Related papers: Superimposed Codes and Threshold Group Testing
We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. These results are proved by two distinct approaches, corresponding to the non-adaptive and adaptive…
New non-asymptotic random coding theorems (with error probability $\epsilon$ and finite block length $n$) based on Gallager parity check ensemble and Shannon random code ensemble with a fixed codeword type are established for discrete input…
The basic goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. The outcome of a test on a subset of items is positive if the subset has at…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
Starting from a practical use of Reed-Solomon codes in a cryptographic scheme published in Indocrypt'09, this paper deals with the threshold of linear $q$-ary error-correcting codes. The security of this scheme is based on the…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
We provide a general formulation for the code-based test compression problem with fixed-length input blocks and propose a solution approach based on Evolutionary Algorithms. In contrast to existing code-based methods, we allow unspecified…
We construct the first asymptotically good relaxed locally correctable codes with polylogarithmic query complexity, bringing the upper bound polynomially close to the lower bound of Gur and Lachish (SICOMP 2021). Our result follows from…
Several generative models with elaborate training and sampling procedures have been proposed to accelerate structure-based drug design (SBDD); however, their empirical performance turns out to be suboptimal. We seek to better understand…
Adaptive (variable-length) codes associate variable-length codewords to symbols being encoded depending on the previous symbols in the input data string. This class of codes has been presented in [Dragos Trinca, cs.DS/0505007] as a new…
Designing Screening Experiments (DSE) is a class of information - theoretical models for multiple - access channels (MAC). We discuss the combinatorial model of DSE called a disjunct channel model. This model is the most important for…
In this paper we solve an open question formulated in the original paper of twisted skew group codes regarding when a twisted skew group code is checkable. Also, we prove that all ideals of dimension 3 over a twisted group algebra are…
Permutation codes have recently garnered substantial research interest due to their potential in various applications including cloud storage systems, genome resequencing and flash memories. In this paper, we study the theoretical bounds…
We demonstrate that certain Johnson-type bounds are asymptotically exact for a variety of classes of codes, namely, constant-composition codes, nonbinary constant-weight codes and multiply constant-weight codes. This was achieved via an…
The goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. A test is positive if it has at least $u$ defective items and negative otherwise. Our…
In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…
Among the challenges that the COVID-19 pandemic outbreak revealed is the problem to reduce the number of tests required for identifying the virus carriers in order to contain the viral spread while preserving the tests reliability. To cope…
Topological subsystem codes proposed recently by Bombin are quantum error correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require…
This work focuses on non-adaptive combinatorial group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of $n$ elements using the fewest possible tests. Non-adaptive…
This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…