Independent Metropolis-Hastings-Klein algorithm for lattice Gaussian sampling

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, a Markov chain Monte Carlo (MCMC) algorithm referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm is proposed for lattice Gaussian sampling, which overcom...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings / IEEE International Symposium on Information Theory pp. 2470 - 2474
Main Authors: Wang, Zheng, Ling, Cong
Format: Conference Proceeding Journal Article
Language:English
Published: IEEE 01.06.2015
Subjects:
Algorithm design and analysis
Algorithms
Convergence
Decoding
Gaussian
Gaussian distribution
lattice coding and decoding
Lattice Gaussian sampling
Lattices
Markov chains
Markov processes
Mathematical analysis
MCMC methods
Metropolis-Hastings sampling
Proposals
Sampling
Standard deviation
ISSN:2157-8095, 2157-8117
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, a Markov chain Monte Carlo (MCMC) algorithm referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm is proposed for lattice Gaussian sampling, which overcomes the restriction on the standard deviation confronted by the Klein algorithm. It is proven that the Markov chain arising from the proposed MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, making it possible to predict the mixing time of the underlying Markov chain.
AbstractList Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, a Markov chain Monte Carlo (MCMC) algorithm referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm is proposed for lattice Gaussian sampling, which overcomes the restriction on the standard deviation confronted by the Klein algorithm. It is proven that the Markov chain arising from the proposed MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, making it possible to predict the mixing time of the underlying Markov chain.
Author Zheng Wang
Cong Ling
Author_xml – sequence: 1
  givenname: Zheng
  surname: Wang
  fullname: Wang, Zheng
– sequence: 2
  givenname: Cong
  surname: Ling
  fullname: Ling, Cong
BookMark eNo1kD1PwzAURQ0qEm3pD0AsGVlS_FHnxSOqoI1oxUCZI7d-KUaOHWJ34N8TqWW59w5HdzgTMvLBIyH3jM4Zo-qp-qh2c06ZnAMvuaL0iswUlGxRgACgC3ZNxpxJyEvGYPS_qZK3ZBLjN6UCBOVjsq28wQ6H8CnbYupDF5yN-VrHZP0x5m8Orc-0O4bepq82a0KfOZ2SPWC20qcYrfZZ1G3nBvyO3DTaRZxdeko-X192y3W-eV9Vy-dNbhkXKVeSA0rkWiA3Yi8aAYUpjRYSODCj5QHkgpbC0KZRhWpKZvYGlJaM00IYJqbk8fzb9eHnhDHVrY0HdE57DKdYs0EBBxBSDejDGbWIWHe9bXX_W1-kiT8s9V_8
ContentType Conference Proceeding
Journal Article
DBID 6IE
6IH
CBEJK
RIE
RIO
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1109/ISIT.2015.7282900
DatabaseName IEEE Electronic Library (IEL) Conference Proceedings
IEEE Proceedings Order Plan (POP) 1998-present by volume
IEEE Xplore All Conference Proceedings
IEEE Electronic Library (IEL)
IEEE Proceedings Order Plans (POP) 1998-present
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Computer and Information Systems Abstracts
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISBN 9781467377041
146737704X
EISSN 2157-8117
EndPage 2474
ExternalDocumentID 7282900
Genre orig-research
GroupedDBID 6IE
6IH
6IK
6IL
6IN
AAWTH
ABLEC
ADZIZ
ALMA_UNASSIGNED_HOLDINGS
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CBEJK
CHZPO
IEGSK
IJVOP
OCL
RIE
RIL
RIO
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-i123t-9527e5e2a3e2d3b3f376d8da357271da5c754083d0ff969f81dbd79a512063d13
IEDL.DBID RIE
ISSN 2157-8095
IngestDate Thu Jul 10 23:21:22 EDT 2025
Wed Aug 27 02:42:56 EDT 2025
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-i123t-9527e5e2a3e2d3b3f376d8da357271da5c754083d0ff969f81dbd79a512063d13
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Conference-1
ObjectType-Feature-3
content type line 23
SourceType-Conference Papers & Proceedings-2
PQID 1770277359
PQPubID 23500
PageCount 5
ParticipantIDs proquest_miscellaneous_1770277359
ieee_primary_7282900
PublicationCentury 2000
PublicationDate 20150601
PublicationDateYYYYMMDD 2015-06-01
PublicationDate_xml – month: 06
  year: 2015
  text: 20150601
  day: 01
PublicationDecade 2010
PublicationTitle Proceedings / IEEE International Symposium on Information Theory
PublicationTitleAbbrev ISIT
PublicationYear 2015
Publisher IEEE
Publisher_xml – name: IEEE
SSID ssj0037302
Score 1.5760937
Snippet Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, a Markov chain Monte Carlo...
