A Coding Algorithm for Constant Weight Vectors: A Geometric Approach Based on Dissections
| Autor: | Vinay A. Vaishampayan, Neil J. A. Sloane, Chao Tian |
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| Rok vydání: | 2009 |
| Předmět: |
Linde–Buzo–Gray algorithm
Discrete mathematics Computational complexity theory Euclidean space Codebook Library and Information Sciences Computer Science Applications Combinatorics TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Bijection Binary code Bijection injection and surjection Decoding methods MathematicsofComputing_DISCRETEMATHEMATICS Computer Science::Information Theory Information Systems Mathematics |
| Zdroj: | IEEE Transactions on Information Theory. 55:1051-1060 |
| ISSN: | 0018-9448 |
| DOI: | 10.1109/tit.2008.2011441 |
| Popis: | We present a novel technique for encoding and decoding constant weight binary vectors that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight of the code. The encoder and decoder mappings are then interpreted as a bijection between a certain hyper-rectangle and a polytope in this Euclidean space. An inductive dissection algorithm is developed for constructing such a bijection. We prove that the algorithm is correct and then analyze its complexity. The complexity depends on the weight of the vector, rather than on the block length as in other algorithms. This approach is advantageous when the weight is smaller than the square root of the block length. |
| Databáze: | OpenAIRE |
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