Upper union bound for the decoding error probability of polar codes with arbitrary binary kernels under the successive cancelation decoding is derived. The proposed approach is based on the representation of polar codes as multilevel ones.

A challenging problem related to the design of polar codes is “robustness against channel parameter variations” as stated in Arıkan’s original work. In this paper, we describe how the problem of robust polar code design can be viewed as a mismatch decoding problem. We propose conditions which ensure a polar encoder/decoder designed for a mismatched B-DMC can be used to communicate reliably. In ...

We give a classification of non-negative or Borel measurable, SL(d) invariant, homogeneous valuations on the space of d-dimensional convex polytopes containing the origin in their interiors. The only examples are volume, volume of the polar body, and the Euler characteristic.