Robust Berrut-Approximated Coded Computing via Discrete Cosine Transforms

Abstract

Coded computing is a reliable and fault-tolerant paradigm for executing large-scale computational tasks over distributed worker nodes. Among existing coded computing frameworks, Berrut Approximated Coded Computing (BACC) enables distributed computation of arbitrary non-polynomial functions through rational interpolation. Although BACC provides provable approximation guarantees and resilience against straggling workers, its robustness against Byzantine workers remains largely unexplored. To fill this research gap, we propose Robust Berrut Approximated Coded Computing (RBACC), which establishes a coding-theoretic framework for BACC by enabling error localization and error correction in the presence of Byzantine workers. In particular, RBACC introduces a new choice of evaluation points that establishes a connection between Berrut interpolation and Discrete Cosine Transform (DCT) codes, thereby enabling error localization and error correction under finite-precision arithmetic. We derive analytical upper bounds on the approximation error of RBACC under multiple operating scenarios, including straggler-only systems and systems with Byzantine workers under finite-precision arithmetic. Building upon this analysis, we formulate several optimization problems for selecting the DCT code dimension and for assigning encoded evaluations to unreliable workers. We show that these are previously unexplored design parameters that can be systematically optimized to improve the reconstruction accuracy. Experimental results demonstrate that the proposed RBACC framework effectively mitigates stragglers and Byzantine workers while offering improved reconstruction accuracy over the baselines.