Successive Cancellation List Decoding of Extended Reed-Solomon Codes

2026-01-30

AI Summary

This work investigates efficient high-performance list decoding of extended Reed–Solomon (RS) codes over finite fields of characteristic two. To this end, the authors propose a novel transformation that reinterprets extended RS codes as equivalent binary polar codes via a pre-transformation matrix, thereby enabling their integration— for the first time—into the successive cancellation list (SCL) decoding framework. This approach innovatively bridges the decoding mechanisms of RS and polar codes. Theoretical analysis reveals that the column-wise linear independence of the pre-transformation matrix critically influences the performance of successive cancellation (SC) decoding. Numerical experiments confirm that the proposed architecture achieves reliable and efficient decoding of extended RS codes over \( \mathbb{F}_{2^n} \).

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Feature Construction/Reformulation
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to their distance property of reaching the Singleton bound, being the maximum distance separable (MDS) codes. This paper proposes a new list decoding for extended RS (eRS) codes defined over a finite field of characteristic two, i.e., F_{2^n}. It is developed based on transforming an eRS code into n binary polar codes. Consequently, it can be decoded by the successive cancellation (SC) decoding and further their list decoding, i.e., the SCL decoding. A pre-transformed matrix is required for reinterpretating the eRS codes, which also determines their SC and SCL decoding performances. Its column linear independence property is studied, leading to theoretical characterization of their SC decoding performance. Our proposed decoding and analysis are validated numerically.

Problem

• Reed-Solomon codes
• list decoding
• extended RS codes
• finite field
• error-correction

Innovation

• Extended Reed-Solomon codes
• Successive Cancellation List Decoding
• Polar Codes
• Pre-transformed Matrix
• Finite Field Characteristic Two