Resilient Data: How Majority Logic Ensures Reliable Code Recovery
![The study demonstrates that bit decoding failure probability transitions across distinct availability regimes-linear, polylogarithmic, and sub-logarithmic-as evidenced by the comparison of empirical and theoretical results with a failure probability of [latex] p_f = 0.2 [/latex] and redundancy of [latex] r = 4 [/latex].](https://arxiv.org/html/2601.08765v1/photos/bit_dec_prob.png)
A new analysis demonstrates that locally repairable codes, when paired with majority-logic decoding, can achieve near-perfect data recovery even with significant data loss.
![The study demonstrates that bit decoding failure probability transitions across distinct availability regimes-linear, polylogarithmic, and sub-logarithmic-as evidenced by the comparison of empirical and theoretical results with a failure probability of [latex] p_f = 0.2 [/latex] and redundancy of [latex] r = 4 [/latex].](https://arxiv.org/html/2601.08765v1/photos/bit_dec_prob.png)
A new analysis demonstrates that locally repairable codes, when paired with majority-logic decoding, can achieve near-perfect data recovery even with significant data loss.

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