Novel Recursive Kernel Construction for Polar Codes with Practical Codeword Lengths

Saha, Souradip; Adrat, Marc; Masny, Luis; Schrammen, Matthias; Jax, Peter

doi:10.1109/icspcs53099.2021.9660284

Cited by 2 publications

(13 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using

, one can design polar codes of length

. An example of a

polarization circuit is shown in Figure 2 , which is same as circuit

from [ 19 ].…”

Section: Preliminariesmentioning

confidence: 99%

“…There have been multiple proposals in the literature to how to polarize 3-bit channels (or how to design the

polarization circuit) like in the set of articles [ 6 , 7 , 8 , 9 ]. In this paper, the focus would be on the

polarization circuits

and

from [ 19 ], to analyze the effect of ordering and placement within a multi-kernel circuit layout.…”

Section: Preliminariesmentioning

confidence: 99%

“…Using a different kernel size in each stage or a different order of kernel sizes in different stages or even different kernel designs of the same size, one can generate different polarization circuits for the same codeword length

for

. In this article, we focus just on such multi-kernel polarization circuits of the form

using

circuits

and

from [ 19 ]. This would be the baseline for our analysis of kernel placement and ordering in multi-kernel polarization circuits in the subsequent sections.…”

Section: Preliminariesmentioning

confidence: 99%

“…Additionally, for higher kernel sizes, there exist a higher number of possibilities for valid polarization circuits and therefore a higher number of configurations of the corresponding multi-kernel designs. The increment of possible circuit designs to kernel sizes is exponential as shown in [ 19 ].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, a simple analytical parameter that can predict polar code design optimality based on system requirements would significantly expand the usability of polar codes for many applications. To address this artifact,

parameter was proposed in [ 19 ], which in turn was developed from the Downsizing Type-Selection (DTS) parameter from [ 17 ]. It was used to quantify the optimality of a specific single kernel design and determine the best choice of kernel circuit over given channel conditions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Saha

Maßny

Adrat

et al. 2022

Entropy

View full text Add to dashboard Cite

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.

show abstract

“…Using

, one can design polar codes of length

. An example of a

polarization circuit is shown in Figure 2 , which is same as circuit

from [ 19 ].…”

Section: Preliminariesmentioning

confidence: 99%

“…There have been multiple proposals in the literature to how to polarize 3-bit channels (or how to design the

polarization circuit) like in the set of articles [ 6 , 7 , 8 , 9 ]. In this paper, the focus would be on the

polarization circuits

and

from [ 19 ], to analyze the effect of ordering and placement within a multi-kernel circuit layout.…”

Section: Preliminariesmentioning

confidence: 99%

for

. In this article, we focus just on such multi-kernel polarization circuits of the form

using

circuits

and

from [ 19 ]. This would be the baseline for our analysis of kernel placement and ordering in multi-kernel polarization circuits in the subsequent sections.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Saha

Maßny

Adrat

et al. 2022

Entropy

View full text Add to dashboard Cite

show abstract

Adaptive Segmented Aggregation and Rate Assignment Techniques for Flexible-Length Polar Codes

Saha,

Mahajan,

Adrat

et al. 2024

Entropy

View full text Add to dashboard Cite

Polar codes have garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provable capacity achieving capability. They have been standardized to be used for encoding information on the control channels in 5G wireless networks due to their robustness for short codeword lengths. The conventional approach to generate polar codes is to recursively use 2×2 kernels and polarize channel capacities. This approach however, has a limitation of only having the ability to generate codewords of length Norig=2n form. In order to mitigate this limitation, multiple techniques have been developed, e.g., polarization kernels of larger sizes, multi-kernel polar codes, and downsizing techniques like puncturing or shortening. However, the availability of so many design options and parameters, in turn makes the choice of design parameters quite challenging. In this paper, the authors propose a novel polar code construction technique called Adaptive Segmented Aggregation which generates polar codewords of any arbitrary codeword length. This approach involves dividing the entire codeword into smaller segments that can be independently encoded and decoded, thereby aggregated for channel processing. Additionally a rate assignment methodology has been derived for the proposed technique, that is tuned to the design requirement.

show abstract

Novel Recursive Kernel Construction for Polar Codes with Practical Codeword Lengths

Cited by 2 publications

References 15 publications

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

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

Adaptive Segmented Aggregation and Rate Assignment Techniques for Flexible-Length Polar Codes

Contact Info

Product

Resources

About