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On Bounded Distance Decoding, Unique Shortest Vectors, and the Minimum Distance Problem [chapter]

Vadim Lyubashevsky, Daniele Micciancio
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We prove the equivalence, up to a small polynomial approximation factor n/ log n, of the lattice problems uSVP (unique Shortest Vector Problem), BDD (Bounded Distance Decoding) and GapSVP (the decision  ...  version of the Shortest Vector Problem).  ...  Acknowledgements We thank the anonymous referees for very useful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-03356-8_34">doi:10.1007/978-3-642-03356-8_34</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/beqnj73tlzeihkvaa5y4pyhfpm">fatcat:beqnj73tlzeihkvaa5y4pyhfpm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20101206235258/http://cseweb.ucsd.edu:80/~vlyubash/papers/uSVP-BDD.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/15/19/1519299bfa9c3eec7818c9e9f9e9d7f37ec7fe7e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-03356-8_34"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On Bounded Distance Decoding for General Lattices [chapter]

Yi-Kai Liu, Vadim Lyubashevsky, Daniele Micciancio
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Specically, in the -Bounded Distance Decoding problem (-BDD), we are given a lattice v and a vector y (within distance ¡1(v) from the lattice), and we are asked to nd a lattice point x P v within distance  ...  Bounded Distance Decoding is a variant of this problem in which the target is guaranteed to be close to the lattice, relative to the minimum distance 1(v) of the lattice.  ...  The variant of the closest vector problem where the target is guaranteed to be close to the lattice relative to the minimum distance, 1 (v), of the lattice is called the Bounded Distance Decoding problem  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11830924_41">doi:10.1007/11830924_41</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t2elribd3fhhzgidxpo652y25m">fatcat:t2elribd3fhhzgidxpo652y25m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808032445/http://cseweb.ucsd.edu/~vlyubash/papers/bdd.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f5/4f/f54f4e6e5e22e0fb35ea7495827d42a1cbee3cb8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11830924_41"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Decoding by embedding: Correct decoding radius and DMT optimality

Cong Ling, Shuiyin Liu, Laura Luzzi, Damien Stehle
<span title="">2011</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ux5tf45dtrgptnezraiii73msm" style="color: black;">2011 IEEE International Symposium on Information Theory Proceedings</a> </i> &nbsp;
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices.  ...  Index Terms-closest vector problem, lattice decoding, lattice reduction, MIMO systems, shortest vector problem  ...  They also wish to thank the anonymous reviewers for their detailed comments and suggestions which helped to improve the presentation of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2011.6033703">doi:10.1109/isit.2011.6033703</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isit/LingLLS11.html">dblp:conf/isit/LingLLS11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3cfwzg6zs5gvzbmenb5mq543ai">fatcat:3cfwzg6zs5gvzbmenb5mq543ai</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170927233240/https://hal.archives-ouvertes.fr/hal-00784077/document" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e5/11/e511588f3c0372901d0e209758e72105461b576e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2011.6033703"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Design criteria for lattice network coding

Chen Feng, Danilo Silva, Frank R. Kschischang
<span title="">2011</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xmt3q74jnnf7nlg25xkjze2uoa" style="color: black;">2011 45th Annual Conference on Information Sciences and Systems</a> </i> &nbsp;
These design criteria imply that finding the optimal receiver parameters is equivalent to solving a shortest vector problem, and designing good lattice partitions can be reduced to the design of good linear  ...  It is shown that the receiver parameters {a ℓ } and α should be chosen such that the quantity 2 is minimized, and the lattice partition should be designed such that the minimum inter-coset distance is  ...  Then the length of the shortest vectors in λ + Λ ′ , denoted by l(λ + Λ ′ ), is given by l(λ + Λ ′ ) = γ c . Further, the shortest vector in λ + Λ ′ is unique due to the uniqueness of c .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ciss.2011.5766229">doi:10.1109/ciss.2011.5766229</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ciss/FengSK11.html">dblp:conf/ciss/FengSK11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hwkzk7c74nfs5p6b2h7m26twaa">fatcat:hwkzk7c74nfs5p6b2h7m26twaa</a> </span>
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Decoding by Embedding: Correct Decoding Radius and DMT Optimality

Laura Luzzi, Damien Stehle, Cong Ling
<span title="">2013</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices.  ...  tradeoff (DMT), and propose practical variants of embedding decoding which require no knowledge of the minimum distance of the lattice and/or further improve the error performance.  ...  They also wish to thank the anonymous reviewers for their detailed comments and suggestions which helped to improve the presentation of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2012.2236144">doi:10.1109/tit.2012.2236144</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/isuyiyhvs5g6fe5cz5bwpp2poa">fatcat:isuyiyhvs5g6fe5cz5bwpp2poa</a> </span>
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Closest point search in lattices

