On OR Many-Access Channels

TL;DR

This paper explores the capacity of OR multi-access channels using Bloom filters, achieving optimal scaling laws for large user populations in activity recognition and message transmission.

Contribution

It introduces Bloom filter-based channel inputs to attain capacity and derives optimal scaling laws in the many-user regime.

Findings

Achieves the capacity region with joint decoding using Bloom filters.

Attains symmetric sum rate of ln 2 bits per channel use without joint decoding.

Establishes optimal scaling laws for activity recognition and message transmission in large user regimes.

Abstract

OR multi-access channel is a simple model where the channel output is the Boolean OR among the Boolean channel inputs. We revisit this model, showing that employing Bloom filter, a randomized data structure, as channel inputs achieves its capacity region with joint decoding and the symmetric sum rate of $\ln 2$ bits per channel use without joint decoding. We then proceed to the "many-access" regime where the number of potential users grows without bound, treating both activity recognition and message transmission problems, establishing scaling laws which are optimal within a constant factor, based on Bloom filter channel inputs.