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SUMMARY This paper investigates the problem of constructing a secret and reliable network coding communication scheme against an adversary that can reselect the μ tapping links in different time slices and inject z erroneous packets into the network, while the network suffers from ρ packet erasures. We first derive a necessary condition for keeping the transmitted information secret from the adversary, while the network is only subject to eavesdropping attack, and no errors are injected. We then provide two network coding schemes for error and erasure correction, which can decode the transmitted information correctly. With that, a secret and reliable network coding is proposed by combining two error and erasure correction schemes with secret communication. We show that under the requirement of 2 z + ρ+ μ < k ⩽2 z + 2 ρ communication can achieve a rate of k − μ− z − ρ packets, where k denotes the network capacity. Moreover, it ensures that the communicated information has complete reliability and information-theoretic security from the adversary. In particular, the requirement of packet length does not need to be sufficiently large, which is close to the practical packet length. Finally, we also compare our scheme's performance with existing work; the numeric results and security analyses illustrate the performance and security of our scheme. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The error control of random network coding has recently received a lot of attention because its solution can increase robustness and reliability of data transmission. To achieve this, additional overhead is needed for error correction. In this paper, we design a compressed error and erasure correcting scheme to decrease the additional overhead of error correction. This scheme reduces the computation overhead dramatically by employing an efficient algorithm to detect and delete linearly dependent received packets in the destination node. It also simplifies the hardware operations when the scheme reduces the received matrix Y to form E k( Y ) instead of E( Y ) in the decoding process. If at most r original packets get combined in k packets of one batch, the payload of one packet can increase from M − k to M − O( rlog q k) for the application of compressed code, where M is the packet length. In particular, the decoding complexity of compressed code is O( rm) operations in an extension field [ABSTRACT FROM AUTHOR]