Network Codes Resilient to Jamming and Eavesdropping

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time, rate-optimal distributed network codes for this scenario, improving on the rates achievable in previous work. Our main contribution shows that as long as the sum of the adversary's jamming rate Zo and his eavesdropping rate Zi is less than the network capacity C, (i.e., Zo+Zi<C), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this to design codes that allow communication at the optimal source rate of C-Zo-Zi, while keeping the communicated message secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. In proving our results we correct an error in prior work by a subset of the authors in this work.Comment: 6 pages, to appear at IEEE NetCod 201

Network Codes Resilient to Jamming and Eavesdropping

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time distributed network codes that are information-theoretically rate-optimal for this scenario, improving on the rates achievable in prior work by Ngai et al. Our main contribution shows that as long as the sum of the number of links the adversary can jam (denoted by Z_O) and the number of links he can eavesdrop on (denoted by Z_I) is less than the network capacity (denoted by C) (i.e., Z(O) + Z_I < C), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this scheme as a module to design codes that allow communication at the source rate of C - Z_O when there are no security requirements, and codes that allow communication at the source rate of C - Z_O - Z_I while keeping the communicated message provably secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. We also prove that the rate-region obtained is information-theoretically optimal. In proving our results, we correct an error in prior work by a subset of the authors in this paper

Coding for Errors and Erasures in Random Network Coding

The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that linear network coding is vector-space preserving, information transmission is modelled as the injection into the network of a basis for a vector space $V$ and the collection by the receiver of a basis for a vector space $U$. A metric on the projective geometry associated with the packet space is introduced, and it is shown that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space $V \cap U$ is sufficiently large. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or, equivalently, a subset of the vertices of the corresponding Grassmann graph. Sphere-packing and sphere-covering bounds as well as a generalization of the Singleton bound are provided for such codes. Finally, a Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style ``list-1'' minimum distance decoding algorithm is provided.Comment: This revised paper contains some minor changes and clarification

Refined Coding Bounds and Code Constructions for Coherent Network Error Correction

Coherent network error correction is the error-control problem in network coding with the knowledge of the network codes at the source and sink nodes. With respect to a given set of local encoding kernels defining a linear network code, we obtain refined versions of the Hamming bound, the Singleton bound and the Gilbert-Varshamov bound for coherent network error correction. Similar to its classical counterpart, this refined Singleton bound is tight for linear network codes. The tightness of this refined bound is shown by two construction algorithms of linear network codes achieving this bound. These two algorithms illustrate different design methods: one makes use of existing network coding algorithms for error-free transmission and the other makes use of classical error-correcting codes. The implication of the tightness of the refined Singleton bound is that the sink nodes with higher maximum flow values can have higher error correction capabilities.Comment: 32 page

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