Related papers: Non-Binary Covering Codes for Low-Access Computati…
Encoding quantum information in a quantum error correction (QEC) code offers protection against decoherence and enhances the fidelity of qubits and gate operations. One of the fundamental challenges of QEC is to construct codes with…
Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain…
We describe a new parameterized family of symmetric error-correcting codes with low-density parity-check matrices (LDPC). Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are…
Binary code analysis has immense importance in the research domain of software security. Today, software is very often compiled for various Instruction Set Architectures (ISAs). As a result, cross-architecture binary code analysis has…
We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…
The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that…
Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…
Recurrent neural networks have achieved excellent performance in many applications. However, on portable devices with limited resources, the models are often too large to deploy. For applications on the server with large scale concurrent…
Digital contents in large scale distributed storage systems may have different reliability and access delay requirements, and for this reason, erasure codes with different strengths need to be utilized to achieve the best storage…
We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…
A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected…
We use density evolution to optimize the parameters of binary product codes (PCs) decoded based on the recently introduced iterative bounded distance decoding with scaled reliability. We show that binary PCs with component codes of 3-bit…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most…
An extension to a recently introduced architecture of clique-based neural networks is presented. This extension makes it possible to store sequences with high efficiency. To obtain this property, network connections are provided with…
In this paper we use the Gr\"obner representation of a binary linear code $\mathcal C$ to give efficient algorithms for computing the whole set of coset leaders, denoted by $\mathrm{CL}(\mathcal C)$ and the set of leader codewords, denoted…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
The main task in analyzing a switching network design (including circuit-, multirate-, and photonic-switching) is to determine the minimum number of some switching components so that the design is non-blocking in some sense (e.g., strict-…