The exponent of a polarizing matrix constructed from the Kronecker product

Authors:
Myung-Kyu Lee;Kyeongcheol Yang
Affiliations:
Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, Korea 790-784;Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, Korea 790-784
Venue:
Designs, Codes and Cryptography
Year:
2014

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Abstract

It was recently shown by Korada et al. that the partial distances of a polarizing matrix completely determine its exponent characterizing the asymptotic performance of a polar code under successive cancellation decoding. In this paper we prove in a purely algebraic way 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. As a result, the exponent of the polarizing matrix is shown to be a weighted sum of the exponents of its component matrices.