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Master-Vortrag: Analysis and Optimization of Multi-Kernel Polar Codes

Luis Maßny
Donnerstag, 22. Oktober 2020
10:00 Uhr
virtueller Konferenzraum

Polar codes are a class of linear block codes that exploit the channel polarization effect in order to provide good error correction capabilities at a low complexity. The channel polarization is based on a recursive channel transformation by a so-called polarization kernel. As a generalization of conventional polar codes, multi-kernel polar codes have been proposed, which allow it to combine polarization kernels of different sizes within a single code. Accordingly, these codes provide many degrees of freedom, which makes it important to properly design such a code in order to optimize its performance. Two major aspects of the multi-kernel polar code design are analyzed in this thesis. Firstly, the design of good polarization kernels for practical codeword lengths is studied. Secondly, the effect of applying a chosen set of polarization kernels in different orders is approached.

In order to systematically construct polarization kernels, a recursive construction rule is developed that describes each kernel as a concatenation of smaller kernels. The performance analysis is based on the computation of Z parameters of the polarized information bit channels for a binary erasure channel. These yield an upper bound on the block error rate. The observations are verified by error rate simulations over an additive white Gaussian noise channel.

The results show that the kernel design depends on the code rate. In particular, it is demonstrated that in some cases an asymptotically suboptimal kernel is the best choice. The optimization of the kernel order in general turns out to be complex and depending on a variety of code parameters.