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ALGORITHMS FOR CONSTRUCTION OF OPTIMAL AND ALMOST-OPTIMAL LENGTH-RESTRICTED CODES
2006
Parallel Processing Letters
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A code is n almost-optimal code with error if for all length-restricted codes where = and P = The idea of our algorithm for almost-optimal length-restricted codes is to replace weights with weights = for ...
Relative weight of an element is We maintain for every item e and every + logn the value of = and < + We also consider the problem of constructing the almost-optimal length-restricted codes. ...
A code is n almost-optimal code with error if for all length-restricted codes where = and P = The idea of our algorithm for almost-optimal length-restricted codes is to replace weights with weights = for ...
doi:10.1142/s0129626406002484
fatcat:rnjrhu6eunh77g4njmsnzp2jbe
Algorithms for Construction of Optimal and Almost-Optimal Length-Restricted Codes
Data Compression Conference
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A code is n almost-optimal code with error if for all length-restricted codes where = and P = The idea of our algorithm for almost-optimal length-restricted codes is to replace weights with weights = for ...
Relative weight of an element is We maintain for every item e and every + logn the value of = and < + We also consider the problem of constructing the almost-optimal length-restricted codes. ...
A code is n almost-optimal code with error if for all length-restricted codes where = and P = The idea of our algorithm for almost-optimal length-restricted codes is to replace weights with weights = for ...
doi:10.1109/dcc.2005.12
dblp:conf/dcc/KarpinskiN05
fatcat:heczskoczfadbmyt5kinc3nqcq
Page 1500 of Mathematical Reviews Vol. , Issue 2002B
[page]
2002
Mathematical Reviews
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They present an approximate Lagrangian algorithm (called WARM-UP) that constructs sub- optimal length restricted prefix codes, and consists of successive constructions of Huffman trees for modified weights ...
optimal codes in many practical settings, and it produces length restricted codes with compression power similar
94 INFORMATION AND COMMUNICATION, CIRCUITS 1500
to those produced by exact algorithms. ...
A search algorithm for linear codes: progressive dimension growth
2007
Designs, Codes and Cryptography
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This paper presents an algorithm, called progressive dimension growth (PDG), for the construction of linear codes with a pre-specified length and a minimum distance. ...
One of the most important and challenging problems in coding theory is to find optimal values of the parameters of a linear code and to explicitly construct codes whose parameters attain, or get as close ...
So, if there was an efficient algorithm to compute the minimum distance of an arbitrary linear code, then randomized algorithms could be used to construct codes with optimal or good (near optimal) parameters ...
doi:10.1007/s10623-007-9113-2
fatcat:u2nvpepcjvgu7mmdm6wjeltapi
Cooperative polar code constructions over multi-channels
2018
IEICE Communications Express
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The constructions consist of several polar codes as mother codes and re-polarization processes, which unify all mother codes into one scheme. ...
Moreover, a cooperative decoding algorithm for the unified scheme, which decodes all mother codes in parallel and spreads the decoding results within each mother code from itself to the others, is provided ...
Algorithm 1 shows the optimized cooperative construction for any DMC with finite input and output alphabet sizes based on greedy-merge degrading [4] . ...
doi:10.1587/comex.2018xbl0060
fatcat:bnvbuh22obcgxkoupuv3nbe2ty
Nonlinear Sparse-Graph Codes for Lossy Compression of Discrete Nonredundant Sources
2007
2007 IEEE Information Theory Workshop
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We also present a suboptimal compression algorithm, which exhibits near-optimal performance for moderate block lengths. ...
We propose a scheme for lossy compression of discrete memoryless sources: The compressor is the decoder of a nonlinear channel code, constructed from a sparse graph. ...
Therefore, (10) follows in view of (69).
III. CODE CONSTRUCTION AND PROOF OF OPTIMALITY FOR THE DISCRETE MEMORYLESS SOURCE
A. ...
doi:10.1109/itw.2007.4313132
fatcat:fknagoh3pnd3hlo77iwobbh45e
Nonlinear Sparse-Graph Codes for Lossy Compression
2009
IEEE Transactions on Information Theory
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We also present a suboptimal compression algorithm, which exhibits near-optimal performance for moderate block lengths. ...
We propose a scheme for lossy compression of discrete memoryless sources: The compressor is the decoder of a nonlinear channel code, constructed from a sparse graph. ...
Therefore, (10) follows in view of (69).
III. CODE CONSTRUCTION AND PROOF OF OPTIMALITY FOR THE DISCRETE MEMORYLESS SOURCE
A. ...
doi:10.1109/tit.2009.2016040
fatcat:j7u2ej5cgzhczhalxsx5f4pp3e
Trees with Minimum Weighted Path Length
[chapter]
2004
Handbook of Data Structures and Applications
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The trie of the code is then an almost full t-ary tree. ...
If for example the initial code words of letters have length 5, we get the compression ratio 55/23 ≈ 2.4.
