On the Formation of Min-Weight Codewords of Polar/PAC Codes and Its Applications

Rowshan, Mohammad; Dau, Son Hoang; Viterbo, Emanuele

doi:10.1109/tit.2023.3319015

Cited by 3 publications

(7 citation statements)

References 32 publications

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“…Then, the minimum distance of the code C(A), is d min = min i∈A w(g i ) [386], [387], [388,Lemma 3].…”

Section: ) Minimum Distance Of Polar Codesmentioning

confidence: 99%

“…Hence, a code design approach that considers both the sub-channel reliability and the error coefficient is of interest; however, optimizing both would be highly complex and requires performing a search for every code. An approach in [388], [414] was suggested that simply improves the error coefficient of an available reliability-based construction, which was discussed above. Also, as shown in [415], we can modify the reliability-based construction by bit-swapping to reduce the possibility of eliminating the correct path in the list decoding.…”

Section: ) Rm-polar Constructionmentioning

confidence: 99%

“…Numerous construction methods for PAC codes, predominantly based on search, have also been suggested in [454]- [457]. It was proposed in [388] to use the reliability-based rateprofile of polar codes as it is easy to construct, and instead to modify it to drastically reduce the number of minimum weight codewords. Furthermore, rate-matching techniques, such as puncturing and shortening, for systematic and nonsystematic PAC codes have also been investigated in [411], [458]- [463].…”

Section: Volume 67mentioning

confidence: 99%

“…Note that there is an approach [387], [388] based on removing many minimum-weight codewords by a simple modification of the 5G-based construction of PAC codes so that it can outperform CRC-polar codes in low and medium SNR regimes for medium blocklengths and all rates.…”

Section: N Error Performancementioning

confidence: 99%

“…Construction of polar codes and their variants considering both the error coefficient (or weight distribution in general, based on the weight structure of polar codes studied extensively in [388], [577]- [579]) and sub-channels reliability with a low-complexity approach is desired. As discussed in Section E, reliability-based code construction is optimal for SC decoding.…”

Section: P Future Directions For Polar Codesmentioning

confidence: 99%

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Channel Coding Toward 6G: Technical Overview and Outlook

Rowshan,

Qiu,

Xie

et al. 2024

IEEE Open J. Commun. Soc.

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Channel coding plays a pivotal role in ensuring reliable communication over wireless channels. With the growing need for ultra-reliable communication in emerging wireless use cases, the significance of channel coding has amplified. Furthermore, minimizing decoding latency is crucial for critical-mission applications, while optimizing energy efficiency is paramount for mobile and the Internet of Things (IoT) communications. As the fifth generation (5G) of mobile communications is currently in operation and 5G-advanced is on the horizon, the objective of this paper is to assess prominent channel coding schemes in the context of recent advancements and the anticipated requirements for the sixth generation (6G). In this paper, after considering the potential impact of channel coding on key performance indicators (KPIs) of wireless networks, we review the evolution of mobile communication standards and the organizations involved in the standardization, from the first generation (1G) to the current 5G, highlighting the technologies integral to achieving targeted KPIs such as reliability, data rate, latency, energy efficiency, spectral efficiency, connection density, and traffic capacity. Following this, we delve into the anticipated requirements for potential use cases in 6G. The subsequent sections of the paper focus on a comprehensive review of three primary coding schemes utilized in past generations and their recent advancements: lowdensity parity-check (LDPC) codes, turbo codes (including convolutional codes), and polar codes (alongside Reed-Muller codes). Additionally, we examine alternative coding schemes like Fountain codes (also known as rate-less codes), sparse regression codes, among others. Our evaluation includes a comparative analysis of error correction performance and the performance of hardware implementation for these coding schemes, providing insights into their potential and suitability for the upcoming 6G era. Lastly, we will briefly explore considerations such as higher-order modulations and waveform design, examining their contributions to enhancing key performance indicators in conjunction with channel coding schemes.

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“…Then, the minimum distance of the code C(A), is d min = min i∈A w(g i ) [386], [387], [388,Lemma 3].…”

Section: ) Minimum Distance Of Polar Codesmentioning

confidence: 99%