping the same diversity order in relay-aided transmission. Furthermore, the modulation order and the Galois field are the same and this solution introduces a constraint on achievable rate and decoding complexity as network code and modulation cannot be chosen independently. In order to overcome this important limitation, in this paper we propose a splitting based approach where network coding and modulation are not necessarily the same. Our results show that if the modulation order is smaller than the Galois field; we are still able to achieve the same diversity order with lower decoding complexity.

The diversity-multiplexing tradeoff (DMT) performances of novel decode-and-forward (DF) relaying protocols for multi-source multi-relay cooperative networks are studied in this paper. For a strong-interference scenario and an isolated-relay scenario, the proposed protocols significantly improve diversity performance over direct source-destination transmissions by using a simple repetition coding strategy in relays. This is in addition to enhancing the multiplexing performance over standard DF protocols, which usually suffer from the half-duplex limitation at relays. Although the DMT performance of DF based relaying protocols is limited by the quality of source relay links in principle, adaptive forms of the proposed protocols at the relays can transmit/not transmit according to source relay transmissions and still provide link reliability and spectral efficiency advantages in general source-relay channel conditions.

Network Coding encourages information coding across a communication network. While the necessity, benefit and complexity of network coding are sensitive to the underlying graph structure of a network, existing theory on network coding often treats the network topology as a black box, focusing on algebraic or information theoretic aspects of the problem. This work aims at an in-depth examination of the relation between algebraic coding and network topologies. We mathematically establish a series of results along the direction of: if network coding is necessary/beneficial, or if a particular finite field is required for coding, then the network must have a corresponding hidden structure embedded in its underlying topology, and such embedding is computationally efficient to verify. Specifically, we first formulate a meta-conjecture, the NC-Minor Conjecture, that articulates such a connection between graph theory and network coding, in the language of graph minors. We next prove that the NC-Minor Conjecture is almost equivalent to the Hadwiger Conjecture, which connects graph minors with graph coloring. Such equivalence implies the existence of K4, K5, K6, and KO(q/ log q) minors, for networks requiring F3, F4, F5 and Fq, respectively. We finally prove that network coding can make a difference from routing only if the network contains a K4 minor, and this minor containment result is tight. Practical implications of the above results are discussed.

Consider a multi-relay cooperative diversity network consisting of a source, N relays, and a destination. For the transmission of a data symbol from the source to the destination, the relays cooperate with the source through the decode and forward protocol. All the links are statistically independent and undergo flat Rayleigh fading. Conventional instantaneous signal-to-noise ratio based selection combining at the destination chooses one link from the set consisting of the source-to-destination link and the N relay-to-destination links. However, this scheme does not account for the effect of the source-to-relay links in the error performance. To overcome this drawback, we present here a scaled selection combining scheme, which accounts for this effect through a deterministic scale factor. The end-to-end symbol error probability (SEP) of this scheme with binary phase-shift keying is derived in closed form. We also give a method of obtaining the optimum scale factor that minimizes the end-to-end SEP.

This paper considers block acknowledgement (BACK) mechanisms in wireless regenerative relay networks. Conventionally, a total of (2N+1) BACK packets are required in wireless regenerative N-relay networks to acknowledge the data transmission between the source and destination via the relays. In this paper, based on network coding (NC) we propose an efficient BACK scheme to significantly reduce the required acknowledgement load by N BACK packets. Importantly, by deriving the error probability of the determination of the packets to be retransmitted at the source or relays, it is found that the utilised NC helps improve the reliability of BACK transmissions. Furthermore, some asymptotic scenarios of the forward links are considered and a general expression of error probability in multi-relay networks is derived for each scenario. Finally, simulation results are shown to verify the analytical findings.

Motivation: The task of engineering a protein to perform a target biological function is known as protein design. A commonly used paradigm casts this functional design problem as a structural one, assuming a fixed backbone. In probabilistic protein design, positional amino acid probabilities are used to create a random library of sequences to be simultaneously screened for biological activity. Clearly, certain choices of probability distributions will be more successful in yielding functional sequences. However, since the number of sequences is exponential in protein length, computational optimization of the distribution is difficult.Results: In this paper, we develop a computational framework for probabilistic protein design following the structural paradigm. We formulate the distribution of sequences for a structure using the Boltzmann distribution over their free energies. The corresponding probabilistic graphical model is constructed, and we apply belief propagation (BP) to calculate marginal amino acid probabilities. We test this method on a large structural dataset and demonstrate the superiority of BP over previous methods. Nevertheless, since the results obtained by BP are far from optimal, we thoroughly assess the paradigm using high-quality experimental data. We demonstrate that, for small scale sub-problems, BP attains identical results to those produced by exact inference on the paradigmatic model. However, quantitative analysis shows that the distributions predicted significantly differ from the experimental data. These findings, along with the excellent performance we observed using BP on the smaller problems, suggest potential shortcomings of the paradigm. We conclude with a discussion of how it may be improved in the future.Contact: fromer@cs.huji.ac.il

