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On Fast Threefold Polarizations of Binary Discrete Memoryless Channels

Authors:
Chengrong Huang
Ying Guo
Clement T Gyamfi
Tae Chul Shin
Moon Ho Lee

Keywords: polar codes; binary discrete memoryless channels; channel coding; fast algorithm.

Abstract:
Motivated by a polarization approach to construct code sequences related to Reed-Muller (RM) codes with generator matrix $G_{2^n}$ of size $2^ntimes 2^n$ to increase the cutoff rate, we consider a problem of systematic constructions of polar codes as splitting threefold input binary discrete memoryless channels (B-DMC) for generator matrix $G_{3^n}$. The polarized channel achieves the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low computation complexity of successive cancellation decoding strategy for any core matrix $mathcal{O}_3$, which is a submatrix of generator matrix $G_4=mathcal{O}_2otimes mathcal{O}_2$. In principle larger matrices $G_{3^n}$ with fast construction algorithms can be used for constructions of polar code sequences that tend to polarize with respect to the rate and reliability under certain fast combining and splitting operations. The proposed polarization code scheme has a salient recursiveness feature and hence can be decoded with a belief propagation (BP) decoder, which renders the scheme analytically tractable and provides a powerful low-complexity coding algorithm.

Pages: 122 to 126

Copyright: Copyright (c) IARIA, 2012

Publication date: May 27, 2012

Published in: conference

ISSN: 2308-4030

ISBN: 978-1-61208-199-1

Location: Stuttgart, Germany

Dates: from May 27, 2012 to June 1, 2012