Coding Theory For Security And Reliability In Wireless Networks
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Wireless networks hold many applications and are an integral part of our lives. Security and reliability are extremely important in wireless networks. These networks must be reliable so that data can be conveyed from transmitters to receivers. Data sent across wireless networks must be kept conﬁdential from unintended users and it is necessary that false packets generated by illegitimate users are rejected by the receiver. Another important task is for the network to determine which network components can be trusted and to what degree. The work presented in this dissertation addresses the security and reliability issues in wireless networks through the use of coding theory. The network is composed of numerous nodes and we consider a classical point to point communication problem. We explore the network reliability issue and develop two algorithms (exponential and polynomial time) which determine minimum redundancy and optimal symbol allocation to assure that the probability of successful decoding is greater than or equal to a speciﬁed threshold. The performance of the algorithms is compared with each other, and MDS, LT, and Raptor codes are compared using the exponential algorithm. We also consider the security problem of keeping a message conﬁdential from an illegitimate eavesdropper in a multiple path network. Carefully crafted Raptor codes are shown to asymptotically achieve perfect secrecy and zero-error probability, and a bit allocation method across the paths is developed. Lastly, we look into the problem of determining the integrity of nodes in the network. In particular, we show how the malicious nodes can be localized in the network through the use of ReedMuller codes. The Reed-Muller codes represent the paths that are necessary in the network. For the case where a path is not realizable according to the network connectivity matrix, we conceived an algorithm to treat the non-realizable paths as erasures and decode to localize malicious nodes. The performance of the algorithm is compared to several techniques.
dissertation or thesis