A transform approach to linear network coding for acyclic networks with delay

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Reliable and energy efficient routing for ad hoc networks

In Mobile Ad hoc NETworks (MANETs), where cooperative behaviour is mandatory, there is a high probability for some nodes to become overloaded with packet forwarding operations in order to support neighbor data exchange. This altruistic behaviour leads to an unbalanced load in the network in terms of traffic and energy consumption. In such scenarios, mobile nodes can benefit from the use of energy efficient and traffic fitting routing protocol that better suits the limited battery capacity and throughput limitation of the network. This PhD work focuses on proposing energy efficient and load balanced routing protocols for ad hoc networks. Where most of the existing routing protocols simply consider the path length metric when choosing the best route between a source and a destination node, in our proposed mechanism, nodes are able to find several routes for each pair of source and destination nodes and select the best route according to energy and traffic parameters, effectively extending the lifespan of the network. Our results show that by applying this novel mechanism, current flat ad hoc routing protocols can achieve higher energy efficiency and load balancing. Also, due to the broadcast nature of the wireless channels in ad hoc networks, other technique such as Network Coding (NC) looks promising for energy efficiency. NC can reduce the number of transmissions, number of re-transmissions, and increase the data transfer rate that directly translates to energy efficiency. However, due to the need to access foreign nodes for coding and forwarding packets, NC needs a mitigation technique against unauthorized accesses and packet corruption. Therefore, we proposed different mechanisms for handling these security attacks by, in particular by serially concatenating codes to support reliability in ad hoc network. As a solution to this problem, we explored a new security framework that proposes an additional degree of protection against eavesdropping attackers based on using concatenated encoding. Therefore, malicious intermediate nodes will find it computationally intractable to decode the transitive packets. We also adopted another code that uses Luby Transform (LT) as a pre-coding code for NC. Primarily being designed for security applications, this code enables the sink nodes to recover corrupted packets even in the presence of byzantine attacks.

The throughput order of multicast traffics with physical-layer network coding in random wireless ad hoc networks

This paper attempts to address the effectiveness of physical-layer network coding (PNC) on the throughput improvement for multi-hop multicast in random wireless ad hoc networks (WAHNs). We prove that the per session throughput order with PNC is tightly bounded as T((nvmR (n))-1) if m = O(R-2 (n)), where n is the total number of nodes, R(n) is the communication range, and m is the number of destinations for each multicast session. We also show that per-session throughput order with PNC is tight bounded as T(n-1), when m = O(R-2(n)). The results of this paper imply that PNC cannot improve the throughput order of multicast in random WAHNs, which is different from the intuition that PNC may improve the throughput order as it allows simultaneous signal access and combination.

Preventing pollution attacks in multi-source network coding

Network coding is a method for achieving channel capacity in networks. The key idea is to allow network routers to linearly mix packets as they traverse the network so that recipients receive linear combinations of packets. Network coded systems are vulnerable to pollution attacks where a single malicious node floods the network with bad packets and prevents the receiver from decoding correctly. Cryptographic defenses to these problems are based on homomorphic signatures and MACs. These proposals, however, cannot handle mixing of packets from multiple sources, which is needed to achieve the full benefits of network coding. In this paper we address integrity of multi-source mixing. We propose a security model for this setting and provide a generic construction.

Single-Generation Network Coding for Networks with Delay

A single-source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the incoming symbols (received at their incoming edges) on their outgoing edges. Memory-free networks with delay using network coding are forced to do inter-generation network coding, as a result of which the problem of some or all sinks requiring a large amount of memory for decoding is faced. In this work, we address this problem by utilizing memory elements at the internal nodes of the network also, which results in the reduction of the number of memory elements used at the sinks. We give an algorithm which employs memory at all the nodes of the network to achieve single- generation network coding. For fixed latency, our algorithm reduces the total number of memory elements used in the network to achieve single- generation network coding. We also discuss the advantages of employing single-generation network coding together with convolutional network-error correction codes (CNECCs) for networks with unit- delay and illustrate the performance gain of CNECCs by using memory at the intermediate nodes using simulations on an example network under a probabilistic network error model.

