Shahriar Etemadi Tajbakhsh

Shahriar Etemadi Tajbakhsh, Parastoo Sadeghi, Rodney Kennedy

We introduce a method for securely delivering a set of messages to a group of clients over a broadcast erasure channel where each client is interested in a distinct message. Each client is able to obtain its own message but not the others'. In the proposed method the messages are combined together using a special variant of random linear network coding. Each client is provided with a private set of decoding coefficients to decode its own message. Our method provides security for the transmission sessions against computational brute-force attacks and also weakly security in information theoretic sense. As the broadcast channel is assumed to be erroneous, the missing coded packets should be recovered in some way. We consider two different scenarios. In the first scenario the missing packets are retransmitted by the base station (centralized). In the second scenario the clients cooperate with each other by exchanging packets (decentralized). In both scenarios, network coding techniques are exploited to increase the total throughput. For the case of centralized retransmissions we provide an analytical approximation for the throughput performance of instantly decodable network coded (IDNC) retransmissions as well as numerical experiments. For the decentralized scenario, we propose a new IDNC based retransmission method where its performance is evaluated via simulations and analytical approximation. Application of this method is not limited to our special problem and can be generalized to a new class of problems introduced in this paper as the cooperative index coding problem.

Shahriar Etemadi Tajbakhsh, Parastoo Sadeghi

We consider a set of $n$ messages and a group of $k$ clients. Each client is privileged for receiving an arbitrary subset of the messages over a broadcast erasure channel, which generalizes scenario of a previous work. We propose a method for secretly delivering each message to its privileged recipients in a way that each receiver can decode its own messages but not the others'. Our method is based on combining the messages using linear network coding and hiding the decoding coefficients from the unprivileged clients. We provide an information theoretic proof for the secrecy of the proposed method. In particular we show that an unprivileged client cannot obtain any meaningful information even if it holds the entire set of coded data packets transmitted over the channel. Moreover, in our method, the decoding complexity is desirably low at the receiver side.