Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Communications

Deep Q-Learning Based Rate-Profile Design for Polarization Adjusted Convolutional (PAC) Codes

Homayoon Hatami, Hamid Saber, Jung Hyun Bae

Published Jun 8, 2025• 3 citations
Publisher

Abstract

This paper introduces a novel rate-profile design for Polarization-Adjusted Convolutional (PAC) codes by simplifying the construction of an information set (inf set) for a PAC code of length$N$into the design of inf sets for$M$component codes of length$\frac{N}{M}$. We define a Markov Decision Process (MDP) that formulates the task of identifying the inf set that minimizes the Block Error Rate (BLER). To achieve this, we employ a Deep QNetwork (DQN) with an experience replay buffer to determine the optimal inf set with the lowest BLER. Simulation results demonstrate that under Successive Cancellation List (SCL) decoding, our designed PAC codes improve BLER compared to state-of-the-art PAC codes. This method is not limited to the design of PAC code inf set; it is applicable to inf set design for the general family of precoded Polar codes and supports any decoder.

DOI
10.1109/icc52391.2025.11161677

Related papers

A Modified Q-Learning Algorithm for Rate-Profiling of Polarization Adjusted Convolutional (PAC) Codes

Samir Kumar Mishra, Digvijay Katyal, Sarvesha Anegundi Ganapathi

In this paper, we propose a reinforcement learning based algorithm for rate-profile construction of Arikan’s Polarization Adjusted Convolutional (PAC) codes. This method can be used for any blocklength, rate, list size under successive cancellation list (SCL) decoding and convolutional precoding polynomial. To the best of our knowledge, we present, for the first time, a set of new reward and update strategies which help the reinforcement learning agent discover much better rate-profiles than those present in existing literature.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 contemporary rate profiling designs 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 rate-profile construction of PAC codes.

arXiv:2110.01563•IEEE Wireless Communications and Networking Conference•Apr 10, 2022•15 citations

A Path Metric Based Construction of Polarization-Adjusted Convolutional Codes

Tyler Kann, Shrinivas Kudekar, Matthieu R. Bloch

We propose an approach to understand and exploit Polarization-Adjusted Convolutional (PAC) Codes that is directly tied to decoders with memory, specifically Successive Cancellation List (SCL) decoding. The crux of our approach is to use a modified Density Evolution Gaussian Approximation (DEGA) to account for errors in the decoding process and accurately track the path metrics (PMs) likely to incur decoding errors. Our approach not only explains the benefits provided by the use of the rate one precoding, but also provides new insight into why certain information sets perform well under PAC. We leverage the approach to design new information sets, and in particular, we design a$($128,42,$L=8)$code that offers half a$\text{dB}$gain over the state-of-the-art at a Frame Error Rate (FER) of$\overline{1}0^{-3}$and outperforms the Reed-Muller (RM) set with$L=32$. We also draw connections between our approach and works studying the minimum weight of PAC codes.

IEEE International Symposium on Information Theory (ISIT)•Jul 7, 2024•4 citations

LLR-Driven Rate-Profiling for Polarization-Adjusted Convolutional Codes under Small-List SCL Decoding

Yeseong Shin, Jeong Woo Lee

Polarization-Adjusted Convolutional (PAC) codes achieve near-capacity performance at short block lengths, yet their error-correction capability depends strongly on where frozen bits are placed. The conventional Reed-Muller rule works well when a Successive Cancellation List (SCL) decoder can employ a large list, but it loses effectiveness when the list size must remain small. We introduce an alternative rate-profiling method that ranks bit positions by the average magnitude of their log-likelihood ratios collected in advance and designates the least reliable positions as frozen. Simulations of a PAC code with block length one hundred twenty-eight and rate one half over an additive white Gaussian noise channel show that the proposed profile yields lower bit- and frame-error rates than the Reed-Muller rule for list sizes up to sixteen, although its performance stops improving for larger lists. These results indicate that the LLR-based profile is a practical choice when decoder complexity limits the list size.

