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Register a new userVariable-Rate Distributed Source Coding in the Presence of Byzantine Sensors
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Added by
Oliver Kosut
Publication date
2007
fields
Informatics Engineering
and research's language is
English
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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.
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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. 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 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.
We determine the rate region of the vector Gaussian one-helper source-coding problem under a covariance matrix distortion constraint. The rate region is achieved by a simple scheme that separates the lossy vector quantization from the lossless spatial compression. The converse is established by extending and combining three analysis techniques that have been employed in the past to obtain partial results for the problem.
Distributed source coding is the task of encoding an input in the absence of correlated side information that is only available to the decoder. Remarkably, Slepian and Wolf showed in 1973 that an encoder that has no access to the correlated side information can asymptotically achieve the same compression rate as when the side information is available at both the encoder and the decoder. While there is significant prior work on this topic in information theory, practical distributed source coding has been limited to synthetic datasets and specific correlation structures. Here we present a general framework for lossy distributed source coding that is agnostic to the correlation structure and can scale to high dimensions. Rather than relying on hand-crafted source-modeling, our method utilizes a powerful conditional deep generative model to learn the distributed encoder and decoder. We evaluate our method on realistic high-dimensional datasets and show substantial improvements in distributed compression performance.
We investigate the impact of Byzantine attacks in distributed detection under binary hypothesis testing. It is assumed that a fraction of the transmitted sensor measurements are compromised by the injected data from a Byzantine attacker, whose purpose is to confuse the decision maker at the fusion center. From the perspective of a Byzantine attacker, under the injection energy constraint, an optimization problem is formulated to maximize the asymptotic missed detection error probability, which is based on the Kullback-Leibler divergence. The properties of the optimal attack strategy are analyzed by convex optimization and parametric optimization methods. Based on the derived theoretic results, a coordinate descent algorithm is proposed to search the optimal attack solution. Simulation examples are provided to illustrate the effectiveness of the obtained attack strategy.
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.
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