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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? 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Partial MDS Codes with Regeneration
Lukas Holzbaur, Sven Puchinger, Eitan Yaakobi, Antonia Wachter-Z · 2020-09-15 · via cs.IT updates on arXiv.org

Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure correcting codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes with local regeneration where each local code is a bandwidth-optimal regenerating MDS code. In the event of a node failure, these codes reduce both, the number of servers that have to be contacted as well as the amount of network traffic required for the repair process. The constructions require significantly smaller field size than the only other construction known in literature. Further, we present a construction of PMDS codes with global regeneration which allow to efficiently repair patterns of node failures that exceed the local erasure correction capability of the code and thereby invoke repair across different local groups.

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