International Conference on Information and Communication Technology Convergence (ICTC)•Oct 14, 2025•0 citations

A Path Probability Perspective on Rate-Profiling Design for Polarization-Adjusted Convolutional (PAC) Codes Under List Decoding

Aolin Liu, Bowen Feng, Chulong Liang +3 more

A novel rate-profiling design is proposed for polarization-adjusted convolutional (PAC) codes under list decoding, adopting a path probability perspective. Inspired by the concepts of Hamming distance and Hamming weight, the concepts of path probability distance (PPD) and path probability weight (PPW) are innovatively introduced to measure the disparity between the erroneous paths and the correct path for PAC codes under probabilistic decoding. An in-depth analysis of the recursion of node log-likelihood ratios (LLRs) in the factor graph is conducted, elucidating the derivation of a lower bound on the PPW as a consequential outcome. Utilizing the concept of the PPW, a rate-profiling design algorithm is proposed to establish the reliability ranking for the bit-channels of PAC codes. Simulation results demonstrate that PAC codes employing the proposed rate-profiling exhibit advantages over alternative rate-profiling and other state-of-the-art polar coding schemes across various block lengths and code rates under short decoding list sizes.

IEEE Transactions on Communications•Dec 30, 2024•2 citations

Reverse PAC Codes: Look-Ahead List Decoding

Xinyi Gu, Mohammad Rowshan, Jinhong Yuan

Convolutional precoding in polarization-adjusted convolutional (PAC) codes is a recently introduced variant of polar codes. It has demonstrated an effective reduction in the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This reduction has the potential to significantly improve the error correction performance. From a codeword formation perspective, this reduction has limitations. Capitalizing on the understanding of the decomposition of minimum-weight codewords, this paper studies reverse precoding that can effectively reduce minimum-weight codewords more than in PAC codes. We propose a look-ahead list decoding for the reverse PAC codes, which has the same order of complexity as list decoding in PAC codes. Through numerical analysis, we demonstrate a notable reduction in error coefficients compared to PAC codes and polar codes, resulting in a remarkable improvement in the block error rate, in particular at high code rates.

arXiv:2406.01903•IEEE International Symposium on Information Theory (ISIT)•Jul 7, 2024•7 citations

A Novel SCL Bit-Flipping Decoding Of Polarization-Adjusted Convolutional (PAC) Codes

Zhang, Wei

Polar codes have attracted the attention of numerous researchers in the past decade due to their excellent performance. However, their performance at short block lengths under standard successive cancellation decoding is far from desirable. An effective method to improve the performance at short lengths is CRC precoding followed by successive-cancellation list decoding. Later, Arikan presented polarization-adjusted convolutional (PAC) codes, which further improve the performance of polar codes. In fact, bit-flipping is another post-processing method that can improve decoding performance. In this paper, we propose a novel SCL Bit-Flipping of PAC Codes. We show that better performance can be achieved using list decoding when the list size is the same for PAC codes (N=128, K=64). The decoding performance of our newly proposed PAC-SCLF with a list size of 32 is 0.3 dB better than that of the traditional PAC-SCL with a list size of 32. We set the maximum number of bit flips to 5. The performance of the list size (L=32) for PAC-SCLF is almost the same as the performance of the list size (L=128) for PAC-SCL.

