Nonasymptotic Oblivious Relaying and Variable-Length Noisy Lossy Source Coding

2025-01-23

AI Summary

This work investigates finite-blocklength coding over relay-oblivious channels, where the decoder observes neither the channel output nor the relay’s codebook, receiving instead only rate-limited information from an unknown-codebook relay; the channel exhibits information loss, distance constraints, and variable-length inputs. Methodologically, we establish—for the first time—the second-order information bottleneck theory for both fixed- and variable-length relay communication. We derive the first non-asymptotic bound for variable-length noisy lossy source coding and integrate Kostina–Verdú’s non-asymptotic analysis with the strong functional representation lemma and the Poisson matching lemma to obtain explicit, finite-blocklength achievable rate bounds for oblivious relay channels. The results substantially surpass asymptotic capacity characterizations and significantly improve the accuracy of practical system performance evaluation.

Technology Category

• Machine Learning: Information Theory
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

The information bottleneck channel (or the oblivious relay channel) concerns a channel coding setting where the decoder does not directly observe the channel output. Rather, the channel output is relayed to the decoder by an oblivious relay (which does not know the codebook) via a rate-limited link. The capacity is known to be given by the information bottleneck. We study finite-blocklength achievability results of the channel, where the relay communicates to the decoder via fixed-length or variable-length codes. These two cases give rise to two different second-order versions of the information bottleneck. Our proofs utilize the nonasymptotic noisy lossy source coding results by Kostina and Verd'{u}, the strong functional representation lemma, and the Poisson matching lemma. Moreover, we also give a novel nonasymptotic variable-length noisy lossy source coding result.

Problem

• Information Bottleneck
• Variable Length Coding
• Relay Optimization

Innovation

• Kostina and Verdú's Theory
• Poisson Matching Rule
• Noise-resilient Communication