Related papers: Gilbert-Varshamov Bound for Codes in $L_1$ Metric …
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
We investigate the upper and lower bounds on the quantization distortions for independent and identically distributed sources in the finite block-length regime. Based on the convex optimization framework of the rate-distortion theory, we…
The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's…
We study Hilbert functions of certain non-reduced schemes A supported at finite sets of points in projective space, in particular, fat point schemes. We give combinatorially defined upper and lower bounds for the Hilbert function of A using…
In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or…
The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…
Programmable quantum systems based on Rydberg atom arrays have recently emerged as a promising testbed for combinatorial optimization. Indeed, the Maximum Weighted Independent Set problem on unit-disk graphs can be efficiently mapped to…
High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…
We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure (L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e errors and t erasures…
In this work we study the reliability and secrecy performance achievable by practical LDPC codes over the Gaussian wiretap channel. While several works have already addressed this problem in asymptotic conditions, i.e., under the hypothesis…
We study properties of rank metric and codes in rank metric over finite fields. We show that in rank metric perfect codes do not exist. We derive an existence bound that is the equivalent of the Gilbert--Varshamov bound in Hamming metric.…
A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross- correlation sums. For multicarrier code-division multiple-access applications, the availability of large…
Variable-length block-coding schemes are investigated for discrete memoryless channels with ideal feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error $P_{e,\min}$ as a…
We develop three approaches of combinatorial flavour to study the structure of minimal codes and cutting blocking sets in finite geometry, each of which has a particular application. The first approach uses techniques from algebraic…
This paper studies the optimal points in the capacity region of Gaussian multiple access channels (GMACs) with constant fading, multiple antennas and various power constraints. The points of interest maximize general rate objectives that…
Most existing image compression approaches perform transform coding in the pixel space to reduce its spatial redundancy. However, they encounter difficulties in achieving both high-realism and high-fidelity at low bitrate, as the…
This paper is concerned with the computation of the capacity region of a continuous, Gaussian vector broadcast channel (BC) with covariance matrix constraints. Since the decision variables of the corresponding optimization problem are…
Motivated by modern network communication applications which require low latency, we study codes that correct erasures with low decoding delay. We provide a simple explicit construction that yields convolutional codes that can correct both…
The hull of a linear code (i.e., a finite field vector space)~\({\mathcal C}\) is defined to be the vector space formed by the intersection of~\({\mathcal C}\) with its dual~\({\mathcal C}^{\perp}.\) Constructing vector spaces with a…
Let $G$ be a graph, and let $\lambda(G)$ denote the smallest eigenvalue of $G$. First, we provide an upper bound for $\lambda(G)$ based on induced bipartite subgraphs of $G$. Consequently, we extract two other upper bounds, one relying on…