IEEE Transactions on Information Theory

We focus on the Age of Information (AoI) performance in a system where each user generates packets periodically to send to a common access point (AP) for status updating. To avoid heavy overhead, we assume that channel sensing, feedback information from the AP, and time synchronization are not available in the system. We adopt a multi-access scheme called the sequence scheme, where each user is a…

Generalized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size. The study of codes that are MDS yet not generalized Reed-Solomon codes, called non-generalized Reed-Solomon MDS codes, started with the work by Roth and Lemple (1989), where the …

Distributed multi-user secret sharing is a cryptographic primitive for secure distributed computing. Khalesi et al. (2021) provided a full information-theoretic characterization of the capacity region under weak privacy and correctness constraints. Their encoding and decoding scheme relied on a randomized Monte-Carlo procedure whose success probability depended on the choice of a very large finit…

In this paper, we present an antiGriesmer lower bound on the subcode support weights of projective linear codes. This bound is a lower bound on the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i>-dimensional subcode support weights of projective linear codes. Based on the r-dimensional subcode support weight distributions (<italic xm…

We study generalized fractional repetition codes that have zero skip cost, and which are based on covering designs. We show that a zero skip cost is always attainable, perhaps at a price of an expansion factor compared with the optimal size of fractional repetition codes based on Steiner systems. We provide three constructions, as well as show non-constructively, that no expansion is needed for a…

This paper studies sparse recovery using expander graphs in the context of the noisy linear model b = Ax0 +e, where x0 ∈ R<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ⁿ</i> is an (approximately) sparse signal and A ∈ {0, 1}<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">^m×n…

Insertion-deletion (insdel for short) codes have received extensive attention due to their ability to correct synchronization errors. It is usually a very challenging problem to determine the insdel distances of linear codes. In this paper, a good lower bound on the insdel distance of a linear code with a certain algebraic structure is provided and it indeed gives an affirmative answer to an open…

Hybrid character sums are an important class of exponential sums which have nice applications in coding theory and sequence design. Let F<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_p^m</i> be the finite field with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p<sup>m</sup…

Data freshness, measured by Age of Information (AoI), is highly relevant in networked applications such as Vehicle to Everything (V2X), smart health systems, and Industrial Internet of Things (IIoT). However, freshness alone does not always equate to utility in decision-making. In decision-critical settings, some <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.or…

The asymptotic equipartition property (AEP) plays an important role in establishing lossless source coding theorems and asymptotic coding theorems through the concepts of typical sets and typical sequences in information theory. In this paper, we shall study the strong law of large numbers and the AEP for hidden Markov tree models. First, we give a strict definition of hidden Markov tree models, …

The mapping <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">χ_n</i> from F<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ⁿ</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> to itself defined by <italic xmlns:mml="http://w…

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs. Entropic regularization has emerged as a promising solution, allowing parametric convergence rates via the plug-in estimator, which can be computed using the Sinkhor…

We present a family of relatively simple and unified lower bounds on the capacity of the Gaussian channel under a set of pointwise additive input constraints. Specifically, the admissible channel input vectors <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> = (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.…

Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst errors. In this work, we characterize the burst error correction ability of QCCs constructed from the Calderbank-Shor-Steane (CSS) and the Hermitian constructions. …

As wireless communication applications evolve from traditional multipath environments to high-mobility scenarios like unmanned aerial vehicles, multiplexing techniques have advanced accordingly. Traditional single-carrier frequency-domain equalization (SC-FDE) and orthogonal frequency-division multiplexing (OFDM) have given way to emerging orthogonal timefrequency space (OTFS) and affine frequenc…

Symmetric multilevel diversity coding (SMDC) is a multi-source coding problem where the independent sources are ordered according to their importance. Prior work demonstrated that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">superposition coding</i>, where sources are encoded independently, is optimal. This paper investigates the <italic xmlns:…