The Exponent of a Polarizing Matrix Constructed from the Kronecker Product

Myung-Kyu Lee; Kyeongcheol Yang

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arXiv · 1108.3417

The Exponent of a Polarizing Matrix Constructed from the Kronecker Product

Myung-Kyu Lee·Kyeongcheol Yang

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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.

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Myung-Kyu Lee, Kyeongcheol Yang. 2011-08-17. The Exponent of a Polarizing Matrix Constructed from the Kronecker Product. https://arxiv.org/abs/1108.3417

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