Analog Zigzag-Decodable Codes for Secure and Numerically-Stable Distributed Computing

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.