List Decoding of Arıkan’s PAC Codes

Yao, Hanwen; Vardy, Alexander

doi:10.1109/isit44484.2020.9174118

Cited by 33 publications

(27 citation statements)

References 15 publications

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“…Under sequential decoding, at a target FER of 10 −5 , the FER performance of PAC codes is just 0.25 dB away from the BI-AWGN dispersion bound approximation. Further, it was observed in [6] and [7] that nearly same FER performance can as well be obtained by list decoding as shown in Figure 1.…”

Section: Introduction Polar Codes Introduced By Arikanmentioning

confidence: 55%

“…2) PAC Decoding scheme: : The decoding of PAC code can be done either by sequential decoding [5] or by list decoding as in [6], [7], [8].…”

Section: A Brief Overview Of Pac Codementioning

confidence: 99%

“…It was observed by Arikan in [5] that the performance of PAC code is more sensitive to the choice of rate-profiling scheme A as compared to the precoding polynomial w. Further, it was also observed in [6], that PAC codes perform better than polar codes owing to improved minimum distance properties.…”

Section: B Our Contributionsmentioning

confidence: 99%

See 2 more Smart Citations

A Heuristic Algorithm for Rate-Profiling of Polarization Adjusted Convolutional (PAC) codes

Mishra¹,

Katyal²,

Ganapathi³

2021

Preprint

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<div>In this paper, we propose a heuristic algorithm for rate-profile construction of Arikan's Polarization Assisted Convolutional (PAC) codes. This method can be used for any blocklength, rate and convolutional precoding polynomial. The proposed algorithm tries to create a rate-profile for which the corresponding PAC code is, in a sense, locally optimized for having maximum possible minimum distance.</div><div>Simulation results show that PAC codes constructed with the proposed algorithm perform better in terms of frame erasure rate (FER) compared to the PAC codes constructed with rate profiling designs in existing literature for various list lengths. Further, by using a (64, 32) PAC code as an example, it is shown that the choice of convolutional precoding polynomial can have a significant impact on FER performance. Finally, we demonstrate that for a target FER of $\mathbf{10^{-5}}$, (128, 72) PAC codes constructed with our proposed algorithm is just 0.35 dB away from the information theoretic limit at this blocklength.</div>

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Section: Introduction Polar Codes Introduced By Arikanmentioning

confidence: 55%

“…2) PAC Decoding scheme: : The decoding of PAC code can be done either by sequential decoding [5] or by list decoding as in [6], [7], [8].…”

Section: A Brief Overview Of Pac Codementioning

confidence: 99%

See 1 more Smart Citation

A Heuristic Algorithm for Rate-Profiling of Polarization Adjusted Convolutional (PAC) codes

Mishra¹,

Katyal²,

Ganapathi³

2021

Preprint

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show abstract

“…This work is apparently independent from and contemporaneous with our results herein. The paper of Rowshan, Burg, and Viterbo [ 48 ] was posted on in February 2020, while our work [ 50 ] was submitted for review in January 2020. Our results became available on in May 2020.…”

Section: Introductionmentioning

confidence: 99%

“…Our results became available on in May 2020. The Rowshan-Viterbo paper [ 49 ] was posted on in July 2020, after our results were presented in [ 50 ].…”

Section: Introductionmentioning

confidence: 99%

List Decoding of Arıkan’s PAC Codes

Yao

Vardy

2021

Entropy

Self Cite

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Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, L⩾128). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as ν=2.

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A fast parallel SC-Fano decoding algorithm for PAC codes

Fan

2023

Sci. China Inf. Sci.

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List Decoding of Arıkan’s PAC Codes

Cited by 33 publications

References 15 publications

A Heuristic Algorithm for Rate-Profiling of Polarization Adjusted Convolutional (PAC) codes

A Heuristic Algorithm for Rate-Profiling of Polarization Adjusted Convolutional (PAC) codes

List Decoding of Arıkan’s PAC Codes

A fast parallel SC-Fano decoding algorithm for PAC codes

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