Construction  and  Lattices: Construction, Goodness, and Decoding Algorithms

Yu-Chih Huang; Krishna R. Narayanan

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Construction and Lattices: Construction, Goodness, and Decoding Algorithms

机译：构造和格：构造，优度和解码算法

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摘要

A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of linear codes over , respectively, and hence is referred to as Construction . The existence of a sequence of such lattices that is good for channel coding (i.e., Poltyrev-limit achieving) under multistage decoding is shown. A new family of multilevel nested lattice codes based on Construction lattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction is also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction as special cases.

机译：提出了一种新颖的格子结构。从有限环上的代码可以将这种构造视为构造A的特殊类，有限环上的代码可以分别表示为上线性代码的笛卡尔积，因此被称为构造。示出了这种格的序列的存在，该序列对于多级解码下的信道编码（即，实现Poltyrev极限）是有利的。提出了一个新的基于构造晶格的多层嵌套晶格码族，并分析了其在加性高斯白噪声通道中的可实现率。还研究了一个名为“构造”的概括，该构造将“构造A”包含在主要字段，“构造D”和“构造”上的代码作为特例。

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来源
《IEEE Transactions on Information Theory》 |2017年第9期|5718-5733|共16页
作者
Yu-Chih Huang; Krishna R. Narayanan;
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作者单位

Department of Communication Engineering, National Taipei University, New Taipei City, Taiwan;

Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Lattices; Decoding; Signal to noise ratio; AWGN channels; Linear codes; Additives;

机译：格;解码;信噪比;AWGN通道;线性代码;添加剂;

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1. Multilevel LDPC Lattices With Efficient Encoding and Decoding and a Generalization of Construction $ext{D}'$ [J] . Branco da Silva Paulo Ricardo, Silva Danilo IEEE Transactions on Information Theory . 2019,第5期

机译：高效编码和解码以及构造通用化的多级LDPC格 $ text {D}'$
2. Multilevel LDPC Lattices With Efficient Encoding and Decoding and a Generalization of Construction $ext{D}'$ [J] . Branco da Silva Paulo Ricardo, Silva Danilo IEEE Transactions on Information Theory . 2019,第5期

机译：具有有效编码和解码的多级LDPC格子和构造的概括 $ text {d}'$
3. Low-Density Parity-Check Lattices: Construction and Decoding Analysis [J] . Sadeghi M.-R., Banihashemi A.H., Panario D. IEEE Transactions on Information Theory . 2006,第期

机译：低密度奇偶校验格：构造和解码分析
4. On decoding algorithms for construction πA lattices [C] . Yu-Chih Huang, Narayanan Krishna R. International Conference on Telecommunications . 2015

机译：关于构造π A 格的解码算法
5. Constructions, Analyses and Decoding Algorithms of LDPC codes and Error Control Codes for Flash Coding. [D] . Huang, Qin. 2011

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6. Origami rules for the construction of localized eigenstates of the Hubbard model in decorated lattices [O] . R. G. Dias, J. D. Gouveia -1

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7. Design and Practical Decoding of Full-Diversity Construction A Lattices for Block-Fading Channels [O] . Hassan Khodaiemehr, Daniel Panario, Mohammad-Reza Sadeghi 2021

机译：全多样性施工的设计与实用解码块衰落通道的格子

Construction and Lattices: Construction, Goodness, and Decoding Algorithms

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