14-4
Handbook of Data Structures and Applications
O(n log n) Time Algorithm The basic algorithm ...
The total cost (sum of values in internal nodes equal to 538) and the levels of original items are the same as in optimal alphabetic tree. ...
doi:10.1201/9781420035179.ch14
fatcat:hrkncjfjpnauhnhveq6yqf5e64
Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks
2019
Numerical Algebra, Control and Optimization
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The algorithm is verified by some numerical examples and the ant colony parameters are tuned by design of experiment method, and the optimal setting for different size of networks are determined. 2010 ...
Then, the shortest path tree is obtained by at most O(n 3 ) time complexity at any iteration and the ants begin to improve the solution and the optimal solution is constructed in a reasonable time. ...
The authors would like to thank the editor and the anonymous reviewers for their precious comments. ...
doi:10.3934/naco.2020028
fatcat:ce3ypzvhkne3bahfz6m3d6fqyi
Bounding the Depth of Search Trees
1993
Computer journal
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However, if an upper bound B is imposed on the length of the codewords, the best known algorithms for the construction of an optimal code have time and space complexities O(Bn 2 ). ...
For an ordered sequence of n weights, Hu man's algorithm constructs in time and space O(n) a search tree with minimum average path length, or, which is equivalent, a minimum redundancy code. ...
Algorithm ROT Our algorithm for the construction of a B-restricted tree consists of Steps 1a, 1b, 2 and 3. The following procedure is used for Step 3. ...
doi:10.1093/comjnl/36.7.668
fatcat:kmmlufp2aja6zaobdbiogwpmfy
Some new results for optimal ternary linear codes
2002
IEEE Transactions on Information Theory
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Let ( ) be the maximum possible minimum Hamming distance of a ternary [ ]-code for given values of and . We describe a package for code extension and use this to prove some new exact values of ( ). ...
Moreover, we classify the ternary [ ( )]-codes for some values of and . ...
A classification of optimal codes of small lengths was given by van Eupen and Lisonek in [12] . They used a geometrical approach for the classification of codes of dimensions 2 and 3. ...
doi:10.1109/18.992814
fatcat:rluiai7a5bhxrpfh56apgjfq3m
The Structure of Optimal Prefix-Free Codes in Restricted Languages: The Uniform Probability Case
[chapter]
2005
Lecture Notes in Computer Science
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Furthermore, [13] showed that the techniques developed for constructing Varn Codes could then be used to construct optimal codes restricted to any regular L that is accepted by a DFA with only one accepting ...
In this paper we discuss the problem of constructing minimum-cost, prefix-free codes for equiprobable words under the assumption that all codewords are restricted to belonging to an arbitrary language ...
This theorem immediately leads to a simple algorithm for constructing such codes given the restriction language L and the number of leaves n. ...
doi:10.1007/11534273_33
fatcat:vjlrr2yocfdvdhvsdjmhag3e4u
Constructions and some search results of ternary LRCs with d = 6
2020
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
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In order to obtain ternary LRCs of distance 6, firstly, we propose constructions with disjoint repair groups and construct several families of LRCs with 1 ≤ r ≤ 6, where codes with 3 ≤ r ≤ 6 are obtained ...
Locally repairable codes (LRCs) are a type of new erasure codes designed for modern distributed storage systems (DSSs). ...
Expanding Code Length of LRCs For an [n, k, 6; r] LRC with a parity-check matrix H, there is an algorithm to expand the code length n without changing the distance 6 and the dimension of parity-check matrix ...
doi:10.1587/transfun.2020eal2070
fatcat:caholyjwqrccdee4rfuvxvc7d4
Source codes as random number generators
1998
IEEE Transactions on Information Theory
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In this paper we show under general conditions that optimal variable-length source codes asymptotically achieve optimal variable-length random bit generation in a rather strong sense. ...
Since optimal noiseless data compression codes produce incompressible outputs, it is natural to investigate their capabilities as optimal random number generators. ...
However, the problem of investigating how far from being truly random is the output of a Lempel-Ziv algorithm (and other optimal source codes) appears to be new. ...
doi:10.1109/18.661497
fatcat:oi7vihtlojgelkblu7fhrivflq
Optimal binary training sequence design for multiple-antenna systems over dispersive fading channels
2002
IEEE Transactions on Vehicular Technology
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The performance enhancement of multibeam adaptive base-stations antennas for cellular land mobile radio systems," IEEE Trans. Veh. ...
A two-stage hybrid approach for CCI/ISI reduction with space-time processing," IEEE Commun. , "Joint spatial and temporal equalization for channels with ISI and CCI-Theoretical and experimental results ...
ACKNOWLEDGMENT The authors would like to thank the reviewers for their valuable comments and suggestion. ...
doi:10.1109/tvt.2002.800638
fatcat:mnjejx2n7fd7fgm6c3lyotjln4
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