Sparse Network Coding (SNC) has been a promising network coding scheme as an improvement for Random Linear Network Coding (RLNC) in terms of the computational complexity. However, in this literature, there has been no analytical expressions for the probability of decoding a fraction of source messages after transmission of some coded packets. In this work, we looked into the problem of the probability of decoding a fraction of source messages, i.e., partial decoding, in the decoder for a system which uses SNC. We exploited the Principle of Inclusion and Exclusion to derive expressions of partial decoding probability. The presented model predicts the probability of partial decoding with an average deviation of 6 . Our results show that SNC has a great potential for recovering a fraction of the source message, especially in higher sparsity and lower Galois Field size. Moreover, to achieve a better probability of partial decoding throughout transmissions, we define a sparsity tuning scheme that significantly increases the probability of partial decoding. Our results show that this tuning scheme achieves a 16 improvement in terms of probability of decoding a fraction of source packets with respect to traditional SNC.
Opportunistic relaying has the potential to achieve full diversity gain, while random linear network coding (RLNC) can reduce latency and energy consumption. In recent years, there has been a growing interest in the integration of both schemes into wireless networks in order to reap their benefits, while considering security concerns. This paper considers a multi-relay network, where relay nodes employ RLNC to encode confidential data and transmit coded packets to a destination in the presence of an eavesdropper. Four relay selection protocols are studied covering a range of network capabilities, such as the availability of the eavesdropper’s channel state information or the possibility to pair the selected relay with a node that intentionally generates interference. For each case, expressions for the probability that a coded packet will not be recovered by a receiver, which can be either the destination or the eavesdropper, are derived. Based on those expressions, a framework is developed that characterizes the probability of the eavesdropper intercepting a sufficient number of coded packets and partially or fully recovering the confidential data. Simulation results confirm the validity and accuracy of the theoretical framework and unveil the security-reliability trade-offs attained by each RLNC-enabled relay selection protocol. We consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show that systematic network coding outperforms conventional network coding. We also develop an algorithm based on Gaussian elimination that allows progressive decoding of source packets. Simulation results show that the proposed decoding algorithm can achieve the theoretical optimal performance. Furthermore, we demonstrate that systematic network codes equipped with the proposed algorithm are good candidates for progressive packet recovery owing to their overall decoding delay characteristics. In the literature, there exist analytical expressions for the probability of a receiver decoding a transmitted source message that has been encoded using random linear network coding. In this letter, we look into the probability that the receiver will decode at least a fraction of the source message, and present an exact solution to this problem for both non-systematic and systematic network coding. Based on the derived expressions, we investigate the potential of these two implementations of network coding for information-theoretic secure communication and progressive recovery of data. In this work we consider the problem of secure data transmission on an acyclic multicast network. A new information theoretic model for security is proposed that defines the system as secure if an eavesdropper is unable to get any “meaningful” information about the source. The “wiretap” network model by Cai and Yeung in which no information of the source is made available to the eavesdropper is a special case in the new model. We consider the case when the number of independent messages available to the eavesdropper is less than the multicast capacity of the network. We show that under the new security requirements communication is possible at the multicast capacity. A linear transformation is provided for networks with a given linear code to make the system secure. The transformation needs to be done only at the source and the operations at the intermediate nodes remain unchanged. We also show that if random coding scheme is used the probability of the system being secure can be made arbitrarily close to one by coding over a large enough field.