When users make personal privacy choices, correlation between their data can cause inadvertent leakage about users who do not want to share their data through other users sharing their data. As a solution, we consider local redaction mechanisms. To model pre-existing approaches, we study the class of data-independent privatization mechanisms within this framework and upper-bound their utility when data correlation is modeled by a stationary Markov process. In contrast, we find a novel family of data-dependent mechanisms, which improve the utility by leveraging a data-dependent leakage measure.

We consider gradient coding in the presence of an adversary controlling so-called malicious workers trying to corrupt the computations. Previous works propose the use of MDS codes to treat the responses from malicious workers as errors and correct them using the error-correction properties of the code. This comes at the expense of increasing the replication, i.e., the number of workerseach partial gradientis computed by. In this work, we propose a way to reduce the replication to$ {s} +1$instead of$2 {s} +1$in the presence ofsmalicious workers. Our method detects erroneous inputs from the malicious workers, transforming them into erasures. This comes at the expense ofsadditional local computations at the main node and additional rounds of light communication between the main node and the workers. We define a general framework and give fundamental limits for fractional repetition data allocations. Our scheme is optimal in terms of replication and local computation and incurs a communication cost that is asymptotically, in the size of the dataset, a multiplicative factor away from the derived bound. We furthermore show how additional redundancy can be exploited to reduce the number of local computations and communication cost, or, alternatively, tolerate straggling workers.

We tackle the problem of Byzantine errors in dis-tributed gradient descent within the Byzantine-resilient gradient coding framework. Our proposed solution can recover the exact full gradient in the presence of$s$malicious workers with a data replication factor of only$s$+ 1. It generalizes previous solutions to any data assignment scheme that has a regular replication over all data samples. The scheme detects malicious workers through additional interactive communication and a small number of local computations at the main node, leveraging group-wise comparisons between workers with a provably optimal grouping strategy. The scheme requires at most$s$interactive rounds that incur a total communication cost logarithmic in the number of data samples.

We consider gradient coding in the presence of an adversary controlling so-called malicious workers trying to corrupt the computations. Previous works propose the use of MDS codes to treat the inputs of the malicious workers as errors and correct them using the error-correction properties of the code. This comes at the expense of increasing the replication, i.e., the number of workers each partial gradient is computed by. In this work, we reduce replication by proposing a method that detects the erroneous inputs from the malicious workers, hence transforming them into erasures. For s malicious workers, our solution can reduce the replication to s+1 instead of 2s+1 for each partial gradient at the expense of only s additional computations at the main node and additional rounds of light communication between the main node and the workers. We give fundamental limits of the general framework for fractional repetition data allocation. Our scheme is optimal in terms of replication and local computation but incurs a communication cost that is asymptotically, in the size of the dataset, a multiplicative factor away from the derived bound.

Over-the-air computation has the potential to in-crease the communication-efficiency of data-dependent distributed wireless systems, but is vulnerable to eavesdropping. We consider over-the-air computation over block-fading additive white Gaussian noise channels in the presence of a passive eaves-dropper. The goal is to design a secure over-the-air computation scheme. We propose a scheme that achieves MSE-security against the eavesdropper by employing zero-forced artificial noise, while keeping the distortion at the legitimate receiver small. In contrast to former approaches, the security does not depend on external helper nodes to jam the eavesdropper’s received signal. We thoroughly design the system parameters of the scheme, propose an artificial noise design that harnesses unused transmit power for security, and give an explicit construction rule. Our design approach is applicable in both cases, if the eavesdropper’s channel coefficients are known and if they are unknown in the signal design. Simulations demonstrate the performance, and show that our noise design outperforms other methods.