Related papers: On the decoding of Barnes-Wall lattices
A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are special…
The main objective of this thesis is a classification project for integral lattices. Using Kneser's neighbour method we have developed the computer program tn to classify complete genera of integral lattices. Main results are detailed…
The computational complexity of the Maximum Likelihood decoding algorithm in [1], [2] for orthogonal space-time block codes is smaller than specified.
In view of the recent excitement about a tension between determinations of f_Ds from experiment and from simulations of lattice QCD with dynamical quarks, we try to clear up the picture of lattice determinations in the continuum limit of…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Successive cancellation list (SCL) decoding enables polar codes and their generalizations to deliver satisfactory performance in finite-length scenarios but it comes with high latency and complexity. To reduce latency, a partitioned SCL…
We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
The Barnes-Wall lattice ${\bf \Lambda}_{16}$ with the center density ${\{1}{16}}$ and the kissing number 4320 was found in 1959 and is the only known densest sphere packing in the dimension 16. J. H. Conway and N.J.A. Sloane conjectured…
This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices $\mathcal{E}_{m}$ and $\mathcal{G}_{m}$. By explicitly linking…
The list-decodable code has been an active topic in theoretical computer science.There are general results about the list-decodability to the Johnson radius and the list-decoding capacity theorem. In this paper we show that rates,…
We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve…
In this paper we show a polar coding scheme for the deletion channel with a probability of error that decays roughly like $2^{-\sqrt{\Lambda}}$, where $\Lambda$ is the length of the codeword. That is, the same decay rate as that of seminal…
Recently, lattice-reduction-aided detectors have been proposed for multiple-input multiple-output (MIMO) systems to give performance with full diversity like maximum likelihood receiver, and yet with complexity similar to linear receivers.…
We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…
Lattice QCD calculation of s-wave hadron scattering lengths in the channels \pi-\pi, \pi-N, K-N, {\bar K}-N and N-N is carried out in the quenched QCD at $\beta=6/g^2=5.7$. A variant of the method of wall sourceis developed for this…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
The lattice method for the calculation of weak decay amplitudes of heavy quark systems is introduced. Results for leptonic and semi-leptonic decays of heavy mesons and $B-\bar{B}$ mixing are reviewed.
The approximation of tensors has important applications in various disciplines, but it remains an extremely challenging task. It is well known that tensors of higher order can fail to have best low-rank approximations, but with an important…
Quasi-twisted (QT) codes generalize several important families of linear codes, including cyclic, constacyclic, and quasi-cyclic codes. Despite their potential, to the best of our knowledge, there exists no efficient decoding algorithm for…