SourceID proquest
ieee
SourceType Aggregation Database
Publisher
StartPage 2470
SubjectTerms Algorithm design and analysis
Algorithms
Convergence
Decoding
Gaussian
Gaussian distribution
lattice coding and decoding
Lattice Gaussian sampling
Lattices
Markov chains
Markov processes
Mathematical analysis
MCMC methods
Metropolis-Hastings sampling
Proposals
Sampling
Standard deviation
Title Independent Metropolis-Hastings-Klein algorithm for lattice Gaussian sampling
URI https://ieeexplore.ieee.org/document/7282900
https://www.proquest.com/docview/1770277359
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PT8IwFH5B4sETKhjxV2ri0QJb23U9G1GiEBLRcCPt2uES3Azb_Pttx8CDXrzt0mV57d772u_7-gBuGOVBoEOKRaAEplRSrJSMMQ8j7dPQF6Zypb0988kknM_FtAG3Oy-MMaYSn5mee6y4fJ1FpTsq6_OK9rMb9D3Og41Xa5t1iV2pjjGwFcxlXcFqBtMbiP7oZTRzIi7Wq19Qd1L5lX6rmjJs_e9rDqHzY85D013ZOYKGSY-hte3OgOqftQ3j0a7DbYHGpqjaISQ5fpS5kzrn-GllkhTJ1TJbJ8X7B7LwFa1k4dRw6EGWubNXolw6yXm67MDr8H5294jr5gk4scWowIL53DDjS2J8TRSJbSbRoZaEWcTiackibsFaSPQgjkUgYotbleZCWgBgUYv2yAk00yw1p4BsPQsIiSIj3V03mtk9VkyV8j2liaRR3IW2i87ic3M_xqIOTBeut-Fd2DXriAiZmqzMFx7njjomTJz9PfQcDtx8bSRZF9As1qW5hP3oq0jy9VU18d_xg64e
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PT4MwFG4WNdHT1M04f9bEo90GbSk9G-fIfmSJ0-xGWlomyQQzwL_flrF50Is3LhDyeH3vK9_39QFwTwnzPOUTxD3JESGCIClFjJgfKZf4LteVK-1tzKZTf7HgswZ42HlhtNaV-Ex37WXF5assKu2vsh6raD-zQd-nhLj9jVtrW3exyVXLGZgeZusupzWH6fR5L3gJ5lbGRbv1I-pZKr8KcNVVBs3_vc8xaP_Y8-Bs13hOQEOnp6C5nc8A6-XaApNgN-O2gBNdVAMRkhwNRW7FzjkarXSSQrFaZuukeP-ABsDClSisHg4-izK3BkuYCys6T5dt8Dp4mj8OUT0-ASWmHRWIU5dpql2BtauwxLGpJcpXAlODWRwlaMQMXPOx6scx93hskKtUjAsDAQxuUQ4-A3tplupzAE1H8zCOIi3saTeKml1WTKR0HamwIFHcAS0bnfBzc0JGWAemA-624Q1N1loqQqQ6K_PQYcySx5jyi79vvQWHw_lkHI6D6egSHNlvtxFoXYG9Yl3qa3AQfRVJvr6pkuAbLJaxZQ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=proceeding&rft.title=Proceedings+%2F+IEEE+International+Symposium+on+Information+Theory&rft.atitle=Independent+Metropolis-Hastings-Klein+algorithm+for+lattice+Gaussian+sampling&rft.au=Zheng+Wang&rft.au=Cong+Ling&rft.date=2015-06-01&rft.pub=IEEE&rft.issn=2157-8095&rft.spage=2470&rft.epage=2474&rft_id=info:doi/10.1109%2FISIT.2015.7282900&rft.externalDocID=7282900
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2157-8095&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2157-8095&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2157-8095&client=summon