Related papers: Random Access Expectation in DNA Storage and Fount…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
The max-flow outer bound is achievable by regenerating codes for functional repair distributed storage system. However, the capacity of exact repair distributed storage system is an open problem. In this paper, the linear programming bound…
Synthetic DNA approaches 227.5 exabytes per gram of storage density with stability over millennial timescales. Realising this capacity requires error-correction codes that recover data from substantial synthesis and sequencing errors.…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
The problem of fast items retrieval from a fixed collection is often encountered in most computer science areas, from operating system components to databases and user interfaces. We present an approach based on hash tables that focuses on…
We examine the problem of creating an encoded distributed storage representation of a data object for a network of mobile storage nodes so as to achieve the optimal recovery delay. A source node creates a single data object and disseminates…
We introduce a new family of Fountain codes that are systematic and also have sparse parities. Given an input of $k$ symbols, our codes produce an unbounded number of output symbols, generating each parity independently by linearly…
For a random set $\mathcal{S} \subset U(d)$ of quantum gates we provide bounds on the probability that $\mathcal{S}$ forms a $\delta$-approximate $t$-design. In particular we have found that for $\mathcal{S}$ drawn from an exact $t$-design…
Exact evaluation of $<{\rm Tr} S^p>$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary…
We consider the problem of distributing a file in a network of storage nodes whose storage budget is limited but at least equals to the size file. We first generate $T$ encoded symbols (from the file) which are then distributed among the…
We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless…
DNA data storage offers a high-density, long-term alternative to traditional storage systems, addressing the exponential growth of digital data. Composite DNA extends this paradigm by leveraging mixtures of nucleotides to increase storage…
A random access code (RAC) is a communication task in which the sender encodes a random message into a shorter one to be decoded by the receiver so that a randomly chosen character of the original message is recovered with some probability.…
Distributed source coding is traditionally viewed in the block coding context -- all the source symbols are known in advance at the encoders. This paper instead considers a streaming setting in which iid source symbol pairs are revealed to…
We consider error-correcting coding for deoxyribonucleic acid (DNA)-based storage using nanopore sequencing. We model the DNA storage channel as a sampling noise channel where the input data is chunked into $M$ short DNA strands, which are…
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…
In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in DNA-based data storage systems where the inner code decoding, which generally has…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
Leveraging recent progress in physical-layer network coding we propose a new approach to random access: When packets collide, it is possible to recover a linear combination of the packets at the receiver. Over many rounds of transmission,…
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…