Exact Tensorization Formulas for Jensen-Shannon Divergence Contraction: The Z-Channel and Binary Erasure Channel

Key Points

• The study aims to derive closed-form formulas for Jensen-Shannon divergence contraction coefficients.
• Developed formulas for tensor-product channels.
• Proved the Edge Reduction Theorem comprehensively.
• Analyzed the dependence of coefficients on support set asymmetry for the Z-channel.
• Established the Chernoff–JSD correspondence for boundary-optimizer channels.
• Provided a thorough proof of the Edge Reduction Theorem.
• Identified that asymmetry in the support set, rather than Hamming distance, influences coefficients for the Z-channel.
• Demonstrated the existence of a Chernoff–JSD correspondence for specific channel types.