Unified Error Analysis for Synchronous and Asynchronous Two-User Random Access
Nazanin Mirhosseini, Jie Luo
TL;DR
The paper addresses decoding in a two-user random-access channel where active users independently choose coding options from a finite ensemble. It introduces a semi-unsourced model and leverages two parallel sub-decoders in the synchronous setting (joint and single-user decoding) and extends the analysis to frame-asynchronous transmissions to reflect practical CSMA/CA-style operation. It derives achievable upper bounds on a generalized error performance that combines incorrect decoding, collision, and miss-detection probabilities, using RCU-based techniques and threshold optimization. The work further discusses practical temporary user identification mechanisms and provides guidance on numerically evaluating the bounds via Gaussian or saddlepoint methods, demonstrating relevance for multi-packet reception in bursty random access scenarios.
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.