The Exponent of a Polarizing Matrix Constructed from the Kronecker Product
Information Theory
2011-08-18 v1 math.IT
Abstract
The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker product are simply expressed as a product of those of its component matrices. We then show that the exponent of the polarizing matrix is shown to be a weighted sum of the exponents of its component matrices. These results may be employed in the design of a large polarizing matrix with high exponent.
Keywords
Cite
@article{arxiv.1108.3417,
title = {The Exponent of a Polarizing Matrix Constructed from the Kronecker Product},
author = {Myung-Kyu Lee and Kyeongcheol Yang},
journal= {arXiv preprint arXiv:1108.3417},
year = {2011}
}
Comments
7 pages, 1 figure, submitted to IEEE Transactions on Information Theory (July 27, 2011)