Related papers: Trace Reconstruction of First-Order Reed-Muller Co…
The complexity of maximal likelihood decoding of the Reed-Solomon codes $[q-1, k]_q$ is a well known open problem. The only known result in this direction states that it is at least as hard as the discrete logarithm in some cases where the…
We study universal compression of sequences generated by monotonic distributions. We show that for a monotonic distribution over an alphabet of size $k$, each probability parameter costs essentially $0.5 \log (n/k^3)$ bits, where $n$ is the…
The problem of string reconstruction based on its substrings spectrum has received significant attention recently due to its applicability to DNA data storage and sequencing. In contrast to previous works, we consider in this paper a setup…
Many important cryptographic primitives offer probabilistic guarantees of security that can be specified as quantitative hyperproperties; these are specifications that stipulate the existence of a certain number of traces in the system…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…
Let $x \in \R$ be given. As we know the, amount of bits needed to binary code $x$ with given accuracy ($h \in \R$) is approximately $ \m_{h}(x) \approx \log_{2}(\max {1, |\frac{x}{h}|}). $ We consider the problem where we should translate…
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…
This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then…
In the literature there exists analytical expressions for the probability of a receiver decoding a transmitted source message that has been encoded using random linear network coding. In this work, we look into the probability that the…
Tensors are a fundamental operation in distributed computing, \emph{e.g.,} machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall…
The problem of reconstructing strings from substring information has found many applications due to its importance in genomic data sequencing and DNA- and polymer-based data storage. One practically important and challenging paradigm…
We study codes that can correct backtracking errors during nanopore sequencing. In this channel, a sequence of length $n$ over an alphabet of size $q$ is being read by a sliding window of length $\ell$, where from each window we obtain only…
Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical…
Most DNA sequencing technologies are based on the shotgun paradigm: many short reads are obtained from random unknown locations in the DNA sequence. A fundamental question, studied in arXiv:1203.6233, is what read length and coverage depth…
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…
A binary string transmitted via a memoryless i.i.d. deletion channel is received as a subsequence of the original input. From this, one obtains a posterior distribution on the channel input, corresponding to a set of candidate…
In this paper, a transmission protocol is studied for a two relay wireless network in which simple repetition coding is applied at the relays. Information-theoretic achievable rates for this transmission scheme are given, and a space-time…
We consider the problem of communication efficient secure distributed matrix multiplication. The previous literature has focused on reducing the number of servers as a proxy for minimizing communication costs. The intuition being, that the…
We propose trace abstraction modulo probability, a proof technique for verifying high-probability accuracy guarantees of probabilistic programs. Our proofs overapproximate the set of program traces using failure automata, finite-state…