Improved code design boosts error correction with list decoding
An SCL-Aware Design of PAC Codes
Information Theory
Summary
Error-correcting codes help reliable data transmission by fixing mistakes during sending. The authors develop a new way to design a special kind of code called PAC codes that are better matched to a decoding method known as successive cancellation list (SCL) decoding. They create new tools to analyze which bits tend to cause errors and use this knowledge to build better codes that correct mistakes more effectively. Their designs outperform traditional PAC codes in tests, showing clearer advantages at common error levels.
What this means in practice
- •For communications engineers: Design more efficient error-correcting codes that improve data reliability in communication systems using finite list decoding.
- •For embedded system developers: Implement sparse precoders for error correction in limited-resource devices, improving decoding performance without adding complexity.
Authors
Tyler Kann, Shrinivas Kudekar, Matthieu R. Bloch
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 $N \leq 512$ 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.