Remote Channel Synthesis

2025/07/21 by Hamdi, Yassine, Gündüz, Deniz
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2507.15757

Abstract

We consider the problem of synthesizing a memoryless channel between an unobserved source and a remote terminal. An encoder has access to a partial or noisy version Zⁿ = (Z₁, …, Z_n) of a remote source sequence Xⁿ = (X₁, …, X_n), with (X_i,Z_i) independent and identically distributed with joint distribution q_X,Z. The encoder communicates through a noiseless link to a decoder which aims to produce an output Yⁿ coordinated with the remote source; that is, the total variation distance between the joint distribution of Xⁿ and Yⁿ and some i.i.d. target distribution q_X,Y^{⊗ n} is required to vanish as n goes to infinity. The two terminals may have access to a source of rate-limited common randomness. We present a single-letter characterization of the optimal compression and common randomness rates. We also show that when the common randomness rate is small, then in most cases, coordinating Zⁿ and Yⁿ using a standard channel synthesis scheme is strictly sub-optimal. In other words, schemes for which the joint distribution of Zⁿ and Yⁿ approaches a product distribution asymptotically are strictly sub-optimal.

Related

• Exact Channel Synthesis
• Output Constrained Lossy Source Coding with Limited Common Randomness
• Broadcast Channel Synthesis from Shared Randomness
• Multi-Terminal Remote Generation and Estimation Over a Broadcast Channel With Correlated Priors
• Sequential Channel Synthesis