Related papers: Algorithms for Encoding and Decoding 3D Hilbert Or…
Hilbert order is widely applied in many areas. However, most of the algorithms are confined to low dimensional cases. In this paper, algorithms for encoding and decoding arbitrary dimensional Hilbert order are presented. Eight algorithms…
This document describes algorithms for generating general Morton and Hilbert orderings for three-dimensional data volumes.
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
We present the first known efficient decoding algorithm for correcting multiple insertion-deletion errors in Helberg codes and their non-binary generalizations, extending a known algorithm for correcting multiple deletion errors.
In this paper, firstly, some applications of Hilbert matrix in image processing and cryptology are mentioned and an algorithm related to the Hilbert view of a digital image is given. In section 2, the new matrix domains are constructed and…
We present an application of Hilbert quasi-polynomials to order domains, allowing the effective check of the second order-domain condition in a direct way. We also provide an improved algorithm for the computation of the related Hilbert…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
In this paper, we investigate the encoding circuit size of Hamming codes and Hadamard codes. To begin with, we prove the exact lower bound of circuit size required in the encoding of (punctured)~Hadamard codes and (extended)~Hamming codes.…
For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise,…
By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which…
This article is about a decoding algorithm for error-correcting subspace codes. A version of this algorithm was previously described by Rosenthal, Silberstein and Trautmann. The decoding algorithm requires the code to be defined as the…
A reduced complexity sequential decoding algorithm for polar (sub)codes is described. The proposed approach relies on a decomposition of the polar (sub)code being decoded into a number of outer codes, and on-demand construction of codewords…
We present an interpretation of Deepcode, a learned feedback code that showcases higher-order error correction relative to an earlier interpretable model. By interpretation, we mean succinct analytical encoder and decoder expressions…
We propose a novel soft-aided hard-decision decoding algorithm for general product-like codes. It achieves error correcting performance similar to that of a soft-decision turbo decoder for staircase and OFEC codes, while maintaining a low…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…
We survey the known list decoding algorithms for polar codes and compare their complexity. Index terms: Polar codes; Reed-Muller codes; successive cancellation decoding.