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.
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Communicated by T. Helleseth.
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Lee, MK., Yang, K. The exponent of a polarizing matrix constructed from the Kronecker product. Des. Codes Cryptogr. 70, 313–322 (2014). https://doi.org/10.1007/s10623-012-9689-z
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DOI: https://doi.org/10.1007/s10623-012-9689-z