An Overview of Capacity Results for Synchronization Channels

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 adversarial synchronization channels.