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Bounding basis reduction properties

Arnold Neumaier
2016 Designs, Codes and Cryptography  
The paper describes improved analysis techniques for basis reduction that allow one to prove strong complexity bounds and reduced basis guarantees for traditional reduction algorithms and some of their  ...  This is achieved by a careful exploitation of the linear equations and inequalities relating various bit sizes before and after one or more reduction steps.  ...  LLL algorithms An LLL algorithm is a block reduction algorithms that operates only on blocks of size 2.  ... 
doi:10.1007/s10623-016-0273-9 pmid:31564770 pmcid:PMC6743704 fatcat:hlkcfbs6ufepfllqkzqhwce37y

Cyclic-Coded Integer-Forcing Equalization

Or Ordentlich, Uri Erez
2012 IEEE Transactions on Information Theory  
An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of ISI.  ...  Leveraging the property that a cyclic code is closed under cyclic integer-valued convolution allows us to perform decoding prior to applying decision feedback.  ...  Nazer, and M. Gastpar for discussions on IF equalization. They also thank Y. Kochman for helpful comments.  ... 
doi:10.1109/tit.2012.2202633 fatcat:bxwo5xvukngrha2hsbppdodw7y

Cyclic coded integer-forcing equalization

Or Ordentlich, Uri Erez
2010 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of ISI.  ...  Leveraging the property that a cyclic code is closed under cyclic integer-valued convolution allows us to perform decoding prior to applying decision feedback.  ...  Nazer, and M. Gastpar for discussions on IF equalization. They also thank Y. Kochman for helpful comments.  ... 
doi:10.1109/allerton.2010.5706944 fatcat:inqiuwfstvde5kmp5tvbnexhrq

On the inherent intractability of certain coding problems (Corresp.)

E. Berlekamp, R. McEliece, H. van Tilborg
1978 IEEE Transactions on Information Theory  
ACKNOWLEDGMENT We wish to thank one of the referees for pointing out to us the relation between the "weight < w" decision problem and the minimum weight problem for linear codes.  ...  THREE-DIMENSIONAL MATCHING can be reduced to SUBSPACE WEIGHTS: The idea is again to construct an A for the SUBSPACE WEIGHTS algorithm from the triple incidence matrix, but here the construction is more  ...  It is conversely intuitively evident that NP is "much Let C be an (n, k) binary linear code which is to be used on a larger" than P; however, no one has yet succeeded in proving binary symmetric channel  ... 
doi:10.1109/tit.1978.1055873 fatcat:sepkw4wkcndknjvrec2l3z7yyy

On decoding BCH codes

G. Forney
1965 IEEE Transactions on Information Theory  
For an input-binary channel the random binary convolutional coder described above achieves this.  ...  But for a binary-tree code there can be no more 1,han 2$' distinct paths which differ from the correct path M branches back.  ...  Burst-Correcting Codes for the Classic Bursty Channel Abstract-The purpose of this paper is to organize and clarify the work of the past decade on burst-correcting codes.  ... 
doi:10.1109/tit.1965.1053825 fatcat:7337oxxh4fdthiehsr7u2ihbom

List decoding of number field codes

Nicholas Coxon
2013 Designs, Codes and Cryptography  
The algorithm is an implementation of the unified framework for list decoding of algebraic codes of Guruswami, Sahai and Sudan [14] , specialised for number field codes.  ...  This paper presents a list decoding algorithm for the number field codes of Guruswami [12] .  ...  Acknowledgements The author would like to thank Dr Victor Scharaschkin for many helpful discussions and suggestions throughout the preparation of this paper.  ... 
doi:10.1007/s10623-013-9803-x fatcat:hrg2wqrqgrajxkcsfadckw5yya

Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance [chapter]

Axel Kohnert, Sascha Kurz
2008 Lecture Notes in Computer Science  
There is an increased interest in space codes since a paper by Koetter and Kschischang were they gave an application in network coding.  ...  We will modify a method of Braun, Kerber and Laue which they used for the construction of designs over finite fields to do the construction of space codes.  ...  To obtain the lower bounds we have used the LLL based algorithm, the coding theoretic motivated heuristic and the ILOG CPLEX solver for integer linear programs.  ... 
doi:10.1007/978-3-540-89994-5_4 fatcat:rw75xnaoabfv5pi4twlfdvnlou

Cyclic-Coded Integer-Forcing Equalization [article]

Or Ordentlich, Uri Erez
2011 arXiv   pre-print
An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of intersymbol interference.  ...  The channel impulse response is linearly equalized to an integer-valued response.  ...  An important representative of this class of algorithms is the celebrated LLL algorithm [19] , which has polynomial complexity and usually gives adequate results in practice.  ... 
arXiv:1012.5553v3 fatcat:tdqoc5ah6nealbujxk5wfmbwda

