# Coding for Segmented Edit Channels

## TL;DR

This paper introduces zero-error coding schemes for segmented insertion and deletion channels, enabling reliable data transmission with segment-based decoding and providing bounds on achievable rates.

## Contribution

It proposes novel code constructions for segmented edit channels using Varshamov-Tenengolts codes with pre-determined prefixes or suffixes, and derives an upper bound on code rates.

## Key findings

- Codes are zero-error and segment-decodable.
- Proposed codes work for any finite alphabet.
- Upper bound matches the rate scaling of maximal codes.

## Abstract

This paper considers insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. No segment markers are available in the received sequence. We propose code constructions for the segmented deletion, segmented insertion, and segmented insertion-deletion channels based on subsets of Varshamov-Tenengolts codes chosen with pre-determined prefixes and/or suffixes. The proposed codes, constructed for any finite alphabet, are zero-error and can be decoded segment-by-segment. We also derive an upper bound on the rate of any zero-error code for the segmented edit channel, in terms of the segment length. This upper bound shows that the rate scaling of the proposed codes as the segment length increases is the same as that of the maximal code.