An Inequality on the Coding Gain of Densest Lattice Packings in Successive Dimensions

被引：0

作者：

Banihashemi A.H. ^{[1
]}

Khandani A.K. ^{[2
]}

机构：

[1] Dept. of Elec. and Comp. Engineering, University of Toronto, Toronto

[2] Dept. of Elec. and Comp. Engineering, University of Waterloo, Waterloo

来源：

Designs, Codes and Cryptography | 1998年 / 14卷 / 3期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Coding gain; Covering radius; Densest lattices; Lattice sphere packing; Minimum distance;

D O I：

10.1023/A:1008288001941

中图分类号：

学科分类号：

摘要：

A lower bound of the form (2n/n+1)1/nγn-1/nn-1 is derived on the coding gain γn of the densest n-dimensional (n-D) lattice(s). The bound is obtained based on constructing an n-D lattice which consists of parallel layers. Each layer is selected as a translated version of a densest (n - 1)-D lattice. The relative positioning of the layers is adjusted to make the coding gain as large as possible. For large values of n, the bound is improved through tightening Ryškov's inequality on covering radius and minimum distance of a lattice.

引用

页码：207 / 212

页数：5

共 12 条

[1] Densest lattice packings of 3-polytopes
Betke, U
Henk, M
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2000, 16 (03): : 157 - 186
[2] LOCALLY QUASI-DENSEST LATTICE PACKINGS OF BALLS
SHTOGRIN, MI
DOKLADY AKADEMII NAUK SSSR, 1974, 218 (01): : 62 - 65
[3] On the trellis complexity of the densest lattice packings in R(n)
Blake, IF
Tarokh, V
SIAM JOURNAL ON DISCRETE MATHEMATICS, 1996, 9 (04) : 597 - 601
[4] The densest lattice in twenty-four dimensions
Cohn, H
Kumar, A
ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 10 : 58 - 67
[5] Efficient linear programming algorithm to generate the densest lattice sphere packings
Marcotte, Etienne
Torquato, Salvatore
PHYSICAL REVIEW E, 2013, 87 (06)
[6] DENSEST PACKINGS OF TYPICAL CONVEX-SETS ARE NOT LATTICE-LIKE
TOTH, GF
DISCRETE & COMPUTATIONAL GEOMETRY, 1995, 14 (01) : 1 - 8
[7] FURTHER LATTICE PACKINGS IN HIGH DIMENSIONS
BOS, A
CONWAY, JH
SLOANE, NJA
MATHEMATIKA, 1982, 29 (58) : 171 - 180
[8] Densest Lattice Packings of 3-Polytopes (vol 16, pg 157, 2000)
Henk, Martin
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[9] Coding gain and lattice codes with small number of symbols
Susnik, R
Tomazic, S
CCCT 2003 VOL, 2, PROCEEDINGS: COMMUNICATIONS SYSTEMS, TECHNOLOGIES AND APPLICATIONS, 2003, : 65 - 70
[10] Vector set-partitioning with successive refinement Voronoi lattice VQ for embedded wavelet image coding
Mukherjee, D
Mitra, SK
1998 INTERNATIONAL CONFERENCE ON IMAGE PROCESSING - PROCEEDINGS, VOL 1, 1998, : 107 - 111

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