Algorithmic complexity in coding theory and the minimum distance problem

Alexander Vardy
1997 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97  
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  ...  I am especially indebted to Noga Alon for referring me to his construction, which is used in Section 3. Finally, I would like to thank Hagit Itzkowitz for her invaluable help.  ...  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  ... 
doi:10.1145/258533.258559 dblp:conf/stoc/Vardy97 fatcat:vkunvltuabfdvnjzldvt6mpihu

Compiling untyped lambda calculus to lower-level code by game semantics and partial evaluation (invited paper)

Daniil Berezun, Neil D. Jones
2017 Proceedings of the 2017 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation - PEPM 2017  
A compiled program is first-order functional and has a fixed set of working variables, whose number is independent of M . The generated LLL code in effect traverses the subexpressions of M .  ...  Further, the untyped lambda calculus ULC is compiled into LLL by partially evaluating a traversal algorithm for ULC. Plotkin posed the problem of existence of a fully abstract semantics of PCF [1].  ...  In [30] interaction nets are used as an intermediate representation for reduction.  ... 
doi:10.1145/3018882.3020004 fatcat:fhqr5xb6bbanhnq4h7jrizvomy

The inapproximability of lattice and coding problems with preprocessing

Uriel Feige, Daniele Micciancio
2004 Journal of computer and system sciences (Print)  
We prove that the closest vector problem with preprocessing (CVPP) is NP-hard to approximate within any factor less than ffiffi 5 3 q : More specifically, we show that there exists a reduction from an  ...  The result easily extends to any c p norm, for pX1; showing that CVPP in the c p norm is hard to approximate within any factor go ffiffi 5 3 p q : As an intermediate step, we establish analogous results  ...  Coding theory problems Our inapproximability results for CVPP are proved using the analogous problem for linear codes as an intermediate step.  ... 
doi:10.1016/j.jcss.2004.01.002 fatcat:buuxtfp63baadll5yhm7gbkzwa

ETRU: NTRU over the Eisenstein integers

Katherine Jarvis, Monica Nevins
2013 Designs, Codes and Cryptography  
We prove through both theory and implementation that ETRU is faster and has smaller keys for the same or better level of security than does NTRU.  ...  An important direction for research about NTRU is the development and analysis of variants in which the integers are replaced by elements of another ring, such as the Gaussian integers [18], integer matrices  ...  The authors would like to thank the anonymous referees for several  ... 
doi:10.1007/s10623-013-9850-3 fatcat:qxdwhb7te5a3bat2e7phhzehg4

Improving GGH Public Key Scheme Using Low Density Lattice Codes [article]

Reza Hooshmand
2015 arXiv   pre-print
algorithm.  ...  However, it has a number of drawbacks such as; large public key length and low security level.  ...  In this attack, by the knowledge of public key , it is tried to apply the LLL lattice reduction algorithm [17] to obtain a reduced basis { } .  ... 
arXiv:1503.03292v2 fatcat:zugd2u3vifg6pkkpxh6wfgmg3q

New group shuffled BP decoding algorithms for LDPC codes

Chi-Yuan Chang, Yu-Liang Chen, Chang-Ming Lee, Yu T. Su
2009 2009 IEEE International Symposium on Information Theory  
The group horizontal shuffled BP (GHSBP) and vertical shuffled BP (GVSBP) algorithms respectively partition the check and variable nodes of the code graph into groups to perform group-by-group message-passing  ...  An obvious complexity-reduction solution is to serialize the decoding process, i.e., dividing a decoding iteration into several serial sub-iterations in which a sub-iteration performs only part of the  ...  A regular binary (N, K) (d v , de) LDPC code C is a linear block code described by an M x N parity check matrix H which has d; ones in each column and de ones in each be viewed as a bipartite graph with  ... 
doi:10.1109/isit.2009.5205781 dblp:conf/isit/ChenLSC09 fatcat:r3dhxrxinbhfrjnvvjro6l7hvu

Perfect Space–Time Block Codes

F. Oggier, G. Rekaya, J.-C. Belfiore, E. Viterbo
2006 IEEE Transactions on Information Theory  
These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping.  ...  We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas.  ...  We then perform a basis reduction on the Gram matrix, using an LLL reduction algorithm (see Appendix VI for more details).  ... 
doi:10.1109/tit.2006.880010 fatcat:76ceq2h2mndsnhvjkxuf5xhh3u
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