Nowadays network coding has attracted a lot of attentions from researchers in fields of information and coding theory, wireless communications, P2P, etc, as it has enormous potential to improve network throughput and to utilize the maximum bandwidth in networks. Whereas due to its high computation complexity, it is not easy to implement network coding in a real network environment. Network Flow Processor (NFP) is a multi-core specific processor, widely used in switches, routers. NPF has a powerful computation capacity, since it is composed of 40 cores and each core can concurrently executes up to 8 threads. In this paper, we discuss about the network coding fundamental and the NFP architecture in order to make NFP support the encoding function of network coding. During the implementation of network coding on NFP, we use loop-based and table-based approaches for multiplication in finite field. With our experimental results, a single card of NFP can offer a throughput of encoding up to 43.9Mbps.

The application of Low-Density Generator Matrix (LDGM) Codes combined with Survey Propagation (SP) in steganography seems to be advantageous, since it is possible to approximate the coset leader directly. Thus, large codeword length can be applied, resulting in an embedding efficiency close to the theoretical upper bound of embedding efficiency. Since this approach is still quite complex, this paper deals with the application of Belief Propagation (BP) to LDGM Codes used to reduce the complexity of embedding while keeping the embedding efficiency constant.

Cooperative communications is a candidate technology for future network designs. In this paper, a design of distributed network coding is introduced. The proposed design are based on algebraic constructions in Finite Field using symmetric Matrices. These set of codes are an alternative to Generalized Dynamic Network Codes (GDNC). A rich feature of these codes are a high diversity and ease of scalability to larger network designs. Finite fields has a unique feature of constraining the signal energy and its performance does not deteriorate much when transmitted through fading channels. Results are compared with theoretical evaluations.

Cooperative communication is shown to be an efficient method of combating fading in wireless networks. By ”sharing” their antennas cooperating single-antenna nodes create a virtual multi-antenna system and therefore, benefit from spatial diversity. Network coding being a particular cooperative communication technique provides substantial gains in data rate, especially in networks with many sink nodes. By allowing intermediate nodes of a network to mix the incoming data streams, one can achieve the multicast capacity. Recently, Xiao and Skoglund showed that binary network coding (BNC) is not optimal for multi-user multi-relay networks in terms of diversity and proposed diversity network coding (DNC) scheme that outperforms BNC approach. Following this approach we examine potential diversity gains of using the DNC scheme for multi-source line networks. We show that the DNC technique outperforms both conventional time-orthogonal transmission and the BNC scheme. Further, the problem of optimal scheduling of the transmission is explored. We formulate the optimization problem and propose efficient solutions. Numerical results are presented to support theoretical findings.

This letter proposes channel training designs for two-hop multi-relay networks, where a source, a destination and multiple amplify-and-forward (AF) relays are all equipped with multi-antenna, based on mean square error (MSE) and signal-to-noise ratio (SNR) criteria with taking into account spatial fading correlation between multiple-input multiple-output (MIMO) channel elements. The minimum MSE and maximum SNR channel estimators are initially derived and, then, optimal structures on source training signal and relay matrices are determined. An iterative and a closed-form power allocation solutions are proposed for both channel estimators. Simulation results show that the proposed schemes outperform the conventional schemes.

Chapter 1 - An Introduction to Network Coding

Cluster-level based link redundancy with network coding in duty cycled relay wireless sensor networks

When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this paper explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.

SUMMARYThis paper introduces limited feedback technique into physical‐layer network coding (PLNC) scheme, which is the most spectrally efficient protocol in two‐way relay channels, consisted of one relay and two end nodes (sources). Decode‐and‐forward (DF) and partial‐decode‐and‐forward (PDF) strategies are considered for PLNC, and all nodes are assumed to have two antennas to allow transmission by Alamouti's orthogonal space–time block code to provide diversity. In DF, by limited feedback, one of the sources is informed about instantaneous channel state information (CSI) to increase the bit error rate (BER) performance at relay. The closed‐form upper and lower bounds on the bit error probability are derived for binary phase‐shift keying (BPSK) and quadrature PSK (QPSK) modulations and approved via computer simulations. In PDF strategy, each source has to know CSI between relay and the other source for decoding, which causes extra protocol complexity. Moreover, for the system in which all nodes have two antennas, classical PDF strategy does not satisfy orthogonality at the end nodes. Therefore, in this paper, a modified‐PDF (MPDF) strategy with limited feedback is proposed. In MPDF, for decoding at the end nodes, differential phase information between channel fading coefficients having maximum amplitudes is fed back to the sources by relay. This approach enables single‐symbol decoding, besides full diversity, and sources do not need to know CSI between relay and the other source. It is shown via computer simulations that MPDF strategy provides significantly better BER performance than the classical PDF for BPSK and QPSK modulations.Copyright © 2012 John Wiley & Sons, Ltd.