Related papers: Reassembly Codes for the Chop-and-Shuffle Channel
Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple…
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…
Varshamov-Tenengolts (VT) codes are a class of codes which can correct a single deletion or insertion with a linear-time decoder. This paper addresses the problem of efficient encoding of non-binary VT codes, defined over an alphabet of…
In the torn paper channel, a transmitted codeword is broken at random locations into fragments that arrive at the decoder in an unordered manner. A central theoretical challenge within this model is global alignment -- the task of…
Consider two remote nodes (encoder and decoder), each with a binary sequence. The encoder's sequence $X$ differs from the decoder's sequence $Y$ by a small number of edits (deletions and insertions). The goal is to construct a message $M$,…
In the paper, the Levenshtein's sequence reconstruction problem is considered in the case where at most $t$ substitution errors occur in each of the $N$ channels and the decoder outputs a list of length $\mathcal{L}$. Moreover, it is…
This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes.…
We consider the problem of communicating over a channel that breaks the message block into fragments of random lengths, shuffles them out of order, and deletes a random fraction of the fragments. Such a channel is motivated by applications…
We study segmented burst-deletion channels motivated by the observation that synchronization errors commonly occur in a bursty manner in real-world settings. In this channel model, transmitted sequences are implicitly divided into…
We consider the problem of constructing codes that can correct $\delta$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes, dating back to 1965, are zero-error single deletion $(\delta=1)$…
Determining the largest size, or equivalently finding the lowest redundancy, of q-ary codes for given length and minimum distance is one of the central and fundamental problems in coding theory. Inspired by the construction of…
In the problem of variable-length $\delta$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated…
We propose a random coding technique for joint source-channel coding of discrete memoryless sources and channels. The approach builds on the random Gilbert-Varshamov code construction of Somekh-Baruch et al. and extends it to the joint…
We consider the problem of constructing codes that can correct $\delta$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions $(\delta=1)$ with an…
We study optimal reconstruction codes over the multiple-burst substitution channel. Our main contribution is establishing a trade-off between the error-correction capability of the code, the number of reads used in the reconstruction…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
A permutation code is a nonlinear code whose codewords are permutation of a set of symbols. We consider the use of permutation code in the deletion channel, and consider the symbol-invariant error model, meaning that the values of the…
We study variable-length feedback (VLF) codes with noiseless feedback for discrete memoryless channels. We present a novel non-asymptotic bound, which analyzes the average error probability and average decoding time of our modified…
Channel coding aims to minimize errors that occur during the transmission of digital information from one place to another. Low-density parity-check (LDPC) codes can detect and correct transmission errors if one encodes the original…