Network error correction with unequal link capacities

This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are considered. Results include new upper bounds, network error correction coding strategies, and examples of network families where our bounds are tight. An example is provided of a network where the capacity is 50% greater than the best rate that can be achieved with linear coding. While coding at the source and sink suffices in networks with equal link capacities, in networks with unequal link capacities, it is shown that intermediate nodes may have to do coding, nonlinear error detection, or error correction in order to achieve the network error correction capacity

Network error correction with unequal link capacities

We study network error correction with unequal link capacities. Previous results on network error correction assume unit link capacities. We consider network error correction codes that can correct arbitrary errors occurring on up to z links. We find the capacity of a network consisting of parallel links, and a generalized Singleton outer bound for any arbitrary network. We show by example that linear coding is insufficient for achieving capacity in general. In our example, the capacity is 50% greater than the linear coding capacity and we achieve using a nonlinear error detection strategy. We also present a method for finding an upper bound on the linear coding capacity for arbitrary network. We show that even for a single source and single sink network, it may be necessary for intermediate nodes to do coding, nonlinear error detection or error correction. This is unlike the equal link capacity case, where coding only at the source and forwarding at intermediate nodes suffices for a single source and sink network. We conjecture that the generalized Singleton outer bound is not achievable in general

Connecting Multiple-unicast and Network Error Correction: Reduction and Unachievability

We show that solving a multiple-unicast network coding problem can be reduced to solving a single-unicast network error correction problem, where an adversary may jam at most a single edge in the network. Specifically, we present an efficient reduction that maps a multiple-unicast network coding instance to a network error correction instance while preserving feasibility. The reduction holds for both the zero probability of error model and the vanishing probability of error model. Previous reductions are restricted to the zero-error case. As an application of the reduction, we present a constructive example showing that the single-unicast network error correction capacity may not be achievable, a result of separate interest.Comment: ISIT 2015. arXiv admin note: text overlap with arXiv:1410.190

Outer bounds on the error correction capacity region for non-multicast networks

In this paper we study the capacity regions of non-multicast networks that are susceptible to adversarial errors. We derive outer bounds on the error correction capacity region and give a family of single- and two-source two-sink 3-layer networks for which these bounds are tight

Encaminhamento confiável e energeticamente eficiente para redes ad hoc

Doutoramento em InformáticaIn 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.Nas redes móveis ad hoc (MANETs), onde o comportamento cooperativo é obrigatório, existe uma elevada probabilidade de alguns nós ficarem sobrecarregados nas operações de encaminhamento de pacotes no apoio à troca de dados com nós vizinhos. Este comportamento altruísta leva a uma sobrecarga desequilibrada em termos de tráfego e de consumo de energia. Nestes cenários, os nós móveis poderão beneficiar do uso da eficiência energética e de protocolo de encaminhamento de tráfego que melhor se adapte à sua capacidade limitada da bateria e velocidade de processamento. Este trabalho de doutoramento centra-se em propor um uso eficiente da energia e protocolos de encaminhamento para balanceamento de carga nas redes ad hoc. Actualmente a maioria dos protocolos de encaminhamento existentes considera simplesmente a métrica da extensão do caminho, ou seja o número de nós, para a escolha da melhor rota entre fonte (S) e um nó de destino (D); no mecanismo aqui proposto os nós são capazes de encontrar várias rotas por cada par de nós de origem e destino e seleccionar o melhor caminho segundo a energia e parâmetros de tráfego, aumentando o tempo de vida útil da rede. Os nossos resultados mostram que pela aplicação deste novo mecanismo, os protocolos de encaminhamento ad hoc actuais podem alcançar uma maior eficiência energética e balanceamento de carga. Para além disso, devido à natureza de difusão dos canais sem fio em redes ad-hoc, outras técnicas, tais como a Codificação de Rede (NC), parecem ser também promissoras para a eficiência energética. NC pode reduzir o número de transmissões, e número de retransmissões e aumentar a taxa de transferência de dados traduzindo-se directamente na melhoria da eficiência energética. No entanto, devido ao acesso dos nós intermediários aos pacotes em trânsito e sua codificação, NC necessita de uma técnica que limite as acessos não autorizados e a corrupção dos pacotes. Explorou-se o mecanismo de forma a oferecer um novo método de segurança que propõe um grau adicional de protecção contra ataques e invasões. Por conseguinte, os nós intermediários mal-intencionados irão encontrar pacotes em trânsito computacionalmente intratáveis em termos de descodificação. Adoptou-se também outro código que usa Luby Transform (LT) como um código de précodificação no NC. Projectado inicialmente para aplicações de segurança, este código permite que os nós de destino recuperem pacotes corrompidos mesmo em presença de ataques bizantinos