The Re-encoding Transform in Algebraic List Decoding of Algebraic Geometric Codes
- Resource Type
- Conference
- Authors
- Wan, Yunqi; Xing, Jiongyue; Huang, Yuliang; Wu, Tingyi; Bai, Bo; Zhang, Gong
- Source
- 2023 IEEE International Symposium on Information Theory (ISIT) Information Theory (ISIT), 2023 IEEE International Symposium on. :19-24 Jun, 2023
- Subject
- Communication, Networking and Broadcast Technologies
Computing and Processing
Signal Processing and Analysis
Reed-Solomon codes
Interpolation
Codes
Simulation
Transforms
Decoding
Complexity theory
Algebraic geometric codes
interpolation
list decoding
re-encoding transform
- Language
- ISSN
- 2157-8117
This paper proposes the re-encoding transformed (ReT) based list decoding using the module basis reduction (BR) interpolation for algebraic geometric (AG) codes on C ab curves. The two ReT approaches are introduced to facilitate the BR interpolation. One is realized by the bivariate Lagrange polynomial. The other is conducted by the ReT of Reed-Solomon (RS) codes based on the mathematical structure of AG codes. The ReT based BR interpolation (ReT-BR) algorithm for decoding the AG codes is further introduced. Finally, complexity of the proposed algorithm is analyzed and validated by the simulation results, demonstrating its complexity advantage over the non-ReT counterpart.