Network Coding for TCP Throughput Enhancement over a Multi-Hop wireless Network

The poor performance of TCP over multi-hop wireless networks is well known. In this paper we explore to what extent network coding can help to improve the throughput performance of TCP controlled bulk transfers over a chain topology multi-hop wireless network. The nodes use a CSMA/ CA mechanism, such as IEEE 802.11’s DCF, to perform distributed packet scheduling. The reverse flowing TCP ACKs are sought to be X-ORed with forward flowing TCP data packets. We find that, without any modification to theMAC protocol, the gain from network coding is negligible. The inherent coordination problem of carrier sensing based random access in multi-hop wireless networks dominates the performance. We provide a theoretical analysis that yields a throughput bound with network coding. We then propose a distributed modification of the IEEE 802.11 DCF, based on tuning the back-off mechanism using a feedback approach. Simulation studies show that the proposed mechanism when combined with network coding, improves the performance of a TCP session by more than 100%.

Generalized bidirectional multi-pair multi-antennawireless network coding

In this paper, we focus on increasing the throughput and diversity of network coded MIMO transmissions in bidirectional multi-pair wireless relay networks. All nodes have multi-antenna capability. Pairs of nodes want to exchange messages via a relay having multi-antenna and encoding/decoding capability. Nodes transmit their messages to the relay in the first (MAC) phase. The relay decodes all the messages and XORs them and broadcasts the XORed message in the second (BC) phase. We develop a generalized framework for bidirectional multi-pair multi-antenna wireless network coding, which models different MIMO transmission schemes including spatial multiplexing (V-BLAST), orthogonal STBC (OSTBC), and non-orthogonal STBC (NO-STBC) in a unified way. Enhanced throughputs are achieved by allowing all nodes to simultaneously transmit at their full rate. High diversity orders are achieved through the use of NO-STBCs, characterized by full rate and full transmit diversity. We evaluate and compare the performance of VBLAST, OSTBC, and NO-STBC schemes in one-dimensional 1-pair linear network (one pair of nodes and a relay) and two-dimensional 2-pair `cross' network (two pairs of nodes and a relay).

Flows with Inertia in a Three-Dimensional Random Fiber Network

A fiber web is modeled as a three-dimensional random cylindrical fiber network. Nonlinear behavior of fluid flowing through the fiber network is numerically simulated by using the lattice Boltzmann (LB) method. A nonlinear relationship between the friction factor and the modified Reynolds number is clearly observed and analyzed by using the Fochheimer equation, which includes the quadratic term of velocity. We obtain a transition from linear to nonlinear region when the Reynolds numbers are sufficiently high, reflecting the inertial effect of the flows. The simulated permeability of such fiber network has relatively good agreement with the experimental results and finite element simulations.

On the capacity improvement of multicast throughput in wireless ad hoc networks with physical-layer network coding

This paper attempts to address the effectiveness of physical-layer network coding (PNC) on the capacity improvement for multi-hop multicast in random wireless ad hoc networks (WAHNs). While it can be shown that there is a capacity gain by PNC, we can prove that the per session throughput capacity with PNC is ? (nR(n))), where n is the total number of nodes, R(n) is the communication range, and each multicast session consists of a constant number of sinks. The result implies that PNC cannot improve the capacity order of multicast in random WAHNs, which is different from the intuition that PNC may improve the capacity order as it allows simultaneous signal reception and combination. Copyright © 2010 ACM.

A new load distribution strategy for linear network with communication delays

In this paper, we propose a new load distribution strategy called `send-and-receive' for scheduling divisible loads, in a linear network of processors with communication delay. This strategy is designed to optimally utilize the network resources and thereby minimizes the processing time of entire processing load. A closed-form expression for optimal size of load fractions and processing time are derived when the processing load originates at processor located in boundary and interior of the network. A condition on processor and link speed is also derived to ensure that the processors are continuously engaged in load distributions. This paper also presents a parallel implementation of `digital watermarking problem' on a personal computer-based Pentium Linear Network (PLN) topology. Experiments are carried out to study the performance of the proposed strategy and results are compared with other strategies found in literature.

