We study the capacity of point-to-point erasure NETWORKs under a restricted form of NETWORK CODING to which we refer as spatial NETWORK CODING. In this form of CODING, the nodes can not perform CODING on successive packets which are received from one incoming link. The CODING at a node is restricted to the packets received at the same time slot from different incoming links to the node. In other words, the temporal aspect of CODING is absent. We prove that the capacity of a unicast session under spatial NETWORK CODING is the statistical average of the minimum cut of the random graph corresponding to the erasure NETWORK. Then, we consider a NETWORK with a complete, directed and acyclic graph in which the nodes are erased independently. We prove that the capacity of the NETWORK under spatial NETWORK CODING is the same as its capacity under general NETWORK CODING. This shows that temporal CODING has no improving effect for this NETWORK. Finally, we compare the capacities under different CODING schemes for the complete graph with the edges that are erased independently.

Routing in wireless sensor NETWORKs is one of the main challenges which directly influences the reliability and efficiency of the NETWORK. In this research, we combined several flows using inter-CODING technique and hierarchical tree alternative path (HTAP) technique in order to efficiently control the congestion. It uses random NETWORK CODING idea to increases NETWORK efficiency and decreases the congestion implicitly. Also, it explicitly reroutes the congested flows along alternative paths when the congestion condition is detected in congested nodes. The proposed method was simulated in different scenarios using MATLAB software and the simulation results showed that it decreases the number of transmitted packets, improves efficiency, and decreases energy consumption in comparison to original HTAP.

Energy constraint in wireless sensor NETWORKs, have been made the packets routing with essential issues. In event based applications, the inherent constraint of these NETWORKs and large packet traffics affects the NETWORKs lifetime. Hence, the energy of sensor nodes near the sink node will be exhusted and the duty of WSNs will be affected with this problem. NETWORK CODING scheme with enCODING and deCODING of data packets, have improved the throughput, reduces the average end-to-end delays and resilient the NETWORKs against the fails. In this paper, we proposes a routing algorithm using NETWORK CODING scheme. For selecting appropriate routing paths, the proposed scheme considers the link quality and residual energy of neighbor nodes. Simulation results show that the proposed scheme increases the NETWORK reliability and decreases the energy consumption in comparing with other relate scheme.

Sparse NETWORK CODING was introduced to reduce the computational complexity of the random linear NETWORK CODING. In this method, most of the deCODING matrix coefficients are zero. Partial deCODING means the possibility of deCODING a part of the raw packets is one of the capabilities of the sparse NETWORK CODING method. We introduce three different models of sparse CODING method as an approach to reduce deCODING latency in real-time communication. More precisely, we first evaluate a sparse NETWORK CODING for a no feedback configuration in terms of the performance of the total number of transmissions required, and the average packet deCODING delay for a generation of raw packets, by introducing a Markov chain-based model. Then we evaluate the accuracy of the proposed model using extensive simulation and show that the proposed model can accurately estimate the number of required transmissions and deCODING delay for a generation of packets. The results also evaluate the accuracy of the model in the erasure channel. In the following, we introduce the feedback-based model and we show that this model can create a better balance between the functions of the number of transmissions and the average deCODING delay per packet. Finally, by focusing on the problem of finding the random spanning tree, we present a graph-based model for analyzing sparse NETWORK CODING and show that although the proposed model is valid only for grade 2 sparsity, it also has the capacity to develop for lower sparsity.

In recent years, NETWORK CODING (NC) has been used to increase performance and efficiency in Wireless Sensor NETWORKs (WSNs). In NC, Sensor Nodes (SNs) of NETWORK first store the received data as a packet, then process and combine them and eventually send them. Since the bandwidth of edges between SNs is limited, management and balancing bandwidth should be used for NS. In this paper, we present an optimization model for routing and balancing bandwidth consumption using NC and multicast flows in WSNs. This model minimizes the ratio of the total maximum bandwidth to the available bandwidth in NETWORK's edges and we use the dual method to solve this model. We also use the Karush– Kuhn– Tucker conditions (KKT) to calculate a lower bound and find the optimal solution and point in optimization model. For this purpose, we need to calculate the derivative of the Lagrangian function relative to its variables, in order to determine the condition as a multi-excited multi-equation device. But since the solution of equations KKT is centralized and for WSNs with a large number of SNs, it is very difficult and time consuming and almost impractical, we provide a distributed and repeatable algorithm for solving proposed model in which instead of deriving derivatives, combination Sub-gradient method and NETWORK flow separation method are used, thus allow each SN locally and based on the information of its neighboring nodes performs optimal routing and balances bandwidth consumption in the NETWORK. The effectiveness of the proposed optimization model and the proposed distributed algorithm with multiple runs of simulation in terms of the number of Source SNs (SSNs) and Lagrange coefficient and step size have been investigated. The results show that the proposed model and algorithm, due to informed routing and NC, can improve the parameters of the average required time to find the route optimal, the total amount of virtual flow in NETWORK’ s edges, the average latency end-to-end of the NETWORK, the consumed bandwidth, the average lifetime of the NETWORK and the consumed energy, or not very weak compared to other models. The proposed algorithm also has great scalability, because computations are done distributed and decentralized, and there is an insignificant dependence between the SNs.

NETWORK CODING is an effective approach for improving the performance of wireless NETWORKs, such that a new generation of routing protocols, known as NETWORK CODING-aware protocols, recognize CODING opportunities during their route discovery process, and try to establish routes containing appropriate CODING opportunities. Most of the research works being done around this type of routing, only try to maximize the number of CODING opportunities along data transmission route. However, merely considering CODING opportunities, may decrease the optimality and the throughput of routes, since sometimes, by considering only the number of CODING opportunities without paying attention to the quality of links along routes, the quality of detected routes will be decreased. In this paper, in order to resolve the deficiencies of previously related works, a new NETWORK CODING-aware routing protocol based on fuzzy logic is proposed, such that the delay of links besides the satus of all nodes along different paths are evaluated through utilizing fuzzy logic, and the overall value of all paths are determined. Finally, paths wirh better status in terms of the quality of links and nodes, are selected for data transmission. Simulation results demonstrate that the proposed protocol has better performance than previous approaches, in terms of throughput, packet delivery ratio, and delay.

Recently, a new technique called NETWORK CODING has been introduced where it has numerous advantages on the computer NETWORKs. NETWORK CODING changes the traditional view of data transfer in store and forward paradigm and allows the nodes to store packets in their memory to combine with other packets, then, send to next nodes. In this paper, an optimization problem is proposed which balance memory utilization in NETWORK-CODING-based-multicast routing of Wireless Sensor NETWORKs (WSNs). In the large WSNs, solving this optimization problem in a centralized manner is impractical and almost impossible, therefore, by using sub-gradient and decomposition techniques, a distributed algorithm is presented in which the nodes make a decision based on local information. The performance evaluation of proposed mechanisms are carried by OMNETT++ simulator and the results show that the proposed model averagely decreases the end to end delay and buffer overflow by 17% and 95%, respectively. However, it increases the energy consumption and consequently decreases lifetime by 14%. The decentralized algorithm decreases buffer overflow 69% and has more delay by 11% than the optimization model, however, it can be utilized in large WSNs due to its distributed computations.