Interference-Free Capacity of a Binary Interference Channel with Causal Observation
Abstract
We determine the capacity region of a two-user binary interference channel with receiver-controlled observation and prove that causal port selection attains the interference-free limit. The physical--observation dual-axis formulation makes the observation kernel a design variable subject to explicit causal and resource constraints. For two equiprobable, initially unknown block states, matching converses and coding constructions give exact sum capacities of 1, 4/3, and 2 bits per channel use for fixed-port, open-loop, and causal policies, respectively. These results hold for every fixed joint error threshold below 1/2, under both average and maximal message error, with error averaged over the block state. Every receiver makes one observation per slot and switches ports at most once; the transmitters receive no feedback and the receivers do not cooperate. Causal observation thus doubles the optimal fixed-port sum capacity and exceeds the optimal open-loop sum capacity by 50\%. With independent erasures of retention probability p, the exact causal region is [0,p]2. A finite-blocklength bound accounts jointly for state-identification pilots and coding redundancy. We also optimize observation policies for fixed codes: an exact finite-horizon solution reduces message error from 10.76\% to 7.52\%, and a second-order approximation bound controls optimization over continuous observation directions. Linear-array designs and coding experiments examine the corresponding training, reliability, and control costs. The capacity result identifies a setting in which observation design removes the entire interference penalty, with the gain established by a converse as well as an achievable construction.
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BibTeX
@misc{meng2026interferencefree,
title = {{Interference-Free Capacity of a Binary Interference Channel with Causal Observation}},
author = {Xianwei Meng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22389},
eprint = {2609.22389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22389},
}
RIS
TY - UNPB
TI - Interference-Free Capacity of a Binary Interference Channel with Causal Observation
AU - Xianwei Meng
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22389
UR - https://arxiv.org/abs/2609.22389
AB - We determine the capacity region of a two-user binary interference channel with receiver-controlled observation and prove that causal port selection attains the interference-free limit. The physical--observation dual-axis formulation makes the observation kernel a design variable subject to explicit causal and resource constraints. For two equiprobable, initially unknown block states, matching converses and coding constructions give exact sum capacities of 1, 4/3, and 2 bits per channel use for fixed-port, open-loop, and causal policies, respectively. These results hold for every fixed joint error threshold below 1/2, under both average and maximal message error, with error averaged over the block state. Every receiver makes one observation per slot and switches ports at most once; the transmitters receive no feedback and the receivers do not cooperate. Causal observation thus doubles the optimal fixed-port sum capacity and exceeds the optimal open-loop sum capacity by 50\%. With independent erasures of retention probability p, the exact causal region is [0,p]^2. A finite-blocklength bound accounts jointly for state-identification pilots and coding redundancy. We also optimize observation policies for fixed codes: an exact finite-horizon solution reduces message error from 10.76\% to 7.52\%, and a second-order approximation bound controls optimization over continuous observation directions. Linear-array designs and coding experiments examine the corresponding training, reliability, and control costs. The capacity result identifies a setting in which observation design removes the entire interference penalty, with the gain established by a converse as well as an achievable construction.
ER -