Computational Polarization: An Information-Theoretic Method for Resilient Computing

نویسندگان

چکیده

We introduce an error resilient distributed computing method based on extension of the channel polarization phenomenon to algorithms. The leverages algorithmic split operation that transforms two identical compute nodes into slow and fast workers, which parallels in Polar Codes. This preserves average runtime, analogous conservation Shannon capacity polarization. By leveraging a recursive construction similar spirit Fast Fourier Transform, synthesizes virtual with dispersed return time distributions, we call computational show runtime distributions form functional martingale process, identify their limiting closed-form expressions together non-asymptotic convergence rates, prove strong results Banach spaces. provide information-theoretic lower bound overall any coded computation approach asymptotically achieves optimal for linear functions. An important advantage is near decoding procedure, significantly faster than Maximum Distance Separable codes.

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ژورنال

عنوان ژورنال: IEEE Transactions on Information Theory

سال: 2022

ISSN: ['0018-9448', '1557-9654']

DOI: https://doi.org/10.1109/tit.2021.3139009