arXiv:2307.05871•Jul 12, 2023•1 citation
This paper introduces a novel rate-profile design for Polarization-Adjusted Convolutional (PAC) codes by simplifying the construction of an information set (inf set) for a PAC code of lengthNNNinto the design of inf sets forMMMcomponent codes of lengthNM\frac{N}{M}MN​. We define a Markov Decision Process (MDP) that formulates the task of identifying the inf set that minimizes the Block Error Rate (BLER). To achieve this, we employ a Deep QNetwork (DQN) with an experience replay buffer to determine the optimal inf set with the lowest BLER. Simulation results demonstrate that under Successive Cancellation List (SCL) decoding, our designed PAC codes improve BLER compared to state-of-the-art PAC codes. This method is not limited to the design of PAC code inf set; it is applicable to inf set design for the general family of precoded Polar codes and supports any decoder.
In this paper, we propose a reinforcement learning based algorithm for rate-profile construction of Arikan’s Polarization Adjusted Convolutional (PAC) codes. This method can be used for any blocklength, rate, list size under successive cancellation list (SCL) decoding and convolutional precoding polynomial. To the best of our knowledge, we present, for the first time, a set of new reward and update strategies which help the reinforcement learning agent discover much better rate-profiles than those present in existing literature.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 contemporary rate profiling designs 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 rate-profile construction of PAC codes.
We propose an approach to understand and exploit Polarization-Adjusted Convolutional (PAC) Codes that is directly tied to decoders with memory, specifically Successive Cancellation List (SCL) decoding. The crux of our approach is to use a modified Density Evolution Gaussian Approximation (DEGA) to account for errors in the decoding process and accurately track the path metrics (PMs) likely to incur decoding errors. Our approach not only explains the benefits provided by the use of the rate one precoding, but also provides new insight into why certain information sets perform well under PAC. We leverage the approach to design new information sets, and in particular, we design a$(128,42,128,42,128,42,L=8)codethatoffershalfacode that offers half acodethatoffershalfa\text{dB}gainoverthestate−of−the−artataFrameErrorRate(FER)ofgain over the state-of-the-art at a Frame Error Rate (FER) ofgainoverthestate−of−the−artataFrameErrorRate(FER)of\overline{1}0^{-3}andoutperformstheReed−Muller(RM)setwithand outperforms the Reed-Muller (RM) set withandoutperformstheReed−Muller(RM)setwithL=32$. We also draw connections between our approach and works studying the minimum weight of PAC codes.
Polarization-Adjusted Convolutional (PAC) codes achieve near-capacity performance at short block lengths, yet their error-correction capability depends strongly on where frozen bits are placed. The conventional Reed-Muller rule works well when a Successive Cancellation List (SCL) decoder can employ a large list, but it loses effectiveness when the list size must remain small. We introduce an alternative rate-profiling method that ranks bit positions by the average magnitude of their log-likelihood ratios collected in advance and designates the least reliable positions as frozen. Simulations of a PAC code with block length one hundred twenty-eight and rate one half over an additive white Gaussian noise channel show that the proposed profile yields lower bit- and frame-error rates than the Reed-Muller rule for list sizes up to sixteen, although its performance stops improving for larger lists. These results indicate that the LLR-based profile is a practical choice when decoder complexity limits the list size.
A novel rate-profiling design is proposed for polarization-adjusted convolutional (PAC) codes under list decoding, adopting a path probability perspective. Inspired by the concepts of Hamming distance and Hamming weight, the concepts of path probability distance (PPD) and path probability weight (PPW) are innovatively introduced to measure the disparity between the erroneous paths and the correct path for PAC codes under probabilistic decoding. An in-depth analysis of the recursion of node log-likelihood ratios (LLRs) in the factor graph is conducted, elucidating the derivation of a lower bound on the PPW as a consequential outcome. Utilizing the concept of the PPW, a rate-profiling design algorithm is proposed to establish the reliability ranking for the bit-channels of PAC codes. Simulation results demonstrate that PAC codes employing the proposed rate-profiling exhibit advantages over alternative rate-profiling and other state-of-the-art polar coding schemes across various block lengths and code rates under short decoding list sizes.
Convolutional precoding in polarization-adjusted convolutional (PAC) codes is a recently introduced variant of polar codes. It has demonstrated an effective reduction in the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This reduction has the potential to significantly improve the error correction performance. From a codeword formation perspective, this reduction has limitations. Capitalizing on the understanding of the decomposition of minimum-weight codewords, this paper studies reverse precoding that can effectively reduce minimum-weight codewords more than in PAC codes. We propose a look-ahead list decoding for the reverse PAC codes, which has the same order of complexity as list decoding in PAC codes. Through numerical analysis, we demonstrate a notable reduction in error coefficients compared to PAC codes and polar codes, resulting in a remarkable improvement in the block error rate, in particular at high code rates.
Polar codes have attracted the attention of numerous researchers in the past decade due to their excellent performance. However, their performance at short block lengths under standard successive cancellation decoding is far from desirable. An effective method to improve the performance at short lengths is CRC precoding followed by successive-cancellation list decoding. Later, Arikan presented polarization-adjusted convolutional (PAC) codes, which further improve the performance of polar codes. In fact, bit-flipping is another post-processing method that can improve decoding performance. In this paper, we propose a novel SCL Bit-Flipping of PAC Codes. We show that better performance can be achieved using list decoding when the list size is the same for PAC codes (N=128, K=64). The decoding performance of our newly proposed PAC-SCLF with a list size of 32 is 0.3 dB better than that of the traditional PAC-SCL with a list size of 32. We set the maximum number of bit flips to 5. The performance of the list size (L=32) for PAC-SCLF is almost the same as the performance of the list size (L=128) for PAC-SCL.