Related papers: Asymptotic Frame Theory for Analog Coding
Analog coding is a low-complexity method to combat erasures, based on linear redundancy in the signal space domain. Previous work examined "band-limited discrete Fourier transform (DFT)" codes for Gaussian channels with erasures or…
Analog codes add redundancy by expanding the dimension using real/complex-valued operations. Frame theory provides a mathematical basis for constructing such codes, with diverse applications in non-orthogonal code-division multiple access…
We draw a random subset of $k$ rows from a frame with $n$ rows (vectors) and $m$ columns (dimensions), where $k$ and $m$ are proportional to $n$. For a variety of important deterministic equiangular tight frames (ETFs) and tight non-ETF…
Analog coding decouples the tasks of protecting against erasures and noise. For erasure correction, it creates an "analog redundancy" by means of band-limited discrete Fourier transform (DFT) interpolation, or more generally, by an…
Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…
The eigenvalue decomposition (EVD) parameters of the second order statistics are ubiquitous in statistical analysis and signal processing. Notably, the EVD of robust scatter $M$-estimators is a popular choice to perform robust probabilistic…
We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited…
An equiangular tight frame (ETF) is a sequence of vectors in a Hilbert space that achieves equality in the Welch bound and so has minimal coherence. More generally, an equichordal tight fusion frame (ECTFF) is a sequence of equi-dimensional…
In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the…
Asymptotic spectral distribution (ASD) of the crosscorrelation matrix is investigated for a random spreading short/long-code asynchronous direct sequence-code division multiple access (DS-CDMA) system. The discrete-time decision statistics…
Frame theory is a powerful tool in the domain of signal processing and communication. Among its numerous configurations, the ones which have drawn much attention recently are Equiangular Tight Frame (ETF) and Grassmannian Frame. These…
Malicious encryption techniques continue to evolve, bypassing conventional detection mechanisms that rely on static signatures or predefined behavioral rules. Spectral analysis presents an alternative approach that transforms system…
In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…
Level curvature is a measure of sensitivity of energy levels of a disordered/chaotic system to perturbations. In the bulk of the spectrum Random Matrix Theory predicts the probability distributions of level curvatures to be given by…
Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as a major theme in theoretical and applied optics. Here we demonstrate, both analytically and…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
An Equiangular tight frame (ETF) - also known as the Welch-bound-equality sequences - consists of a sequence of unit norm vectors whose absolute inner product is identical and minimal. Due to this unique property, these frames are preferred…
Frames have become standard tools in signal processing due to their robustness to transmission errors and their resilience to noise. Equiangular tight frames (ETFs) are particularly useful and have been shown to be optimal for transmission…
Language models cannot be random. This paper introduces Entropic Deviation (ED), the normalised KL divergence between a model's token distribution and the uniform distribution, and measures it systematically across 31,200 generations…
Equiangular tight frames (ETFs) have found significant applications in signal processing and coding theory due to their robustness to noise and transmission losses. ETFs are characterized by the fact that the coherence between any two…