Problem
Research questions and friction points this paper is trying to address.
game of coding
adversarial noise
input-dependent noise
computation-dependent noise
coding theory
Game of Coding under Computation-Dependent Adversarial Noise
🤖 AI Summary
This work addresses the limitations of traditional coding theory, which assumes a majority of honest nodes and struggles to handle adaptively chosen adversarial noise dependent on computational outputs. The study investigates coding games under input-dependent adversarial noise and establishes, for the first time, their equivalence to input-independent joint noise models. By integrating game-theoretic and information-theoretic frameworks, the authors develop an equivalent transformation mechanism for conditional noise distributions and rigorously prove that both models exhibit identical achievable performance regions and equilibrium utilities. This result significantly extends the theoretical foundation and applicability of coding games in adaptive adversarial environments.
📝 Abstract
The game of coding framework was introduced to extend coding-theoretic recovery beyond its traditional limit, under which the number of honest reports must exceed the number of adversarial or corrupted reports. It does so by exploiting the rational behavior of adversarial participants and their incentive to keep the system live. Existing game-of-coding formulations, however, assume that the adversarial-noise distribution is independent of the realized ground-truth computation. This assumption may be restrictive when an informed adversary can adapt its reports to the value being computed.
In this paper, we study the game of coding with input-dependent adversarial noise. We introduce a unified multi-node, multidimensional formulation. For every family of conditional adversarial-noise distributions, we construct an input-independent joint noise distribution, and prove that this reduction exactly preserves the probability of acceptance and the accepted mean-squared estimation error. Consequently, the input-dependent and input-independent models have identical achievable performance regions, and the same equilibrium utilities.
Innovation
Methods, ideas, or system contributions that make the work stand out.
game of coding
input-dependent adversarial noise
computation-dependent noise
multi-node formulation
equilibrium utility
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