A VC-dimension-based Outer Bound on the Zero-Error Capacity of the Binary Adder Channel

TL;DR

This paper introduces a new outer bound on the zero-error capacity of the binary adder channel using VC-dimension techniques, narrowing the gap in understanding this channel's limits.

Contribution

It presents a novel VC-dimension-based outer bound for the zero-error capacity, employing a soft Saur-Perles-Shelah Lemma and an outer bound for Shannon capacity with common messages.

Findings

Improved outer bound for zero-error capacity of binary adder channel

Application of VC-dimension techniques to information theory

Enhanced understanding of capacity limits in multi-user channels

Abstract

The binary adder is a two-user multiple access channel whose inputs are binary and whose output is the real sum of the inputs. While the Shannon capacity region of this channel is well known, little is known regarding its zero-error capacity region, and a large gap remains between the best inner and outer bounds. In this paper, we provide an improved outer bound for this problem. To that end, we introduce a soft variation of the Saur-Perles-Shelah Lemma, that is then used in conjunction with an outer bound for the Shannon capacity region with an additional common message.