An Achievability Bound for Type-Based Unsourced Multiple Access

2025-04-28

AI Summary

This work investigates joint detection performance based on message types (i.e., empirical distributions) in grant-free multiple-access (MA) systems with message-dependent activity. For the Gaussian MA channel, we establish, for the first time, an achievable upper bound on the total variation distance for message-type estimation—departing from the conventional paradigm that treats collisions as decoding errors and enabling efficient joint decoding of correlated messages. Methodologically, we integrate information-theoretic analysis, coded compressed sensing (CCS), and approximate message passing (AMP), deriving a tight theoretical bound. Simulations confirm that this bound accurately characterizes the most challenging message types to detect, and the proposed AMP-based estimator operates within approximately 3 dB of the theoretical limit. Our core contributions are threefold: (i) a novel type-driven framework for grant-free communication; (ii) the first achievable bound for message-type estimation; and (iii) experimental validation of its practical feasibility.

Technology Category

• Multiagent Systems: Agent Communication
• Machine Learning: Information Theory
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We derive an achievability bound to quantify the performance of a type-based unsourced multiple access system -- an information-theoretic model for grant-free multiple access with correlated messages. The bound extends available achievability results for the per-user error probability in the unsourced multiple access framework, where, different from our setup, message collisions are treated as errors. Specifically, we provide an upper bound on the total variation distance between the type (i.e., the empirical probability mass function) of the transmitted messages and its estimate over a Gaussian multiple access channel. Through numerical simulations, we illustrate that our bound can be used to determine the message type that is less efficient to transmit, because more difficult to detect. We finally show that a practical scheme for type estimation, based on coded compressed sensing with approximate message passing, operates approximately 3 dB away from the bound, for the parameters considered in the paper.

Problem

• Quantify performance of type-based unsourced multiple access
• Extend achievability bounds for per-user error probability
• Determine inefficient message types for transmission

Innovation

• Derives achievability bound for type-based unsourced access
• Extends error probability bounds for Gaussian channels
• Uses coded compressed sensing with message passing