Best Readings in Polar Coding

Alexios Balatsoukas-Stimming, Ingmar Land, Ido Tal, Peter Trifonov, Emanuele Viterbo

Research output: Other contributionOther

Abstract

Polar codes were introduced by Erdal Arıkan in 2008. They are the first family of error-correcting codes that attain the capacity of binary-input memoryless and symmetric channels with efficient encoding, decoding, and construction algorithms. Since their introduction, polar codes have been generalized and shown to be capacity achieving in numerous other communications settings.

The original construction of polar codes relies on the recursive application of an invertible linear transformation, which, when combined with a successive-cancellation decoder, effectively splits the original binary-input memoryless and symmetric communication channel into a number of bit subchannels. Increasing the recursion depth causes these bit subchannels to converge either to noiseless or purely noisy channels. Virtually error-free transmission can be achieved by sending the data over noiseless subchannels. While related code constructions had been suggested before (e.g., N. Stolte, I. Dumer and K. Shabunov), Arıkan’s work was the first to prove the polarization phenomenon and thus prove that polar codes are capacity achieving.

Unfortunately, the subchannels converge to these limiting cases relatively slowly, meaning that the error-correcting performance of Arıkan’s polar codes improves more slowly with the blocklength than other widely-used codes, such as Turbo and LDPC codes. However, polar codes have been shown to provide excellent error-correcting performance with low decoding complexity for practical blocklengths when combined with more advanced decoding algorithms. These favorable traits have led to polar codes being used in the 5G wireless standard, which is a testament to their outstanding performance.

In this Best Readings, we summarize several papers on the theoretical foundations of polarization theory, the construction and decoding of practical polar codes, as well as some generalized polar codes, which can help to overcome limitations of classical Arıkan polar codes. We also focus on practical implementation issues because, despite the simple structure of the encoding and decoding algorithms of polar codes, their practical implementation poses numerous challenges.

Contributors:
Alexios Balatsoukas-Stimming, EPFL, Switzerland
Ingmar Land, Huawei Technologies, France
Ido Tal, Technion – Israel Institute of Technology, Israel
Peter Trifonov, Peter the Great St. Petersburg Polytechnic University, Russia
Emanuele Viterbo, Monash University, Australia
Original languageEnglish
TypeBest Readings in Polar Coding
Media of outputWebsite
PublisherIEEE, Institute of Electrical and Electronics Engineers
Publication statusPublished - Jun 2019

Publication series

NameBest Readings
PublisherIEEE, Institute of Electrical and Electronics Engineers

Keywords

  • Polar codes

Cite this

Balatsoukas-Stimming, A., Land, I., Tal, I., Trifonov, P., & Viterbo, E. (2019, Jun). Best Readings in Polar Coding. IEEE, Institute of Electrical and Electronics Engineers.
Balatsoukas-Stimming, Alexios ; Land, Ingmar ; Tal, Ido ; Trifonov, Peter ; Viterbo, Emanuele. / Best Readings in Polar Coding. 2019. IEEE, Institute of Electrical and Electronics Engineers. (Best Readings).
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Balatsoukas-Stimming, A, Land, I, Tal, I, Trifonov, P & Viterbo, E 2019, Best Readings in Polar Coding. IEEE, Institute of Electrical and Electronics Engineers.

Best Readings in Polar Coding. / Balatsoukas-Stimming, Alexios; Land, Ingmar; Tal, Ido; Trifonov, Peter; Viterbo, Emanuele.

IEEE, Institute of Electrical and Electronics Engineers. 2019, Best Readings in Polar Coding. (Best Readings).

