An Overview of Capacity Results for Synchronization Channels

Abstract

Synchronization channels, such as the well-known deletion channel, are surprisingly harder to analyze than memoryless channels, and they are a source of many fundamental problems in information theory and theoretical computer science.One of the most basic open problems regarding synchronization channels is the derivation of an exact expression for their capacity. Unfortunately, most of the classic information-theoretic techniques at our disposal fail spectacularly when applied to synchronization channels. Therefore, new approaches must be considered to tackle this problem. This survey gives an account of the great effort made over the past few decades to better understand the (broadly defined) capacity of synchronization channels, including both the main results and the novel techniques underlying them. Besides the usual notion of channel capacity, we also discuss the zero-error capacity of synchronization channels.

Coded trace reconstruction in a constant number of traces

“…deletions with probability q. See the recent survey by Cheraghchi and Ribeiro [CR19] for an overview of various models for random insertions, deletions, substitutions and replications. The authors suspect that similar primitives to those used in this paper could be useful in these more general settings.…”

Covering Codes Using Insertions or Deletions

“…Previous work has mostly studied covering codes with respect to substitutions (i.e., the Hamming distance). Recently, due to the large amount of textual and biological data, there has been a resurgence of interest in the Levenshtein distance and in channels with insertion and deletion errors (e.g., [6], [7], [8], [9], [10], [11], [12]). Despite this substantial progress, the Levenshtein distance remains poorly understood compared to other metrics on discrete spaces, and many fundamental questions remain open.…”