arXiv subjects

Charles Pillet

Publications and source records attributed to Charles Pillet.

17 recordsLinked to original sources

arXiv2026

On Reducing Decoding Complexity of Successive-Cancellation List Flip Decoding of Polar Codes

The recently proposed SCLF decoding algorithm for polar codes improves the error-correcting performance of state-of-the-art SCL decoding. However, it comes at the cost of a higher complexity. In this paper, partitioned polar codes tailored for the proposed PSCLF decoding algorithm are used to reduce the complexity of SCLF. Indeed, compared to SCLF, PSCLF allows early termination and is able to restart by skipping part of the decoding tree traversed sequentially. In order to maximize the coding gain, design of partitions tailored to PSCLF is proposed. In this extended paper, dynamic flip metric is used, as well as the possibility to flip multiple times during SCL. An analysis on the impact of this strategy on the early-termination or the CRC collisions encountered in PSCLF is carried out. Error-correction performance of multiple code rates and multiple partition strategies are shown. With the baseline algorithm SCL with $L=2$, degradation of $0.05$ dB is shown with respect to SCL-64, using $\omega=3$ flip per trial with $T_{max}=300$ trials. Numerical results show that the proposed PSCLF algorithm has an error-correction performance gain of up to 0.1 dB with respect to SCLF with same decoding parameters. This work is also compared with existing techniques to reduce the complexity of the SCLF decoding algorithm. The proposed algorithm reduces the complexity up to 77 % at the frame-error rate of $0.01$ with respect to SCLF and is able to reduce more the decoding complexity of SCLF embedding as well a restart mechanism. The average execution time of PSCLF matches the latency of SCL at $\text{FER}=4\cdot10^{-3}$ and lower.

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arXiv2026

Sequential Automorphism Ensemble Decoding with Early Stopping

In this paper, a low-complexity approach for the automorphism ensemble decoder (AED) using successive cancellation (SC) as constituent decoders is proposed. The approach sequentially activates sub-decoders and terminates the decoding process based on pre-optimized parameters, derived from the strong correlation observed between the decoding outcome and the SC path metric. An algorithm is proposed to find a list of early termination thresholds that minimize average decoding complexity subject to a block-error rate (BLER) constraint. For various code parameters and a BLER below $10^{-3}$, simulation results show that average decoding complexity is reduced by a factor of at least $6 \times$, and up to $22 \times$, compared to the original AED complexity, with a negligible degradation in BLER.

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arXiv2025

Generalized Restart Mechanism for Successive-Cancellation Flip Decoding of Polar Codes

Polar codes are a class of linear error-correction codes that have received a lot of attention due to their ability to achieve channel capacity in an arbitrary binary discrete memoryless channel (B-DMC) with low-complexity successive-cancellation (SC) decoding. However, practical implementations often require better error-correction performance than what SC decoding provides, particularly at short to moderate code lengths. Successive-cancellation flip (SCF) decoding algorithm was proposed to improve error-correction performance with an aim to detect and correct the first wrongly estimated bit in a codeword before resuming SC decoding. At each additional SC decoding trial, i.e., decoding attempt beyond the initial unsuccessful trial, one bit estimated as the least reliable is flipped. Dynamic SCF (DSCF) is a variation of SCF, where multiple bits may be flipped simultaneously per trial. Despite the improved error-correction performance compared to the SC decoder, SCF-based decoders have variable execution time, which leads to high average execution time and latency. In this work, we propose the generalized restart mechanism (GRM) that allows to skip decoding computations that are identical between the initial trial and any additional trial. Under DSCF decoding with up to 3-bit flips per decoding trial, our proposed GRM is shown to reduce the average execution time by 25% to 60% without any negative effect on error-correction performance. The proposed mechanism is adaptable to state-of-the-art latency-reduction techniques. When applied to Fast-DSCF-3 decoding, the additional reduction brought by the GRM is 15% to 22%. For the DSCF-3 decoder, the proposed mechanism requires approximately 4% additional memory.

