An unobservable false data injection (FDI) attack on AC state estimation (SE) is introduced and its consequences on the physical system are studied. With a focus on understanding the physical consequences of FDI attacks, a bi-level optimization probl
em is introduced whose objective is to maximize the physical line flows subsequent to an FDI attack on DC SE. The maximization is subject to constraints on both attacker resources (size of attack) and attack detection (limiting load shifts) as well as those required by DC optimal power flow (OPF) following SE. The resulting attacks are tested on a more realistic non-linear system model using AC state estimation and ACOPF, and it is shown that, with an appropriately chosen sub-network, the attacker can overload transmission lines with moderate shifts of load.
Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher-order asymptotics regimes. Optimal third-order coding rates are derived for general fixed-to-variable codes and for prefix codes
. It is shown that the non-prefix Type Size code, in which codeword lengths are chosen in ascending order of type class size, achieves the optimal third-order rate and outperforms classical Two-Stage codes. Converse results are proved making use of a result on the distribution of the empirical entropy and Laplaces approximation. Finally, the fixed-to-variable coding problem without a prefix constraint is shown to be essentially the same as the universal guessing problem.
We address the problem of finding the capacity of noisy networks with either independent point-to-point compound channels (CC) or arbitrarily varying channels (AVC). These channels model the presence of a Byzantine adversary which controls a subset o
f links or nodes in the network. We derive equivalence results showing that these point-to-point channels with state can be replaced by noiseless bit-pipes without changing the network capacity region. Exact equivalence results are found for the CC model, and for some instances of the AVC, including all nonsymmetrizable AVCs. These results show that a feedback path between the output and input of a CC can increase the equivalent capacity, and that if common randomness can be established between the terminals of an AVC (either by feedback, a forward path, or via a third-party node), then again the equivalent capacity can increase. This leads to an observation that deleting an edge of arbitrarily small capacity can cause a significant change in network capacity. We also analyze an example involving an AVC for which no fixed-capacity bit-pipe is equivalent.
Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the network, in tha
t linear codes are insufficient. To solve the node problem, the class of Polytope Codes is introduced. Polytope Codes are constant composition codes operating over bounded polytopes in integer vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that Polytope Codes achieve a cut-set bound for a class of planar networks. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network.
The distributed source coding problem is considered when the sensors, or encoders, are under Byzantine attack; that is, an unknown group of sensors have been reprogrammed by a malicious intruder to undermine the reconstruction at the fusion center. T
hree different forms of the problem are considered. The first is a variable-rate setup, in which the decoder adaptively chooses the rates at which the sensors transmit. An explicit characterization of the variable-rate achievable sum rates is given for any number of sensors and any groups of traitors. The converse is proved constructively by letting the traitors simulate a fake distribution and report the generated values as the true ones. This fake distribution is chosen so that the decoder cannot determine which sensors are traitors while maximizing the required rate to decode every value. Achievability is proved using a scheme in which the decoder receives small packets of information from a sensor until its message can be decoded, before moving on to the next sensor. The sensors use randomization to choose from a set of coding functions, which makes it probabilistically impossible for the traitors to cause the decoder to make an error. Two forms of the fixed-rate problem are considered, one with deterministic coding and one with randomized coding. The achievable rate regions are given for both these problems, and it is shown that lower rates can be achieved with randomized coding.
The distributed source coding problem is considered when the sensors, or encoders, are under Byzantine attack; that is, an unknown number of sensors have been reprogrammed by a malicious intruder to undermine the reconstruction at the fusion center.
Three different forms of the problem are considered. The first is a variable-rate setup, in which the decoder adaptively chooses the rates at which the sensors transmit. An explicit characterization of the variable-rate minimum achievable sum rate is stated, given by the maximum entropy over the set of distributions indistinguishable from the true source distribution by the decoder. In addition, two forms of the fixed-rate problem are considered, one with deterministic coding and one with randomized coding. The achievable rate regions are given for both these problems, with a larger region achievable using randomized coding, though both are suboptimal compared to variable-rate coding.
