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We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…
We consider the problem of recovering $n$ i.i.d samples from a zero mean multivariate Gaussian distribution with an unknown covariance matrix, from their modulo wrapped measurements, i.e., measurement where each coordinate is reduced modulo…
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the…
Large Multi-modal Models (LMMs) have recently demonstrated remarkable abilities in visual context understanding and coherent response generation. However, alongside these advancements, the issue of hallucinations has emerged as a…
Deterministic linear network coding (DLNC) is an important family of network coding techniques for wireless packet broadcast. In this paper, we show that DLNC is strongly related to and can be effectively studied using matroid theory…
Fault-tolerant quantum computing relies on Quantum Error Correction, which encodes logical qubits into data and parity qubits. Error decoding is the process of translating the measured parity bits into types and locations of errors. To…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
Surface codes are a popular error-correction route to fault-tolerant quantum computation. The so-called exponential backlog problem that can arise when one has to do logical $T$-gates within the surface code demands real-time decoding of…
Here, we study the problem of decoding information transmitted through unknown quantum states. We assume that Alice encodes an alphabet into a set of orthogonal quantum states, which are then transmitted to Bob. However, the quantum channel…
In this paper, we investigate the problem of recovering source information from an incomplete set of network coded data. We first study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and derive the…
We study blind fingerprinting, where the host sequence into which fingerprints are embedded is partially or completely unknown to the decoder. This problem relates to a multiuser version of the Gel'fand-Pinsker problem. The number of…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
In this paper, we consider the community detection problem in signed networks, where there are two types of edges: positive edges (friends) and negative edges (enemies). One renowned theorem of signed networks, known as Harary's theorem,…
Existing knowledge probing methods rely on pre-defined queries, limiting extraction to known concepts. We introduce DecompressionLM, a stateless framework for zero-shot concept graph extraction that discovers what language models encode…
Hallucinations in Large Language Models (LLMs), i.e., the tendency to generate plausible but non-factual content, pose a significant challenge for their reliable deployment in high-stakes environments. However, existing hallucination…
Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique…
We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower…
Matching algorithms can be used for identifying errors in quantum systems, being the most famous the Blossom algorithm. Recent works have shown that small distance quantum error correction codes can be efficiently decoded by employing…
Labelled Markov chains (LMCs) are widely used in probabilistic verification, speech recognition, computational biology, and many other fields. Checking two LMCs for equivalence is a classical problem subject to extensive studies, while the…
We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the…