An Efficient Load Distribution Strategy for a Distributed Linear Network of Processors with Communication Delays

In this paper, we present an improved load distribution strategy, for arbitrarily divisible processing loads, to minimize the processing time in a distributed linear network of communicating processors by an efficient utilization of their front-ends. Closed-form solutions are derived, with the processing load originating at the boundary and at the interior of the network, under some important conditions on the arrangement of processors and links in the network. Asymptotic analysis is carried out to explore the ultimate performance limits of such networks. Two important theorems are stated regarding the optimal load sequence and the optimal load origination point. Comparative study of this new strategy with an earlier strategy is also presented.

Interference Alignment as a Tool in Network Coding as Applied to Distributed Storage

In this paper, we outline an approach to the task of designing network codes in a non-multicast setting. Our approach makes use of the concept of interference alignment. As an example, we consider the distributed storage problem where the data is stored across the network in n nodes and where a data collector can recover the data by connecting to any k of the n nodes and where furthermore, upon failure of a node, a new node can replicate the data stored in the failed node while minimizing the repair bandwidth.

On network coding for acyclic networks with delays

Problems related to network coding for acyclic, instantaneous networks (where the edges of the acyclic graph representing the network are assumed to have zero-delay) have been extensively dealt with in the recent past. The most prominent of these problems include (a) the existence of network codes that achieve maximum rate of transmission, (b) efficient network code constructions, and (c) field size issues. In practice, however, networks have transmission delays. In network coding theory, such networks with transmission delays are generally abstracted by assuming that their edges have integer delays. Using enough memory at the nodes of an acyclic network with integer delays can effectively simulate instantaneous behavior, which is probably why only acyclic instantaneous networks have been primarily focused on thus far. However, nulling the effect of the network delays are not always uniformly advantageous, as we will show in this work. Essentially, we elaborate on issues ((a), (b) and (c) above) related to network coding for acyclic networks with integer delays, and show that using the delay network as is (without adding memory) turns out to be advantageous, disadvantageous or immaterial, depending on the topology of the network and the problem considered i.e., (a), (b) or (c).

Performance analysis of adaptive physical layer network coding for wireless two-way relaying

The performance analysis of adaptive physical layer network-coded two-way relaying scenario is presented which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. The deep channel fade conditions which occur at the relay referred as the singular fade states fall in the following two classes: (i) removable and (ii) non-removable singular fade states. With every singular fade state, we associate an error probability that the relay transmits a wrong network-coded symbol during the BC phase. It is shown that adaptive network coding provides a coding gain over fixed network coding, by making the error probabilities associated with the removable singular fade states contributing to the average Symbol Error Rate (SER) fall as SNR-2 instead of SNR-1. A high SNR upper-bound on the average end-to-end SER for the adaptive network coding scheme is derived, for a Rician fading scenario, which is found to be tight through simulations. Specifically, it is shown that for the adaptive network coding scheme, the probability that the relay node transmits a wrong network-coded symbol is upper-bounded by twice the average SER of a point-to-point fading channel, at high SNR. Also, it is shown that in a Rician fading scenario, it suffices to remove the effect of only those singular fade states which contribute dominantly to the average SER.

Physical Layer Network Coding for the K-User Multiple Access Relay Channel

We propose a Physical layer Network Coding (PNC) scheme for the K-user wireless Multiple Access Relay Channel, in which K source nodes want to transmit messages to a destination node D with the help of a relay node R. The proposed scheme involves (i) Phase 1 during which the source nodes alone transmit and (ii) Phase 2 during which the source nodes and the relay node transmit. At the end of Phase 1, the relay node decodes the messages of the source nodes and during Phase 2 transmits a many-to-one function of the decoded messages. To counter the error propagation from the relay node, we propose a novel decoder which takes into account the possibility of error events at R. It is shown that if certain parameters are chosen properly and if the network coding map used at R forms a Latin Hypercube, the proposed decoder offers the maximum diversity order of two. Also, it is shown that for a proper choice of the parameters, the proposed decoder admits fast decoding, with the same decoding complexity order as that of the reference scheme based on Complex Field Network Coding (CFNC). Simulation results indicate that the proposed PNC scheme offers a large gain over the CFNC scheme.