An SCL-Aware Design of PAC Codes
Abstract
We develop design methodologies for the rate profile of polarization-adjusted convolutional (PAC) codes tailored to successive cancellation list (SCL) decoding. The crux of our approach is two-fold: first is the creation of a modified density evolution Gaussian approximation (DEGA), called conditional DEGA (CDEGA), to analyze the decoding process in the presence of errors; second is the creation of a dangerous-path occupancy metric to find the conditional occupancy of bit-errors in a finite list. Our approach not only illuminates the role of rate-one precoding, but also provides insight into why certain information sets are particularly well suited to PAC codes. We demonstrate the usefulness of CDEGA and dangerous-path metrics with algorithms that create new information sets, as well as precoders that are extremely sparse yet competitive. In particular, we design codes of length N ≤ 512 with various rates and list sizes, all of which offer at least half a dB gain over traditional PAC codes at an FER of 10−3 and improve upon state-of-the-art results.
Related
- Model selection for imperfect computer codes under discrepancy-aware calibration: application to IATE closure modelling
- Local Automorphism-Aware Syndrome Compilation for General Quantum LDPC Codes
- Design of a Family of Rate-Adaptive LDPC Convolutional Codes with Short Constraint Length
- On Almost MDS codes holding (n−k−1)-designs and an open problem on Witt design
- Efficient construction of subspace design codes over constant alphabet
BibTeX
@misc{kann2026sclaware,
title = {{An SCL-Aware Design of PAC Codes}},
author = {Tyler Kann and Shrinivas Kudekar and Matthieu R. Bloch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40512},
eprint = {2610.40512},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40512},
}
RIS
TY - UNPB
TI - An SCL-Aware Design of PAC Codes
AU - Tyler Kann
AU - Shrinivas Kudekar
AU - Matthieu R. Bloch
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40512
UR - https://arxiv.org/abs/2610.40512
AB - We develop design methodologies for the rate profile of polarization-adjusted convolutional (PAC) codes tailored to successive cancellation list (SCL) decoding. The crux of our approach is two-fold: first is the creation of a modified density evolution Gaussian approximation (DEGA), called conditional DEGA (CDEGA), to analyze the decoding process in the presence of errors; second is the creation of a dangerous-path occupancy metric to find the conditional occupancy of bit-errors in a finite list. Our approach not only illuminates the role of rate-one precoding, but also provides insight into why certain information sets are particularly well suited to PAC codes. We demonstrate the usefulness of CDEGA and dangerous-path metrics with algorithms that create new information sets, as well as precoders that are extremely sparse yet competitive. In particular, we design codes of length N ≤ 512 with various rates and list sizes, all of which offer at least half a dB gain over traditional PAC codes at an FER of 10^−3 and improve upon state-of-the-art results.
ER -