A binary deletion channel with a fixed number of deletions

TL;DR

This paper investigates the conditions under which a binary message can be reconstructed when transmitted repeatedly over a channel that randomly deletes a fixed number of digits, focusing on the minimal number of surviving digits needed for accurate recovery.

Contribution

It introduces a model of a binary deletion channel with a fixed number of deletions and analyzes the requirements for message reconstruction.

Findings

Determines the minimal number of surviving digits needed for reliable reconstruction.

Provides bounds on the size of the fixed number of deletions for successful decoding.

Analyzes the probability of successful message recovery under the fixed-deletion model.

Abstract

Suppose a binary string x = x_1...x_n is being broadcast repeatedly over a faulty communication channel. Each time, the channel delivers a fixed number m of the digits (m<n) with the lost digits chosen uniformly at random, and the order of the surviving digits preserved. How large does m have to be to reconstruct the message?