Related papers: Asymptotic Frame Theory for Analog Coding
This is a manuscript of a chapter prepared for a book. The good codes possess large information length and large minimum distance. A class of codes is said to be asymptotically good if there exists a positive real $\delta$ such that, for…
An equiangular tight frame (ETF) is a set of equal norm vectors in a Euclidean space whose coherence is as small as possible, equaling the Welch bound. Also known as Welch-bound-equality sequences, such frames arise in various applications,…
This paper studies several properties of channel codes that approach the fundamental limits of a given (discrete or Gaussian) memoryless channel with a non-vanishing probability of error. The output distribution induced by an…
Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and…
This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the…
The output distribution, when rate is above capacity, is investigated. It is shown that there is an asymptotic equipartition property (AEP) of the typical output sequences, independently of the specific codebook used, as long as the…
An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. They arise in numerous applications. It is well known that real ETFs are equivalent to a certain…
Transcriptional networks represent one of the most extensively studied types of systems in synthetic biology. Although the completeness of transcriptional networks for digital logic is well-established, *analog* computation plays a crucial…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…
An original expectation propagation (EP) based message passing framework is introduced, wherein transmitted symbols are considered to belong to the multivariate white Gaussian distribution family. This approach allows deriving a novel class…
We study the spectrum of a random multigraph with a degree sequence ${\bf D}_n=(D_i)_{i=1}^n$ and average degree $1 \ll \omega_n \ll n$, generated by the configuration model, and also the spectrum of the analogous random simple graph. We…
We present the first empirical evaluation of techniques for encoding distributions of quantitative edge values within adjacency matrices. In many real-world networks, edges represent not a single value but a set of measurements. While…
It is known that the frame error rate of turbo codes on quasi-static fading channels can be accurately approximated using the convergence threshold of the corresponding iterative decoder. This paper considers quasi-static fading channels…
Excess of probabilities of elastic processes over inelastic ones is a characteristic feature of the chaotic resonance scattering predicted by the random matrix theory (RMT). Quantitatively, this phenomenon is characterized by the elastic…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
Our companion work \cite{Stojnicl1BnBxasymldp} considers random under-determined linear systems with box-constrained sparse solutions and provides an asymptotic analysis of a couple of modified $\ell_1$ heuristics adjusted to handle such…
Changes in real-world dynamic processes are often described in terms of differences in energies $\textbf{E}(\underline{\alpha})$ of a set of spectral-bands $\underline{\alpha}$. Given continuous spectra of two classes $A$ and $B$, or in…
It has been widely observed that there exists a fundamental trade-off between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity achieving code ensembles typically…
Path diversity works by setting up multiple parallel connections between the end points using the topological path redundancy of the network. In this paper, \textit{Forward Error Correction} (FEC) is applied across multiple independent…