English
Related papers

Related papers: Min-Sum algorithm for lattices constructed by Cons…

200 papers

The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…

Information Theory · Computer Science 2018-03-14 Eliya Nachmani , Elad Marciano , Loren Lugosch , Warren J. Gross , David Burshtein , Yair Beery

In this letter, we propose a two-stage design method to construct memory efficient mutual information-maximizing quantized min-sum (MIM-QMS) decoder for rate-compatible low-density parity-check (LDPC) codes. We first develop a modified…

Information Theory · Computer Science 2022-01-19 Peng Kang , Kui Cai , Xuan He , Jinhong Yuan

We propose two low-complexity lattice code constructions that have competitive coding and shaping gains. The first construction, named systematic Voronoi shaping, maps short blocks of integers to the dithered Voronoi integers, which are…

Information Theory · Computer Science 2016-08-04 Nuwan S. Ferdinand , Brian M. Kurkoski , Matthew Nokleby , Behnaam Aazhang

We describe a polynomial time algorithm for, given an undirected graph G, finding the minimum dimension d such that G may be isometrically embedded into the d-dimensional integer lattice Z^d.

Data Structures and Algorithms · Computer Science 2007-05-23 David Eppstein

We present a low-complexity and low-latency decoding algorithm for a class of Reed-Muller (RM) subcodes that are defined based on the product of smaller RM codes. More specifically, the input sequence is shaped as a multi-dimensional array,…

Information Theory · Computer Science 2022-02-09 Mohammad Vahid Jamali , Mohammad Fereydounian , Hessam Mahdavifar , Hamed Hassani

Lattice and special nonlattice multilevel constellations constructed from binary codes, such as Constructions A, C, and D, have relevant applications in Mathematics (sphere packing) and in Communication (multi-stage decoding and efficient…

Information Theory · Computer Science 2019-06-10 Maiara Francine Bollauf , Ram Zamir , Sueli Irene Rodrigues Costa

We propose a quantized decoding algorithm for low- density parity-check codes where the variable node update rule of the standard min-sum algorithm is replaced with a look-up table (LUT) that is designed using an information-theoretic…

Information Theory · Computer Science 2015-12-02 Michael Meidlinger , Alexios Balatsoukas-Stimming , Andreas Burg , Gerald Matz

Low density parity check (LDPC) lattices are obtained from Construction D' and a family of nested binary LDPC codes. We consider an special case of these lattices with one binary LDPC code as underlying code. This special case of LDPC…

Information Theory · Computer Science 2016-08-15 Hassan Khodaiemehr , Dariush Kiani , Mohammad-Reza Sadeghi

This paper introduces three key initiatives in the pursuit of a hybrid decoding framework characterized by superior decoding performance, high throughput, low complexity, and independence from channel noise variance. Firstly, adopting a…

Information Theory · Computer Science 2024-02-06 Guangwen Li , Xiao Yu

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…

Metric Geometry · Mathematics 2007-05-23 Boris Hemkemeier

Recent work has suggested that low-density generator matrix (LDGM) codes are likely to be effective for lossy source coding problems. We derive rigorous upper bounds on the effective rate-distortion function of LDGM codes for the binary…

Information Theory · Computer Science 2007-07-13 Emin Martinian , Martin J. Wainwright

Minkowski proved that any $n$-dimensional lattice of unit determinant has a nonzero vector of Euclidean norm at most $\sqrt{n}$; in fact, there are $2^{\Omega(n)}$ such lattice vectors. Lattices whose minimum distances come close to…

Information Theory · Computer Science 2021-09-13 Ethan Mook , Chris Peikert

Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a message-passing algorithm. In the original LDLC decoder, the message exchanged between variable nodes and check nodes are continuous…

Information Theory · Computer Science 2018-06-15 Shuiyin Liu , Yi Hong , Emanuele Viterbo , Alessia Marelli , Rino Micheloni

Conditional neural text generation models generate high-quality outputs, but often concentrate around a mode when what we really want is a diverse set of options. We present a search algorithm to construct lattices encoding a massive number…

Computation and Language · Computer Science 2022-05-04 Jiacheng Xu , Siddhartha Reddy Jonnalagadda , Greg Durrett

Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper presents randomized lattice decoding based on…

Information Theory · Computer Science 2016-11-17 Shuiyin Liu , Cong Ling , Damien Stehlé

Approaching the 1.5329-dB shaping (granular) gain limit in mean-squared error (MSE) quantization of R^n is important in a number of problems, notably dirty-paper coding. For this purpose, we start with a binary low-density generator-matrix…

Information Theory · Computer Science 2008-01-17 Qingchuan Wang , Chen He

Lattice reduction algorithms, such as the LLL algorithm, have been proposed as preprocessing tools in order to enhance the performance of suboptimal receivers in MIMO communications. In this paper we introduce a new kind of lattice…

Information Theory · Computer Science 2010-01-12 Laura Luzzi , Ghaya Rekaya-Ben Othman , Jean-Claude Belfiore

The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space…

Numerical Analysis · Mathematics 2015-06-16 Christoph Wiesmeyr , Nicki Holighaus , Peter L. Soendergaard

While iterative quantizers based on low-density generator-matrix (LDGM) codes have been shown to be able to achieve near-ideal distortion performance with comparatively moderate block length and computational complexity requirements, their…

Information Theory · Computer Science 2013-09-12 Qingchuan Wang , Chen He , Lingge Jiang

This paper is an investigation of a procedure for constructing lattices by means of taking the sum of a pair of isometric lattices. We present various general results pertaining to this construction and discuss several examples of it…

Group Theory · Mathematics 2010-09-02 Paul Lewis