Marker+Codeword+Marker: A Coding Structure for Segmented Single-Insdel/-Edit Channels

Abstract

An insdel refers to a deletion or an insertion, and an edit refers to an insdel or a substitution. In this paper, we consider the segmented single-insdel (resp. single-edit) channel, where the channel's input bit stream is partitioned into segments of length $n$ and each segment can suffer from at most a single insdel (resp. edit) error. The value of $n$ is known to the receiver but the boundaries of segments are not. We propose to encode each segment following a marker+codeword+marker structure, where the two markers are carefully selected and the codewords are chosen from Varshamov-Tenegolts (VT) codes. In this way, we are able to construct a new class of binary codes that can correct segmented single-insdel errors. Our codes have the lowest redundancy of $\log_2(n-6)+7$ bits and are the first one that has linear-time encoder/decoder in the literature. Moreover, by enhancing the VT codes and one of the markers, we are able to construct the first class of binary codes that can correct segmented single-edit errors. This class of codes has redundancy $\log_2(n-9)+10$ bits and has linear-time encoder/decoder.