In this work we consider the communication of information in the presence of a causal adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=(x_1,...,x_n) bit-by-bit over a communication channel. The adversarial jammer can view the transmitted bits x_i one at a time, and can change up to a p-fraction of them. However, the decisions of the jammer must be made in an online or causal manner. Namely, for each bit x_i the jammer's decision on whether to corrupt it or not (and on how to change it) must depend only on x_j for j <= i. This is in contrast to the "classical" adversarial jammer which may base its decisions on its complete knowledge of x. We present a non-trivial upper bound on the amount of information that can be communicated. We show that the achievable rate can be asymptotically no greater than min 1-H(p),(1-4p)^+ . Here H(.) is the binary entropy function, and (1-4p)^+ equals 1-4p for p < 0.25, and 0 otherwise.
Robust and adaptive communication under uncertain interference by Anand Dilip Sarwate Doctor of Philosophy in Engineering—Electrical Engineering and Computer Sciences and the Designated Emphasis in Communication, Computation, and Statistics University of California, Berkeley Professor Michael Gastpar, Chair In the future, wireless communication systems will play an increasingly integral role in society. Cutting-edge application areas such as cognitive radio, ad-hoc networks, and sensor networks are changing the way we think about wireless services. The demand for ubiquitous communication and computing requires flexible communication protocols that can operate in a range of conditions. This thesis adopts and extends a mathematical model for these communication systems that accounts for uncertainty and time variation in link qualities. The arbitrarily varying channel (AVC) is an information theoretic channel model that has a time varying state with no statistical description. We assume the state is chosen by an adversarial jammer, reflecting the demand that our constructions work for all state sequences. In this thesis we show how resources such as secret keys, feedback, and side-information can help communication under this kind of uncertainty. In order to put our results in context we provide a detailed taxonomy of the known results on AVCs in a unified setting. We then prove new results on list decoding Csiszr and Krner's book is widely regarded as a classic in the field of information theory, providing deep insights and expert treatment of the key theoretical issues. It includes in-depth coverage of the mathematics of reliable information transmission, both in two-terminal and multi-terminal network scenarios. Updated and considerably expanded, this new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics. The presentations of all core subjects are self contained, even the advanced topics, which helps readers to understand the important connections between seemingly different problems. Finally, 320 end-of-chapter problems, together with helpful solving hints, allow readers to develop a full command of the mathematical techniques. It is an ideal resource for graduate students and researchers in electrical and electronic engineering, computer science and applied mathematics. In a recent paper, , presented a distributed polynomial-time rate-optimal network-coding scheme that works in the presence of Byzantine faults.We revisit their adversarial models and augment them with three, arguably realistic, models. In each of the models, we present a distributed scheme that demonstrates the usefulness of the model. In particular, all of the schemes obtain optimal rate C-z, where C is the network capacity and z is a bound on the number of links controlled by the adversary. In this paper, we review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if the channel is intended to be used as part of a feedback loop to stabilize an unstable scalar linear system. While classical capacity is not enough, another sense of capacity (parametrized by reliability) called "anytime capacity" is necessary for the stabilization of an unstable process. The required rate is given by the log of the unstable system gain and the required reliability comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk-Kailath scheme for communication over the additive white Gaussian noise (AWGN) channel with feedback. In cases of sufficiently rich information patterns between the encoder and decoder, adequate anytime capacity is also shown to be sufficient for there to exist a stabilizing controller. These sufficiency results are then generalized to cases with noisy observations, delayed control actions, and without any explicit feedback between the observer and the controller. Both necessary and sufficient conditions are extended to continuous time systems as well. We close with comments discussing a hierarchy of difficulty for communication problems and how these results establish where stabilization problems sit in that hierarchy We design codes to transmit information over a network, some subset of which is controlled by a malicious adversary. The computationally unbounded, hidden adversary knows the message to be transmitted, and can observe and change information over the part of the network being controlled. The network nodes do not share resources such as shared randomness or a private key. We first consider a unicast problem in a network with |epsiv parallel, unit-capacity, directed edges. The rate-region has two parts. If the adversary controls a fraction p < 0.5 of the |epsiv edges, the maximal throughput equals (1 - p) |epsiv|. We describe low-complexity codes that achieve this rate-region. We then extend these results to investigate more general multicast problems in directed, acyclic networks A hang glider which relies upon ground effect forces in order to dynamically support a person suspended therefrom.