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Entropy of Bernoulli Measures Conditioned on Affine Subspaces and a Problem of Ancheta-Massey

For a Bernoulli(p)(p) source with 0<p<120<p<\frac12, the paper proves that the best lossy compression achievable by a linear encoder is exactly the simple time-sharing strategy that losslessly compresses a fraction of the bits and estimates the rest as zero. Equivalently, every full-row-rank H∈F2k×nH\in\mathbb F_2^{k\times n} satisfies kn≥h(p)(1−D(H)p).\frac{k}{n}\ge h(p)\left(1-\frac{D(H)}p\right). This resolves Massey's question affirmatively for all p<12p<\frac12; Ancheta had already proved the p=12p=\frac12 case.

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Occurred: Aug 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Entropy of Bernoulli Measures Conditioned on Affine Subspaces and a Problem of Ancheta-Massey · Ancheta-Massey linear lossy compression

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VibeMathed
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GPT-5.6 Sol
model · ai model contributor · OpenAI

Yihong Wu
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Entropy of Bernoulli Measures Conditioned on Affine Subspaces and a Problem of Ancheta-Massey parent of this event

For a Bernoulli(p)(p) source with 0<p<120<p<\frac12, the paper proves that the best lossy compression achievable by a linear encoder is exactly the simple time-sharing strategy that losslessly compresses a fraction of the bits and estimates the rest as zero. Equivalently, every full-row-rank H∈F2k×nH\in\mathbb F_2^{k\times n} satisfies kn≥h(p)(1−D(H)p).\frac{k}{n}\ge h(p)\left(1-\frac{D(H)}p\right). This resolves Massey's question affirmatively for all p<12p<\frac12; Ancheta had already proved the p=12p=\frac12 case. parent of this event

This event attributed to Yihong Wu

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This event attributed to GPT-5.6 Sol

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