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This paper introduces a unified multi-node, multidimensional formulation of the game of coding with input-dependent adversarial noise, and constructs an input-independent joint noise distribution that exactly preserves the probability of acceptance and the accepted mean-squared estimation error.
Inspired by graph-based manifold learning, a manifold-aware encoding strategy for general coded computing (GCC) is proposed and experiments demonstrate that the proposed strategy consistently and significantly reduces the mean squared recovery error under straggling compared with standard GCC.
GCC formulates coded computing through a natural end-to-end mean-squared error loss that directly measures the discrepancy between the desired computations and their recovered estimates, and enables theoretical performance guarantees for GCC under two complementary straggler regimes.
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