Unified Error Analysis for Synchronous and Asynchronous Two-User Random Access

TL;DR

This paper develops a unified error analysis framework for two-user random access systems, addressing both synchronous and asynchronous settings with multiple decoding strategies and deriving bounds on error probabilities.

Contribution

It introduces a comprehensive error analysis method that applies to both synchronous and asynchronous two-user random access, including novel decoding schemes and error bounds.

Findings

Derived upper bounds on error probabilities for both settings.

Unified analysis framework applicable to synchronous and asynchronous systems.

Quantified trade-offs between decoding accuracy and collision detection.

Abstract

We consider a two-user random access system in which each user independently selects a coding scheme from a finite set for every message, without sharing these choices with the other user or with the receiver. The receiver aims to decode only user 1 message but may also decode user 2 message when beneficial. In the synchronous setting, the receiver employs two parallel sub-decoders: one dedicated to decoding user 1 message and another that jointly decodes both users messages. Their outputs are synthesized to produce the final decoding or collision decision. For the asynchronous setting, we examine a time interval containing $L$ consecutive codewords from each user. The receiver deploys $2^{2L}$ parallel sub-decoders, each responsible for decoding a subset of the message-code index pairs. In both synchronous and asynchronous cases, every sub-decoder partitions the coding space into three disjoint regions: operation, margin, and collision, and outputs either decoded messages or a collision report according to the region in which the estimated code index vector lies. Error events are defined for each sub-decoder and for the overall receiver whenever the expected output is not produced. We derive achievable upper bounds on the generalized error performance, defined as a weighted sum of incorrect-decoding, collision, and miss-detection probabilities, for both synchronous and asynchronous scenarios.