Related papers: Repeat-Free Codes
In this work we consider a generalization of the well-studied problem of coding for ``stuck-at'' errors, which we refer to as ``strong stuck-at'' codes. In the traditional framework of stuck-at codes, the task involves encoding a message…
We investigate the problem of encoding data into an $(n, t)$-break-resilient code ($(n, t)$-BRC), i.e., a collections of sequences of length~$n$ from which the original data can be reconstructed even if they are adversarially broken at up…
The serial concatenation of a repetition code with two or more accumulators has the advantage of a simple encoder structure. Furthermore, the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with…
In this work, we present a new version of non-binary VT codes that are capable of correcting a single deletion or single insertion. Moreover, we provide the first known linear time algorithms that encode user messages into these codes of…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…
We study the maximum multiplicity $\mathcal{M}(k,n)$ of a simple transposition $s_k=(k \: k+1)$ in a reduced word for the longest permutation $w_0=n \: n-1 \: \cdots \: 2 \: 1$, a problem closely related to much previous work on sorting…
In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be ($\tau$-)recurrent if every trajectory that starts in the set returns to it (within at most $\tau$ units of time).…
Recurrent neural networks (RNNs) have been used extensively and with increasing success to model various types of sequential data. Much of this progress has been achieved through devising recurrent units and architectures with the…
Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check codes and variations…
We consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering \topk{} queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be…
It is known that the majority of the human genome consists of repeated sequences. Furthermore, it is believed that a significant part of the rest of the genome also originated from repeated sequences and has mutated to its current form. In…
Run-Length Encoding (RLE) is one of the most fundamental tools in data compression. However, its compression power drops significantly if there lacks consecutive elements in the sequence. In extreme cases, the output of the encoder may…
Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and complemented copy of a substring of length $k$ adjacent to its…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…
A new random linear network coding scheme for reliable communications for time division duplexing channels is proposed. The setup assumes a packet erasure channel and that nodes cannot transmit and receive information simultaneously. The…
Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…
We consider questions related to the computation of the capacity of codes that avoid forbidden difference patterns. The maximal number of $n$-bit sequences whose pairwise differences do not contain some given forbidden difference patterns…