Related papers: Code Construction and Decoding Algorithms for Semi…
The concept of group divisible codes, a generalization of group divisible designs with constant block size, is introduced in this paper. This new class of codes is shown to be useful in recursive constructions for constant-weight and…
In order to leverage and profit from unlabelled data, semi-supervised frameworks for semantic segmentation based on consistency training have been proven to be powerful tools to significantly improve the performance of purely supervised…
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…
Let $1 \le s < t$, $N \ge 1$ be integers and a complex electronic circuit of size $t$ is said to be an $s$-active, $\; s \ll t$, and can work as a system block if not more than $s$ elements of the circuit are defective. Otherwise, the…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC). This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes by…
In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item. Specifically, we assume that there are multiple disjoint \emph{semi-defective…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
We construct several explicit instances of quantum Tanner codes, a class of asymptotically good quantum low-density parity check (qLDPC) codes. The codes are constructed using dihedral groups and random pairs of classical codes and exhibit…
We analyze a class of high performance, low decoding-data-flow error-correcting codes suitable for high bit-rate optical-fiber communication systems. A spatially-coupled split-component ensemble is defined, generalizing from the most…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…
We study the problem of group testing with a non-adaptive randomized algorithm in the random incidence design (RID) model where each entry in the test is chosen randomly independently from $\{0,1\}$ with a fixed probability $p$. The…
The fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests (measurements). The key contribution of this paper is in adopting a new…
The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over…
In a distributed space-time coding scheme, based on the relay channel model, the relay nodes co-operate to linearly process the transmitted signal from the source and forward them to the destination such that the signal at the destination…
We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product. To this end, we run numerical simulations of the…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
The motivation for this paper comes from the ongoing SARS-CoV-2 Pandemic. Its goal is to present a previously neglected approach to non-adaptive group testing and describes it in terms of residuated pairs on partially ordered sets. Our…
Dense coding or super-dense coding in the case of high-dimension quantum states between two parties and multi-parties has been studied in this paper. We construct explicitly the measurement basis and the forms of the single-body unitary…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…