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arXiv2025

Successive-Cancellation Flip and Perturbation Decoder of Polar Codes

In this paper, two decoding algorithms based on Successive Cancellation (SC) are proposed to improve the error-correction performance of cyclic redundancy check (CRC)-aided polar codes while aiming for a low-complexity implementation. Comparisons with Dynamic SC Flip (DSCF) and SC Perturbation (SCP) are carried out since the proposed DSCF and Perturbation (DSCFP) and Perturbed DSCF (PDSCF) algorithms combine both methods. The analysis includes comparisons with several code lengths $N$ and various number of decoding attempts $T_{max}$. For $N=1024$ and the coding rate $R=\frac{1}{2}$, the DSCFP and the SCP algorithms with $T_{max}=17$ are bested by approximately $0.1$\,dB at block error rate (BLER) of $0.001$. At $\text{BLER}=10^{-6}$ and for $T_{max}=64$, the gain is of $0.375$ dB and $>0.5$ dB with respect to DSCF and SCP, respectively. At high signal-to-noise ratio, the average computational complexity of the proposed algorithms is virtually equivalent to that of SC.

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arXiv2024

Successive-Cancellation Flip Decoding of Polar Codes Under Fixed Channel-Production Rate

Polar codes are a class of error-correcting codes that provably achieve the capacity of practical channels under the low-complexity successive-cancellation flip (SCF) decoding algorithm. However, the SCF decoding algorithm has a variable execution time with a high (worst-case) decoding latency. This characteristic poses a challenge to the design of receivers that have to operate at fixed data rates. In this work, we propose a multi-threshold mechanism that restrains the delay of a SCF decoder depending on the state of the buffer to avoid overflow. We show that the proposed mechanism provides better error-correction performance compared to a straightforward codeword-dropping mechanism at the cost of a small increase in complexity. In the region of interest for wireless communications, the proposed mechanism can prevent buffer overflow while operating with a fixed channel-production rate that is 1.125 times lower than the rate associated to a single decoding trial.

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arXiv2024

Partitioned Successive-Cancellation List Flip Decoding of Polar Codes

The recently proposed Successive-Cancellation List Flip (SCLF) decoding algorithm for polar codes improves the error-correcting performance of state-of-the-art SC List (SCL) decoding. However, it comes at the cost of a higher complexity. In this paper, we propose the Partitioned SCLF decoding algorithm, an algorithm that divides a word in partitions and applies SCLF decoding to each partition separately. Compared to SCLF, PSCLF allows early termination but is more susceptible to cyclic-redundancy check (CRC) collisions. In order to maximize the coding gain, a new partition design tailored to PSCLF is proposed as well as the possibility to support different CRC lengths. Numerical results show that the proposed PSCLF algorithm has an error-correction performance gain of up to 0.15 dB with respect to SCLF. Moreover, the proposed CRC structure permits to mitigate the error-correction loss at low frame-error rate (FER) due to CRC collisions, showing a gain of 0.2 dB at $\text{FER}=10^{-4}$ with respect to the regular CRC structure. The average execution time of PSCLF is shown to be 1.5 times lower than that of SCLF, and matches the latency of SCLF at $\text{FER}=4\cdot10^{-3}$ and lower.

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arXiv2024

Shortened Polar Codes under Automorphism Ensemble Decoding

In this paper, we propose a low-latency decoding solution of shortened polar codes based on their automorphism groups. The automorphism group of shortened polar codes, designed according to two existing shortening patterns, are shown to be limited but non-empty, making the Automorphism Ensemble (AE) decoding of shortened polar codes possible. Extensive simulation results for shortened polar codes under AE are provided and are compared to the SC-List (SCL) algorithm. The block-error rate of shortened polar codes under AE matches or beats SCL while lowering the decoding latency.

