Abstract
Polar codes, which have been proposed as a family of linear block codes, has garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provably capacity-achieving capability. Thus, they have been proposed to be used for encoding information on the control channels in the upcoming 5G wireless networks. The basic approach introduced by Arikan in his landmark paper to polarize bit channels of equal capacities to those of unequal capacities can be used to design only codewords of length N=2n, which is a major limitation when codewords of different lengths are required for the underlying applications. In the predecessor paper, this aspect was partially addressed by using a 3×3 kernel circuit (used to generate codewords of length M=3m), along with downsizing techniques such as puncturing and shortening to asses the optimal design and resizing techniques based on the underlying system parameters. In this article, we extend this research to include the assessment of multi-kernel rate-matched polar codes for applicability over a much wider range of codeword lengths.
Highlights
As polar codes of length N = 2n might not always be suitable for an underlying system, developing techniques to generate more versatile codeword lengths is very important to realize their utilities in a wider range of practical systems
In [24], this aspect has been validated for multi-kernel polar codes as well, using a downsizing type selection (DTS) parameter, based on density evolution (DE), which provides a more accurate prediction of the optimality of choice of downsizing technique based on the desired system parameter settings
The disadvantage of a limited choice of codeword lengths is a major obstacle for utilizing polar codes over a wide range of applications
Summary
By assessing the error rate performances and complexities of polar code designs generated by these different construction and downsizing techniques, we determine the effect of different parameters and how to optimally design polar codes for a given set of parameter values This expands the scope of practical applications of polar codes to include scenarios when nonconventional (2n) codeword lengths are desirable.
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