#### On Intercept Probability Minimization under Sparse Random Linear Network Coding

##### Andrea Tassi, Robert J. Piechocki, Andrew Nix

This paper considers a network where a node wishes to transmit a source message to a legitimate receiver in the presence of an eavesdropper. The transmitter secures its transmissions employing a sparse implementation of Random Linear Network Coding (RLNC). A tight approximation to the probability of the eavesdropper recovering the source message is provided. The proposed approximation applies to both the cases where transmissions occur without feedback or where the reliability of the feedback channel is impaired by an eavesdropper jamming the feedback channel. An optimization framework for minimizing the intercept probability by optimizing the sparsity of the RLNC is also presented. Results validate the proposed approximation and quantify the gain provided by our optimization over solutions where non-sparse RLNC is used.

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