Capacity of a Mixed Multiple-Access Channel with Causal Observation
Abstract
We determine the capacity region of a mixed binary multiple-access channel whose receiver can choose how each observation is formed. Two ports reveal the sum modulo two of the transmitted symbols with retention probabilities pg>pb; their roles are interchanged by an unknown state that remains fixed during the block. With one observation per channel use, no transmitter feedback, and zero switching cost, the region is R1+R2≤pg for every fixed error threshold below one, and a strong converse holds. For error thresholds below one half, the largest open-loop sum rate is (pg+pb)/2, whereas a fixed port permits only pb. A causal receiver attains the larger region by learning the state from erasure flags while using every channel use for data. A posterior port rule makes only finitely many incorrect selections almost surely, with a uniformly bounded expected number of mistakes. Exact random linear-code formulas and output-counting converses quantify the finite-block consequences. At blocklength 256 with (pg,pb)=(0.9,0.4), independent numerical validation supports 214 message bits at a one-percent ensemble failure target, compared with 148 bits for the best open-loop allocation in the same code ensemble. The resulting 44.59\% increase is achieved with the same transmission and observation budgets. The analysis exhibits an explicit capacity gain from controlling the observation axis and separates that gain from information lost after a record has already been formed.
Related
- Interference-Free Capacity of a Binary Interference Channel with Causal Observation
- Unlocking Exponential and Unbounded Robust Gains in Shannon Capacity of Classical Multiple Access Channels with Causal CSIT via Quantum Entanglement Assistance
- Rates and Nearly-Lossless State over a Multi-Access Channel with Causal State Information
- Information Spectrum Methods for ε-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint
- The Capacity of the Relay Channel
BibTeX
@misc{meng2026capacity,
title = {{Capacity of a Mixed Multiple-Access Channel with Causal Observation}},
author = {Xianwei Meng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22391},
eprint = {2609.22391},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22391},
}
RIS
TY - UNPB
TI - Capacity of a Mixed Multiple-Access Channel with Causal Observation
AU - Xianwei Meng
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22391
UR - https://arxiv.org/abs/2609.22391
AB - We determine the capacity region of a mixed binary multiple-access channel whose receiver can choose how each observation is formed. Two ports reveal the sum modulo two of the transmitted symbols with retention probabilities pg>pb; their roles are interchanged by an unknown state that remains fixed during the block. With one observation per channel use, no transmitter feedback, and zero switching cost, the region is R_1+R_2≤pg for every fixed error threshold below one, and a strong converse holds. For error thresholds below one half, the largest open-loop sum rate is (pg+pb)/2, whereas a fixed port permits only pb. A causal receiver attains the larger region by learning the state from erasure flags while using every channel use for data. A posterior port rule makes only finitely many incorrect selections almost surely, with a uniformly bounded expected number of mistakes. Exact random linear-code formulas and output-counting converses quantify the finite-block consequences. At blocklength 256 with (pg,pb)=(0.9,0.4), independent numerical validation supports 214 message bits at a one-percent ensemble failure target, compared with 148 bits for the best open-loop allocation in the same code ensemble. The resulting 44.59\% increase is achieved with the same transmission and observation budgets. The analysis exhibits an explicit capacity gain from controlling the observation axis and separates that gain from information lost after a record has already been formed.
ER -