Research output: Other contributionOther

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N2 - Polar codes were introduced by Erdal Arıkan in 2008. They are the first family of error-correcting codes that attain the capacity of binary-input memoryless and symmetric channels with efficient encoding, decoding, and construction algorithms. Since their introduction, polar codes have been generalized and shown to be capacity achieving in numerous other communications settings.The original construction of polar codes relies on the recursive application of an invertible linear transformation, which, when combined with a successive-cancellation decoder, effectively splits the original binary-input memoryless and symmetric communication channel into a number of bit subchannels. Increasing the recursion depth causes these bit subchannels to converge either to noiseless or purely noisy channels. Virtually error-free transmission can be achieved by sending the data over noiseless subchannels. While related code constructions had been suggested before (e.g., N. Stolte, I. Dumer and K. Shabunov), Arıkan’s work was the first to prove the polarization phenomenon and thus prove that polar codes are capacity achieving.Unfortunately, the subchannels converge to these limiting cases relatively slowly, meaning that the error-correcting performance of Arıkan’s polar codes improves more slowly with the blocklength than other widely-used codes, such as Turbo and LDPC codes. However, polar codes have been shown to provide excellent error-correcting performance with low decoding complexity for practical blocklengths when combined with more advanced decoding algorithms. These favorable traits have led to polar codes being used in the 5G wireless standard, which is a testament to their outstanding performance.In this Best Readings, we summarize several papers on the theoretical foundations of polarization theory, the construction and decoding of practical polar codes, as well as some generalized polar codes, which can help to overcome limitations of classical Arıkan polar codes. We also focus on practical implementation issues because, despite the simple structure of the encoding and decoding algorithms of polar codes, their practical implementation poses numerous challenges.Contributors:Alexios Balatsoukas-Stimming, EPFL, SwitzerlandIngmar Land, Huawei Technologies, FranceIdo Tal, Technion – Israel Institute of Technology, IsraelPeter Trifonov, Peter the Great St. Petersburg Polytechnic University, RussiaEmanuele Viterbo, Monash University, Australia

AB - Polar codes were introduced by Erdal Arıkan in 2008. They are the first family of error-correcting codes that attain the capacity of binary-input memoryless and symmetric channels with efficient encoding, decoding, and construction algorithms. Since their introduction, polar codes have been generalized and shown to be capacity achieving in numerous other communications settings.The original construction of polar codes relies on the recursive application of an invertible linear transformation, which, when combined with a successive-cancellation decoder, effectively splits the original binary-input memoryless and symmetric communication channel into a number of bit subchannels. Increasing the recursion depth causes these bit subchannels to converge either to noiseless or purely noisy channels. Virtually error-free transmission can be achieved by sending the data over noiseless subchannels. While related code constructions had been suggested before (e.g., N. Stolte, I. Dumer and K. Shabunov), Arıkan’s work was the first to prove the polarization phenomenon and thus prove that polar codes are capacity achieving.Unfortunately, the subchannels converge to these limiting cases relatively slowly, meaning that the error-correcting performance of Arıkan’s polar codes improves more slowly with the blocklength than other widely-used codes, such as Turbo and LDPC codes. However, polar codes have been shown to provide excellent error-correcting performance with low decoding complexity for practical blocklengths when combined with more advanced decoding algorithms. These favorable traits have led to polar codes being used in the 5G wireless standard, which is a testament to their outstanding performance.In this Best Readings, we summarize several papers on the theoretical foundations of polarization theory, the construction and decoding of practical polar codes, as well as some generalized polar codes, which can help to overcome limitations of classical Arıkan polar codes. We also focus on practical implementation issues because, despite the simple structure of the encoding and decoding algorithms of polar codes, their practical implementation poses numerous challenges.Contributors:Alexios Balatsoukas-Stimming, EPFL, SwitzerlandIngmar Land, Huawei Technologies, FranceIdo Tal, Technion – Israel Institute of Technology, IsraelPeter Trifonov, Peter the Great St. Petersburg Polytechnic University, RussiaEmanuele Viterbo, Monash University, Australia

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Balatsoukas-Stimming A, Land I, Tal I, Trifonov P, Viterbo E. Best Readings in Polar Coding. 2019.