On the Capacity of Insertion Channels for Small Insertion Probabilities
Abstract
Channels with synchronization errors, such as deletion and insertion errors, are crucial in DNA storage, data reconstruction, and other applications. These errors introduce memory to the channel, complicating its capacity analysis. This paper analyzes binary insertion channels for small insertion probabilities, identifying dominant terms in the capacity expansion and establishing capacity in this regime. Using Bernoulli(1/2) inputs for achievability and a converse based on the use of stationary and ergodic processes, we demonstrate that capacity closely aligns with achievable rates using independent and identically distributed (i.i.d.) inputs, differing only in higher-order terms.
Cite
@article{arxiv.2504.14035,
title = {On the Capacity of Insertion Channels for Small Insertion Probabilities},
author = {Busra Tegin and Tolga M Duman},
journal= {arXiv preprint arXiv:2504.14035},
year = {2025}
}
Comments
6 pages. arXiv admin note: substantial text overlap with arXiv:2411.14771