Low-Complexity Puncturing and Shortening of Polar Codes

Bioglio, Valerio; Gabry, Frédéric; Land, Ingmar

doi:10.1109/wcncw.2017.7919040

Cited by 76 publications

(62 citation statements)

References 12 publications

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“…In puncturing, the untransmitted code bits are treated as erased at the decoder, while shortening introduces a sub-code imposing the untransmitted code bits to assume a fixed value, typically zero, such that their value is already known by the decoder. It has been observed that for polar codes, shortening works better for high rates, and puncturing for low rates [31].…”

Section: Rate Matchingmentioning

confidence: 99%

“…Shortening, on the contrary, improves the bit channel reliabilities by introducing overcapable bits, i.e. bits with conceptually infinite reliability that are always correctly decoded [31]. However, code bits in the matching pattern must depend on frozen bits only, which forces to freeze the most reliable bit-channels worsening the error correction capabilities of the code.…”

Section: Rate Matchingmentioning

confidence: 99%

See 1 more Smart Citation

Design of Polar Codes in 5G New Radio

Bioglio

Condo

Land

2021

IEEE Commun. Surv. Tutorials

Self Cite

220

107

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Polar codes have attracted the attention of academia and industry alike in the past decade, such that the 5 th generation wireless systems (5G) standardization process of the 3 rd generation partnership project (3GPP) chose polar codes as a channel coding scheme. In this tutorial, we provide a description of the encoding process of polar codes adopted by the 5G standard. We illustrate the struggles of designing a family of polar codes able to satisfy the demands of 5G systems, with particular attention to rate flexibility and low decoding latency. The result of these efforts is an elaborate framework that applies novel coding techniques to provide a solid channel code for NR requirements.

show abstract

Section: Rate Matchingmentioning

confidence: 99%

Section: Rate Matchingmentioning

confidence: 99%

Design of Polar Codes in 5G New Radio

Bioglio

Condo

Land

2021

IEEE Commun. Surv. Tutorials

Self Cite

220

107

View full text Add to dashboard Cite

show abstract

“…However, the codeword length was limited to N = l n . For the sake of obtaining arbitrary codeword lengths, puncturing and shorterning techniques were exploited in [50]- [52], while multi-kernel polar codes, invoking multiple l-bit kernels, were conceived in [53], [54]. Nonetheless, in this paper, we will focus on Arikan's polar codes.…”

Section: B Non-arikan Polar Codesmentioning

confidence: 99%

Polar Codes and Their Quantum-Domain Counterparts

Babar

Egilmez

Xiang

et al. 2020

IEEE Commun. Surv. Tutorials

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Arikan's polar codes are capable of achieving the Shannon's capacity at a low encoding and decoding complexity, while inherently supporting rate adaptation. By virtue of these attractive features, polar codes have provided fierce competition to both the turbo as well as the Low Density Parity Check (LDPC) codes, making its way into the 5G New Radio (NR). Realizing the significance of polar codes, in this paper we provide a comprehensive survey of polar codes, highlighting the major milestones achieved in the last decade. Furthermore, we also provide tutorial insights into the polar encoder, decoders as well as the code construction methods. We also extend our discussions to quantum polar codes with an emphasis on the underlying quantum-to-classical isomorphism and the syndromebased quantum polar codes.

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“…Numerous rate-matching schemes for polar codes have been widely studied in the literature [5]- [17]. Among them, puncturing and shortening have been commonly studied.…”

Section: Introductionmentioning

confidence: 99%

Rate Matching for Polar Codes Based on Binary Domination

Jang

Ahn

Jeong

et al. 2019

IEEE Trans. Commun.

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In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made incapable (by puncturing) or to be shortened are governed by binary domination. In particular, we show that binary domination completely determines incapable or shortened bit patterns for polar codes, and that all the possible incapable or shortened bit patterns can be identified. We then present the patterns of the corresponding encoder output bits to be punctured or fixed, when the incapable or shortened bits are given. We also demonstrate that the order and the pattern of puncturing and shortening for polar codes can be aligned. In the previous work on the rate matching for polar codes, puncturing of encoder output bits begins from a low-indexed bit, while shortening starts from a high-indexed bit. Unlike such a conventional approach, we show that encoder output bits can be punctured from high-indexed bits, while keeping the incapable bit pattern exactly the same. This makes it possible to design a unified circular-buffer rate matching (CB-RM) scheme that includes puncturing, shortening, and repetition.

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Low-Complexity Puncturing and Shortening of Polar Codes

Cited by 76 publications

References 12 publications

Design of Polar Codes in 5G New Radio

Design of Polar Codes in 5G New Radio

Polar Codes and Their Quantum-Domain Counterparts

Rate Matching for Polar Codes Based on Binary Domination

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