This paper investigates coded distributed matrix-vector multiplications in the context of eavesdropping, denial-of-service attacks, and computational accuracy. It is demonstrated that the coding problem can be reduced to analog secret sharing. The first analog zigzag-decodable secret-sharing scheme is introduced, and its mutual information security is derived. The encoding and decoding algorithms are shown to be numerically stable, relying solely on shift and addition operations, in contrast to existing methods that require matrix inversions or the solution of linear systems. The proposed scheme achieves comparable security levels while exhibiting a significantly smaller relative computation error than the analog Shamir’s secret-sharing scheme. Additionally, it is shown to outperform the analog Shamir’s scheme in model training accuracy when applied to linear regression and logistic regression problems.

With the development of wireless computing devices, extending distributed computing to wireless networks deserves a closer look. This paper considers distributed computing over unreliable and insecure device-to-device (D2D) networks, in which each device is not always available to perform computation. The process of distributed devices exchanging calculated results with each other is vulnerable to eavesdropping in wireless environments. To handle the unreliable devices, we adopt repetition codes to build a novel system that supports general computations, called$\rho $-replication system, where each device has$\rho -1$replicas with duplicate data. A coded computation scheme for the$\rho $-replication system is proposed, which not only achieves the minimum communication load of the system but also ensures weak security of wireless transmissions during data exchange. Furthermore, the replication nature of the system can be exploited for beamforming transmissions, naturally leading to the idea of energy optimization. Simulation results show that increasing$\rho $does not necessarily improve energy efficiency, as the benefit of increased beamforming gain may be outweighed by the drawback of heavier communication load.

This paper studies distributed storage for protecting the confidentiality of partial data in the presence of storage node failures. It is required that not only the original data can be reconstructed from the remaining surviving nodes, but also the data lost by a failed node can be repaired from as few nodes as possible. The minimum number of surviving nodes required to repair a failed node is called the repair degree. Inspired by the zigzag-decodable secret sharing scheme, we propose a new shift-add secret sharing scheme based on the XOR and bitwise-shift operations, in which confidential data is protected by using random keys generated from non-confidential data. The reliability and repairability of the proposed scheme are measured by the message loss probability and the maximum repair degree among all nodes, respectively, and then compared with three benchmark schemes. In contrast to conventional zigzag-decodable codes, the special structure of our proposed scheme allows the design of fast parallel algorithms for modern devices with multi-core processors, which have a linear speedup in decoding time compared with various versions of serial zigzag decoding. Experiments are implemented on a multi-core computer, and the empirical results on decoding time are consistent with our theoretical observations.

Federated learning is emerging as a new paradigm for joint training of machine learning models across multiple distributed devices. In contrast to many existing works that require a central server to facilitate the exchange of local parameters with a star topology, this work considers fully decentralized operations over a wireless ring network. By increasing the radio coverage of each device, the convergence time, as indicated by the second largest singular value of the weighted adjacency matrix, can be shortened, but the mutual interference will be increased causing larger communication delay. The tradeoff between learning and communication delays is characterized by mathematical analysis of the singular-value gap and by numerical experiments on a linear regression problem. By carefully designing the consensus coefficients of the learning algorithm, a network coding scheme is crafted to improve the entire tradeoff curve without consuming more radio resources. It points to a new direction of using network coding to speed up wireless decentralized learning.

This paper considers the design of heterogeneous multi-cloud systems for big data storage and computing in the presence of cloud collusion and failures. A fundamental concept of such a system is the secrecy capacity, which represents the maximum amount of information that can be stored for each unit of storage space under the requirements of secure distributed computing. A capacity-achieving code is designed for matrix multiplication, a computing subroutine widely used in machine learning applications. The code allows fast parallel decoding and unequal data allocation in the clouds. Such a flexibility leads naturally to the idea of optimizing data allocation to minimize the computing time. Given any feasible storage budget, the optimal solution is derived, characterizing explicitly the fundamental tradeoff between storage and computing. Furthermore, it is shown via majorization theory that the whole tradeoff curve improves if the cloud computing rates are more even. Experiments on Amazon EC2 clusters are conducted, corroborating our theoretical observations and the negligibility of decoding overhead.

This paper considers a distributed computing system where nodes are grouped such that nodes in the same group compute the same function. To complete a computing task distributedly, nodes need to exchange their local computation results with each other, which incurs communication cost and security concerns. The objective of this work is to study the tradeoff between computation and communication and avoid exchanged information leakage to eavesdroppers. Given a fixed computation load, we derive lower bounds on the communication load for 1-group and 2-group systems. New coding schemes are proposed and shown to be weakly secure and achieve the optimal tradeoffs for 1-group systems and for 2-group systems with large computation load.

Cloud computing provides a flexible and cost-effective solution to big data applications. Data privacy, however, is a main concern. To avoid information leakage to a cloud service provider, a user may store portions of encoded data in multiple clouds and perform computing tasks in a distributed way. In this work, nested MDS codes and the criterion of perfect secrecy are adopted. The allocation of encoded data to be stored in heterogeneous clouds with different computing capability is formulated as an optimization problem, subject to data reliability and security constraints. The problem is shown to be feasible if and only if the storage budget is above a certain level. The tradeoff between minimum computation time and storage budget is analytically characterized, and the former is proved to be a piecewise-linear decreasing function of the latter. When the storage budget increases beyond a certain threshold, the optimal computation time levels off. Closed-form expressions of minimum computation time and optimal storage allocation are obtained. Numerical results show that the optimized allocation outperforms equal allocation significantly if the computing rates of different clouds have large variation.