On the Effects of Kernel Configuration in Multi-Kernel Polar Codes

Abstract

Polar codes are a relatively new family of linear block codes which have garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provably capacity achieving capability. They have been proposed to be used for encoding information on the control channels in 5G wireless networks due to their robustness for short codeword lengths. The basic approach introduced by Arikan can only be used to generate polar codes of length N=2n, ∀n∈N. To overcome this limitation, polarization kernels of size larger than 2×2 (like 3×3, 4×4, and so on), have already been proposed in the literature. Additionally, kernels of different sizes can also be combined together to generate multi-kernel polar codes, further improving the flexibility of codeword lengths. These techniques undoubtedly improve the usability of polar codes for various practical implementations. However, with the availability of so many design options and parameters, designing polar codes that are optimally tuned to specific underlying system requirements becomes extremely challenging, since a variation in system parameters can result in a different choice of polarization kernel. This necessitates a structured design technique for optimal polarization circuits. We developed the DTS-parameter to quantify the best rate-matched polar codes. Thereafter, we developed and formalized a recursive technique to design polarization kernels of higher order from component smaller order. A scaled version of the DTS-parameter, namely SDTS-parameter (denoted by the symbol ζ in this article) was used for the analytical assessment of this construction technique and validated for single-kernel polar codes. In this paper, we aim to extend the analysis of the aforementioned SDTS parameter for multi-kernel polar codes and validate their applicability in this domain as well.

Hybrid Billiards Archimedes optimization of Multi-kernel polar codesfor 5G communications

“…, mentioned as the kernel of the transformation [4][5]. The outcome of this procedure in a transformation matrix is n N T T  = 2 where, n crease Kronecker influence of the kernel matrix 2 T , transforming the physical channel to N simulated channels are categorized as very low or very high reliability [6][7]. When the code length tends to infinity, this channel polarisation effect produces a share of totally reliable channels that tends to the channel capacity for symmetric binary-input memory less channels [8].…”

“…The error probability of SC is lower bounded by equation(5) denotes the mean value of LLR of i  . Equations(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) shows the DE/GA for kernels…”