Math @ Duke

Publications [#319317] of Henry Pfister
Papers Published
 Rengaswamy, N; Pfister, HD, Cyclic polar codes,
Ieee International Symposium on Information Theory Proceedings, vol. 2015June
(September, 2015),
pp. 12871291, IEEE, ISBN 9781467377041 [doi]
(last updated on 2019/07/19)
Abstract: © 2015 IEEE. Arikan introduced polar codes in 2009 and proved that they achieve the symmetric capacity, under lowcomplexity successive cancellation decoding, of any binaryinput discrete memoryless channel. Arikan's construction is based on the Kronecker product of 2by2 matrices and it was extended to larger matrices by Şaşoǧlu et al. in 2010. In this paper, we construct cyclic polar codes based on a mixedradix CooleyTukey decomposition of the Galois field Fourier transform. Ignoring the twiddle factors between stages, the derived fast Fourier transform is essentially a Kronecker product of small Fourier transform matrices. Thus, one can define a successive cancellation decoder and observe that the coordinate channels polarize. Choosing the locations of the frozen symbols in the resulting polar code is identical to choosing the locations of zeros in the Fourier transform of the codewords and, thus, the code is cyclic.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