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arXiv2023

On the Distribution of Partially Symmetric Codes for Automorphism Ensemble Decoding

Automorphism Ensemble (AE) decoding has recently drawn attention as a possible alternative to list decoding of polar codes. In this letter, we investigate the distribution of Partially-Symmetric Reed-Muller (PS-RM) codes, a family of polar codes yielding good performances under AE decoding. We prove the existence of these codes for almost all code dimensions for code lengths $N\leq 256$. Moreover, we analyze the absorption group of this family of codes under SC decoding, proving that valuable permutations in AE decoding always exist. Finally, we experimentally show that PS-RM codes can outperform state-of-the-art polar-code-construction algorithms in terms of error-correction performance for short code lengths, while reducing decoding latency.

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arXiv2023

Dynamic Frozen-Function Design for Reed-Muller Codes With Automorphism-Based Decoding

In this letter, we propose to add dynamic frozen bits to underlying polar codes with a Reed-Muller information set with the aim of maintaining the same sub-decoding structure in Automorphism Ensemble (AE) and lowering the Maximum Likelihood (ML) bound by reducing the number of minimum weight codewords. We provide the dynamic freezing constraint matrix that remains identical after applying a permutation linear transformation. This feature also permits to drastically reduce the memory requirements of an AE decoder with polar-like codes having dynamic frozen bits. We show that, under AE decoding, the proposed dynamic freezing constraints lead to a gain of up to 0.25dB compared to the ML bound of the R(3,7) Reed-Muller code, at the cost of small increase in memory requirements.

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arXiv2023

Successive-Cancellation Flip Decoding of Polar Codes with a Simplified Restart Mechanism

Polar codes are a class of error-correcting codes that provably achieve the capacity of practical channels. The successive-cancellation flip (SCF) decoder is a low-complexity decoder that was proposed to improve the performance of the successive-cancellation (SC) decoder as an alternative to the high-complexity successive-cancellation list (SCL) decoder. The SCF decoder improves the error-correction performance of the SC decoder, but the variable execution time and the high worst-case execution time pose a challenge for the realization of receivers with fixed-time algorithms. The dynamic SCF (DSCF) variation of the SCF decoder further improves the error-correction performance but the challenge of decoding delay remains. In this work, we propose a simplified restart mechanism (SRM) that reduces the execution time of SCF and DSCF decoders through conditional restart of the additional trials from the second half of the codeword. We show that the proposed mechanism is able to improve the execution time characteristics of SCF and DSCF decoders while providing identical error-correction performance. For a DSCF decoder that can flip up to 3 simultaneous bits per decoding trial, the average execution time, the average additional execution time and the execution-time variance are reduced by approximately 31%, 37% and 57%, respectively. For this setup, the mechanism requires approximately 3.9% additional memory.

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arXiv2022

Group Properties of Polar Codes for Automorphism Ensemble Decoding

In this paper, we propose an analysis of the automorphism group of polar codes, with the scope of designing codes tailored for automorphism ensemble (AE) decoding. We prove the equivalence between the notion of decreasing monomial codes and the universal partial order (UPO) framework for the description of polar codes. Then, we analyze the algebraic properties of the affine automorphisms group of polar codes, providing a novel description of its structure and proposing a classification of automorphisms providing the same results under permutation decoding. Finally, we propose a method to list all the automorphisms that may lead to different candidates under AE decoding; by introducing the concept of redundant automorphisms, we find the maximum number of permutations providing possibly different codeword candidates under AE-SC, proposing a method to list all of them. A numerical analysis of the error correction performance of AE algorithm for the decoding of polar codes concludes the paper.

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arXiv2021

Classification of Automorphisms for the Decoding of Polar Codes

This paper proposes new polar code design principles for the low-latency automorphism ensemble (AE) decoding. Our proposal permits to design a polar code with the desired automorphism group (if possible) while assuring the decreasing monomial property. Moreover, we prove that some automorphisms are redundant under AE decoding, and we propose a new automorphisms classification based on equivalence classes. Finally, we propose an automorphism selection heuristic based on drawing only one element of each class; we show that this method enhances the block error rate (BLER) performance of short polar codes even with a limited number of automorphisms.