E. Agrell, T. Eriksson, A. Vardy, K. Zeger
<span title="">2002</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
Modifications of the algorithm are developed to solve a number of related search problems for lattices, such as finding a shortest vector, determining the kissing number, computing the Voronoi-relevant  ...  Index Terms-Closest point search, kissing number, Korkine-Zolotareff (KZ) reduction, lattice decoding, lattice quantization, nearest neighbor, shortest vector, Voronoi diagram. Manuscript  ...  They also thank Emanuele Viterbo and Joseph Boutrous for valuable suggestions, especially regarding optimization of the Viterbo-Boutros algorithm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2002.800499">doi:10.1109/tit.2002.800499</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x5su52tnh5fndmdgymtzb6enwq">fatcat:x5su52tnh5fndmdgymtzb6enwq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060918032752/http://code.ucsd.edu/~zeger/publications/journals/AgErVaZe02-IT-Lattices/AgErVaZe02-IT-Lattices.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ea/3a/ea3a0430ac4e66492c1c0296a4e0904523c7aff3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2002.800499"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Hard Problems of Algebraic Geometry Codes [article]

Qi Cheng
<span title="2005-07-08">2005</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code.  ...  We achieve this by reducing a well-known NP-complete problem to these problems using a randomized algorithm. The family of codes in the reductions are based on elliptic curves.  ...  Acknowledgments We thank Daqing Wan and Elizabeth Murray for helpful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0507026v1">arXiv:cs/0507026v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/txre47ut7rdtvhsxejbb4hynfm">fatcat:txre47ut7rdtvhsxejbb4hynfm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171008212407/https://core.ac.uk/download/pdf/2420953.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d5/7d/d57d97a0c8818416a8737005f9571724e4fececa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0507026v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Error Correction for Index Coding With Side Information

Son Hoang Dau, Vitaly Skachek, Yeow Meng Chee
<span title="">2013</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
It is shown that in order to decode correctly the desired symbol, the decoder is required to find one of the vectors, belonging to an affine space containing the actual error vector.  ...  It yields another inexplicit bound on the length of an optimal linear ECIC. Further, the problem of error-correcting decoding by a linear ECIC is studied.  ...  ACKNOWLEDGMENT The authors would like to thank the authors of [7] for providing a preprint of their paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2012.2227674">doi:10.1109/tit.2012.2227674</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uaaat43sdrh7vexvho5wbmyo6u">fatcat:uaaat43sdrh7vexvho5wbmyo6u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705110143/http://www1.spms.ntu.edu.sg/%7Eymchee/papers/ECIC.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/70/04/7004d252e30f8a7433246049f0f4ce5f8c6ae4f0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2012.2227674"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Algorithmic complexity in coding theory and the minimum distance problem

Alexander Vardy
<span title="">1997</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC &#39;97</a> </i> &nbsp;
We start withan overviewof algorithmiccomplexity problemsin coding theory We then show that the problemof computing the minimumdiktanceof a binaryIinwr code is NP-hard,and the corresponding deci~"on problemis  ...  This constitutes a proof of the conjecture Bedekamp, McEliece,vanTilborg, dating back to 1978. Extensionsand applicationsof this result to other problemsin codingtheqv are discussed.  ...  acknowledge helpful dkicusaions with Noga Alon, Alexander Barg, Yoram Bresler, Shuki Bruck, Ilya Dumer, Herbert Edelsbrunner, Mike Fellows, Nabil Kahale, Moni Naor, Ronny Roth, Dilip Sarwate, Leonard Schulman, and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/258533.258559">doi:10.1145/258533.258559</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/Vardy97.html">dblp:conf/stoc/Vardy97</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vkunvltuabfdvnjzldvt6mpihu">fatcat:vkunvltuabfdvnjzldvt6mpihu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120324194733/http://www.busim.ee.boun.edu.tr:80/~mihcak/teaching/ee684-spring07/proposed-project-papers/hard-problems/random-linear-codes/vardy-complexity.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/12/ce/12cedcc79bec6403ffab5d4c85a1bf7500683eca.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/258533.258559"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Augmented Lattice Reduction for MIMO decoding [article]

Laura Luzzi, Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore
<span title="2010-01-11">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A theoretical bound on the complexity is also derived.  ...  In this paper we introduce a new kind of lattice reduction-aided decoding technique, called augmented lattice reduction, which recovers the transmitted vector directly from the change of basis matrix,  ...  First of all, the LLL algorithm finds at least one basis vector whose length is not too far from the minimum distance d H of the lattice.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1001.1625v1">arXiv:1001.1625v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mrsjdtxgvfflnd5c2jlqaghmqq">fatcat:mrsjdtxgvfflnd5c2jlqaghmqq</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1001.1625/1001.1625.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d0/9f/d09f22ae9a6493294ec8d739a4e3667d293e6ece.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1001.1625v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Hardness of approximating the minimum distance of a linear code

