An algorithm is given for placing relays at spatial positions to improve the reliability of communicated data in a sensor network. The network consists of many power-limited sensors, a small set of relays, and a receiver. For each sensor, the receiver receives a direct signal as well as an indirect signal from one of the available relays. The relays rebroadcast the transmissions in order to achieve diversity at the receiver. Both amplify-and-forward and decode-and-forward relay networks are considered. Channels are modeled with Rayleigh fading, path loss, and additive white Gaussian noise. Performance analysis and numerical results are given.

We study network coding capacity under a constraint on the total number of network nodes that can perform coding. That is, only a certain number of network nodes can produce coded outputs, whereas the remaining nodes are limited to performing routing. We prove that every nonnegative, monotonically nondecreasing, eventually constant, rational-valued function on the nonnegative integers is equal to the capacity as a function of the number of allowable coding nodes of some directed acyclic network.

We define the routing capacity of a network to be the supremum of all possible fractional message throughputs achievable by routing. We prove that the routing capacity of every network is achievable and rational, we present an algorithm for its computation, and we prove that every rational number in (0, 1] is the routing capacity of some solvable network. We also determine the routing capacity for various example networks. Finally, we discuss the extension of routing capacity to fractional coding solutions and show that the coding capacity of a network is independent of the alphabet used

We define the routing capacity of a network to be the supremum of all possible fractional message throughputs achievable by routing. We prove that the routing capacity of every network is achievable and rational, we present an algorithm for its computation, and we prove that every non-negative rational number is the routing capacity of some network. We also determine the routing capacity for various example networks. Finally, we discuss the extension of routing capacity to fractional coding solutions and show that the coding capacity of a network is independent of the alphabet used

This paper develops a joint hashing/watermarking scheme in which a short hash of the host signal is available to a detector. Potential applications include content tracking on public networks and forensic identification. The host data into which the watermark is embedded are selected from a secret subset of the full-frame discrete cosine transform of an image, and the watermark is inserted through multiplicative embedding. The hash is a binary version of selected original image coefficients. We propose a maximum likelihood watermark detector based on a statistical image model. The availability of a hash as side information to the detector modifies the posterior distribution of the marked coefficients. We derive Chernoff bounds on the receiver operating characteristic performance of the detector. We show that host-signal interference can be rejected if the hash function is suitably designed. The relative difficulty of an eavesdropper's detection problem is also determined; the eavesdropper does not know the secret key used. Monte Carlo simulations are performed using photographic test images. Finally, various attacks on the watermarked image are introduced to study the robustness of the derived detectors. The joint hashing/watermarking scheme outperforms the traditional "hashless" watermarking technique.