Published January 14, 2026
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Exact Tensorization Formulas for Jensen-Shannon Divergence Contraction: The Z-Channel and Binary Erasure Channel
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Description
Closed-form formulas for JSD contraction coefficients of tensor-product channels.
Key results:
- Edge Reduction Theorem with full proof
- Z-channel: coefficient depends on support set asymmetry, not Hamming distance
- Chernoff–JSD correspondence for boundary-optimizer channels
Note (March 2026): By the general identity η_f(W) = η_χ²(W) for all f-divergences (Ordentlich-Polyanskiy; Polyanskiy-Wu Theorem 33.6), all formulas in this work simultaneously give η_χ² for the same tensor-product channels. The results are not JSD-specific.
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alex_shvets_jsd_tensorization.pdf
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