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arXiv2021

Polar Codes for Automorphism Ensemble Decoding

In this paper we deal with polar code automorphisms that are beneficial under low-latency automorphism ensemble (AE) decoding, and we propose polar code designs that have such automorphisms. Successive-cancellation (SC) decoding and thus SC-based AE decoding are invariant with respect to the only known polar code automorphisms, namely those of the lower-triangular affine (LTA) group. To overcome this problem, we provide methods to determine whether a given polar code has non-LTA automorphisms and to identify such automorphisms. Building on this, we design specific polar codes that admit automorphisms in the upper-diagonal linear (UTL) group, and thus render SC-based AE decoding effective. Demonstrated by examples, these new polar codes under AE decoding outperform conventional polar codes under SC list decoding in terms of error rate, while keeping the latency comparable to SC decoding. Moreover, state-of-the-art BP-based permutation decoding for polar codes is beaten by BP-based AE thanks to this design.

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arXiv2021

Staircase codes with non-systematic polar codes

In this work we propose an encoding and decoding framework for staircase codes based on non-systematic polar codes as component codes. The staircase structure allows for efficient parallelized decoding, while the polar component codes allow to benefit from the flexible structure and efficient soft-decision decoding algorithms. To enhance the performance of the polar staircase codes, we concatenate the polar component codes with cyclic redundancy check (CRC) outer codes, and we add interleavers within the staircase structure that are specific to polar code properties. The CRCs also allow to substantially reduce the decoding complexity. Simulation results evaluate the gain brought by our proposed techniques, and analyze the dependence of the error-correction performance on code and decoder parameters. Comparison with the state of the art on staircase polar codes shows an improvement in BER up to 0.9~dB, or considerable complexity reduction at the same BER.

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arXiv2020

Fast-SCAN decoding of Polar Codes

Polar codes are able to achieve the capacity of memoryless channels under successive cancellation (SC) decoding. Soft Cancellation (SCAN) is a soft-output decoder based on the SC schedule, useful in iterative decoding and concatenation of polar codes. However, the sequential nature of this decoder leads to high decoding latency compared to state-of-the-art codes. To reduce the latency of SCAN, in this paper we identify special nodes in the decoding tree, corresponding to specific frozen-bit sequences, and propose dedicated low-latency decoding approaches for each of them. The resulting fast-SCAN decoder does not alter the soft-output compared to the standard SCAN while dramatically reducing the decoding latency and yielding the same error-correction performance.

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arXiv2020

SCAN List Decoding of Polar Codes

In this paper we propose an enhanced soft cancellation (SCAN) decoder for polar codes based on decoding stages permutation. The proposed soft cancellation list (SCANL) decoder runs $L$ independent SCAN decoders, each one relying on a different permuted factor graph. The estimated bits are selected among the $L$ candidates through a dedicated metric provided by the decoders. Furthermore, we introduce an early-termination scheme reducing decoding latency without affecting error correction performance. We investigate the error-correction performance of the proposed scheme under various combinations of number of iterations used, permutation set and early-termination condition. Simulation results show that the proposed SCANL provides similar results when compared with belief propagation list, while having a smaller complexity. Moreover, for large list sizes, SCANL outperforms non-CRC aided successive cancellation list decoding.

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arXiv2020

On List Decoding of 5G-NR Polar Codes

The 5th generation wireless systems (5G) standardization process of the 3rd generation partnership project (3GPP) chose polar codes as a channel coding scheme for the control channel. In case of downlink control information, polar codes are concatenated with distributed distributed cyclic redundancy check (CRC). Whereas CRC bits allow to improve the performance of successive cancellation list (SCL) decoders by improving distance properties, distributed CRC bits allow for path pruning and decoding early-termination. In this paper, we show how to take advantage of the distributed CRC to improve SCL decoding, analyzing various schemes having different earlytermination and error correction properties. Simulation results compare the proposed decoding schemes, showing different tradeoffs between error-correction performance and early-termination with different decoder parameters.

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