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ALGORITHMS FOR CONSTRUCTION OF OPTIMAL AND ALMOST-OPTIMAL LENGTH-RESTRICTED CODES

2006
*
Parallel Processing Letters
*

A

doi:10.1142/s0129626406002484
fatcat:rnjrhu6eunh77g4njmsnzp2jbe
*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*...##
###
Algorithms for Construction of Optimal and Almost-Optimal Length-Restricted Codes

*
Data Compression Conference
*

A

doi:10.1109/dcc.2005.12
dblp:conf/dcc/KarpinskiN05
fatcat:heczskoczfadbmyt5kinc3nqcq
*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*...##
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Page 1500 of Mathematical Reviews Vol. , Issue 2002B
[page]

2002
*
Mathematical Reviews
*

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*. ...##
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A search algorithm for linear codes: progressive dimension growth

2007
*
Designs, Codes and Cryptography
*

This paper presents an

doi:10.1007/s10623-007-9113-2
fatcat:u2nvpepcjvgu7mmdm6wjeltapi
*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 ...##
###
Cooperative polar code constructions over multi-channels

2018
*
IEICE Communications Express
*

The

doi:10.1587/comex.2018xbl0060
fatcat:bnvbuh22obcgxkoupuv3nbe2ty
*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] . ...##
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Nonlinear Sparse-Graph Codes for Lossy Compression of Discrete Nonredundant Sources

2007
*
2007 IEEE Information Theory Workshop
*

We also present a suboptimal compression

doi:10.1109/itw.2007.4313132
fatcat:fknagoh3pnd3hlo77iwobbh45e
*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. ...##
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Nonlinear Sparse-Graph Codes for Lossy Compression

2009
*
IEEE Transactions on Information Theory
*

We also present a suboptimal compression

doi:10.1109/tit.2009.2016040
fatcat:j7u2ej5cgzhczhalxsx5f4pp3e
*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. ...##
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Trees with Minimum Weighted Path Length
[chapter]

2004
*
Handbook of Data Structures and Applications
*

The trie

doi:10.1201/9781420035179.ch14
fatcat:hrkncjfjpnauhnhveq6yqf5e64
*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. ...##
###
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
*

The

doi:10.3934/naco.2020028
fatcat:ce3ypzvhkne3bahfz6m3d6fqyi
*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. ...##
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Bounding the Depth of Search Trees

1993
*
Computer journal
*

However, if an upper bound B is imposed on the

doi:10.1093/comjnl/36.7.668
fatcat:kmmlufp2aja6zaobdbiogwpmfy
*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. ...##
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Some new results for optimal ternary linear codes

2002
*
IEEE Transactions on Information Theory
*

Let ( ) be the maximum possible minimum Hamming distance

doi:10.1109/18.992814
fatcat:rluiai7a5bhxrpfh56apgjfq3m
*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. ...##
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The Structure of Optimal Prefix-Free Codes in Restricted Languages: The Uniform Probability Case
[chapter]

2005
*
Lecture Notes in Computer Science
*

Furthermore, [13] showed that the techniques developed

doi:10.1007/11534273_33
fatcat:vjlrr2yocfdvdhvsdjmhag3e4u
*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. ...##
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Constructions and some search results of ternary LRCs with d = 6

2020
*
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
*

In order to obtain ternary LRCs

doi:10.1587/transfun.2020eal2070
fatcat:caholyjwqrccdee4rfuvxvc7d4
*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 ...##
###
Source codes as random number generators

1998
*
IEEE Transactions on Information Theory
*

In this paper we show under general conditions that

doi:10.1109/18.661497
fatcat:oi7vihtlojgelkblu7fhrivflq
*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. ...##
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Optimal binary training sequence design for multiple-antenna systems over dispersive fading channels

2002
*
IEEE Transactions on Vehicular Technology
*

The performance enhancement

doi:10.1109/tvt.2002.800638
fatcat:mnjejx2n7fd7fgm6c3lyotjln4
*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. ...
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