A Lower Bound on the Essential Interactive Capacity of Binary Memoryless Symmetric Channels

TL;DR

This paper establishes a lower bound on the maximum reliable interactive communication rate over binary symmetric channels, showing it is at least 3.02% of the Shannon capacity, using a novel coding scheme.

Contribution

It introduces a new lower bound on the essential interactive capacity of BMS channels and presents a simple coding scheme to achieve this bound.

Findings

Essential interactive capacity is at least 0.0302 of Shannon capacity.

A coding scheme based on extended-Hamming codes achieves the lower bound for BSC.

The scheme is adapted to all BMS channels using Bhattacharyya parameters.

Abstract

The essential interactive capacity of a discrete memoryless channel is defined in this paper as the maximal rate at which the transcript of any interactive protocol can be reliably simulated over the channel, using a deterministic coding scheme. In contrast to other interactive capacity definitions in the literature, this definition makes no assumptions on the order of speakers (which can be adaptive) and does not allow any use of private / public randomness; hence, the essential interactive capacity is a function of the channel model only. It is shown that the essential interactive capacity of any binary memoryless symmetric (BMS) channel is at least $0.0302$ its Shannon capacity. To that end, we present a simple coding scheme, based on extended-Hamming codes combined with error detection, that achieves the lower bound in the special case of the binary symmetric channel (BSC). We then adapt the scheme to the entire family of BMS channels, and show that it achieves the same lower bound using extremes of the Bhattacharyya parameter.