A coding algorithm for constant weight vectors: a geometric approach based on dissections

Authors:
Chao Tian;Vinay A. Vaishampayan;N. J. A. Sloane
Affiliations:
AT&T Shannon Laboratory, Florham Park, NJ;AT&T Shannon Laboratory, Florham Park, NJ;AT&T Shannon Laboratory, Florham Park, NJ
Venue:
IEEE Transactions on Information Theory
Year:
2009

Citing 8
Cited 0

Efficient balanced codes

IEEE Transactions on Information Theory
Arithmetic coding for data compression

Communications of the ACM
Efficient Encoding and Decoding Schemes for Balanced Codes

IEEE Transactions on Computers
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)

Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Exhaustive Test Pattern Generation with Constant Weight Vectors

IEEE Transactions on Computers
Error-Correcting Codes and Self-Checking Circuits

Computer
Generalizations of Schöbi’s Tetrahedral Dissection

Discrete & Computational Geometry
Arithmetic coding

IBM Journal of Research and Development

Quantified Score

Hi-index	754.84

Visualization

Abstract

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.