I. Dumer, D. Micciancio, M. Sudan
<span title="">2003</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
Index Terms-Approximation algorithms, bounded distance decoding, computational complexity, dense codes, linear codes, minimum-distance problem, NP-hardness, relatively near codeword problem.  ...  Our results for the minimum distance problem strengthen (though using stronger assumptions) a previous result of Vardy who showed that the minimum distance cannot be computed exactly in deterministic polynomial  ...  One problem that has been defined to study the latter phenomenon is the "bounded distance decoding problem" (BDD, see [23] , [22] ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2002.806118">doi:10.1109/tit.2002.806118</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sdq337o4kjfqhnadzdtyxsd2le">fatcat:sdq337o4kjfqhnadzdtyxsd2le</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070418075011/http://www.ee.ucr.edu/~dumer/ieee49-1-03-np.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e0/db/e0db86ffd4c651df658108b19f1cf412a24395c6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2002.806118"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Lattice (List) Decoding Near Minkowski's Inequality [article]

Ethan Mook, Chris Peikert
<span title="2021-09-09">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Lattices whose minimum distances come close to Minkowski's bound provide excellent sphere packings and error-correcting codes in ℝ^n.  ...  The focus of this work is a certain family of efficiently constructible n-dimensional lattices due to Barnes and Sloane, whose minimum distances are within an O(√(log n)) factor of Minkowski's bound.  ...  We thank Daniele Micciancio and the anonymous reviewers for helpful comments on the presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.04809v2">arXiv:2010.04809v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/axbnoat2rfc4lewjvssz4ibzze">fatcat:axbnoat2rfc4lewjvssz4ibzze</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210917210444/https://arxiv.org/pdf/2010.04809v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/00/f6/00f6769b8dadf0f4e23a1e1bcef4435c8e748846.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.04809v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Sublinear-Space Distance Labeling using Hubs [article]

Paweł Gawrychowski, Adrian Kosowski, Przemysław Uznański
<span title="2016-07-20">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For a queried pair of nodes (u,v), the length of a shortest u-v-path passing through a hub node from S(u)∩ S(v) is then used as an upper bound on the distance between u and v.  ...  By using similar techniques, we then present a 2-additive labeling scheme for general graphs, i.e., one in which the decoder provides a 2-additive-approximation of the distance between any pair of nodes  ...  Acknowledgments Most of the work was done while PU was affiliated to Aalto University, Finland. Research partially supported by the National Science Centre, Poland -grant number 2015/17/B/ST6/01897.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.06240v3">arXiv:1507.06240v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ewkcbc2cdrgixkkgkni5hqz6zm">fatcat:ewkcbc2cdrgixkkgkni5hqz6zm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200910073318/https://arxiv.org/pdf/1507.06240v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/91/7b/917bd298e7a9e47c458199605e84b93d38aca14b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.06240v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A Deterministic Reduction for the Gap Minimum Distance Problem

Qi Cheng, Daqing Wan
<span title="">2012</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
Determining the minimum distance of a linear code is one of the most important problems in algorithmic coding theory. The exact version of the problem was shown to be NPcomplete in [15] .  ...  minimum distance of C.  ...  Although the idea in Ajtai and Micciancio's work on the shortest vector problem in L 2 norm inspired the results on the gap minimum distance problem, the reduction for the latter problem is now derandomized  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2012.2209198">doi:10.1109/tit.2012.2209198</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/agmckkrxqjedtjgcpwno5oe5cu">fatcat:agmckkrxqjedtjgcpwno5oe5cu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706071610/http://www.cs.ou.edu/%7Eqcheng/paper/gd.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b6/2c/b62ca2637b7f4c07bd85f44f244a1716de3d9807.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2012.2209198"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Systematic space-time trellis code construction for correlated Rayleigh-fading channels

Z. Safar, K.J. Ray Liu
<span title="">2004</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
Moreover, we introduce a new design criterion and analyze the properties of the space-time trellis codes satisfying the proposed criterion.  ...  We derive the performance criteria that take into account both spatial and temporal channel correlation, assuming that the space-time correlation matrix is of full rank.  ...  criterion): The minimum number of time instants when the correct and the decoded channel symbol vectors are different (the minimum value of ) taken over all possible correct and erroneously decoded channel  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2004.836926">doi:10.1109/tit.2004.836926</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xu7vsjropbffzavswokktftly4">fatcat:xu7vsjropbffzavswokktftly4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808190841/http://sig.umd.edu/publications/safar_STtrellis_200411.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b8/bb/b8bb124d8b234941663a8f1b4f8ca700e8185730.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2004.836926"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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