信息论
We work in the setting of linear skew constacyclic codes over a commutative base ring $S$. We show that the notions of $(n,\sigma)$-isometry and $(n,\sigma)$-equivalence introduced by Ou-azzou et al coincide for most skew…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…
We attack the problem of getting a strict ranking (i.e. a ranking without equally ranked items) of $n$ items from a pairwise comparisons matrix. Basic structures are described, a first heuristical approach based on a condition, the…
Particularly motivated by DNA storage channels, we consider channels with synchronization errors modeled as insertions and deletions, along with substitutions. We focus on the case where the synchronization error process has memory and…
An information measure based on fractional partitions of a set is used to derive a general dependence balance inequality for communication. This inequality is used to obtain new upper bounds on reliable and secret rates for multiterminal…
When two agents of different computational capacities interact with the same environment, they need not compress a common semantic alphabet differently; they can induce different semantic alphabets altogether. We show that the quotient…
We study the spectral recovery problem for dynamical sampling on a finite cyclic grid. Given time snapshots obtained from a fixed uniform spatial subsampling of the orbit $x_{\ell}=A^{\ell}f$, we aim to recover the spectrum of the unknown…
Beamforming design for extremely large-scale multiple-input multiple-output (XL-MIMO) systems is challenging due to prohibitive computational complexity and complex near-field propagation effects. To address this, this paper introduces a…
In this paper, we study the shortest $t$-dimensional hull embeddings of linear codes in both Euclidean and Hermitian cases, extending the existing research on the shortest LCD and self-orthogonal embeddings to arbitrary hull dimensions and…
This paper considers the problem of multi-bit generative watermarking for large language models under a worst-case false-alarm constraint. Prior work established a lower bound on the achievable miss-detection probability in the finite-token…
Traditional coding theory guarantees valid decoding only if a minority of symbols are adversarially manipulated. In contrast, the game of coding framework ensures reliable decoding, even in the presence of an adversarial majority. This…
In downlink massive random access (DMRA), a base station transmits messages to a typically small subset of active users, selected randomly from a massive number of total users. Explicitly encoding the identities of active users would incur…
In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite…
This paper addresses the reconstruction of sparse signals from generalized linear measurements. Signal sparsity is assumed to be sublinear in the signal dimension while it was proportional to the signal dimension in conventional research.…
Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information…
The purpose of this paper is two-fold. First we show that Kim's building-up construction of binary self-dual codes is equivalent to Chinburg-Zhang's Hilbert symbol construction. Second we introduce a $q$-ary version of Chinburg-Zhang's…
The conventional power allocation strategy via water-filling relies on the premise that the power amplifier (PA) operates sufficiently below saturation such that a linear RF chain model holds. This work integrates the PA nonlinearity…
Assume $n=2m\geq 2$ and let $F(x)=x^{d_1}+x^{d_2}$ be a binomial vectorial function over $\F_{2^n}$ possessing the maximal number (i.e. $2^n-2^m$) of bent components. Suppose the $2$-adic Hamming weights $\wt_2(d_1)$ and $\wt_2(d_2)$ are…
A single coloring channel is defined by a subset of letters it allows to pass through, while deleting all others. A sequence of coloring channels provides multiple views of the same transmitted letter sequence, forming a type of…