| Paper ID | D2-S1-T2.3 |
| Paper Title |
Algebraic Soft Decoding of Elliptic Codes |
| Authors |
Yunqi Wan, Li Chen, Fangguo Zhang, Sun Yat-sen University, China |
| Session |
D2-S1-T2: Algebraic Geometry Codes |
| Chaired Session: |
Tuesday, 13 July, 22:00 - 22:20 |
| Engagement Session: |
Tuesday, 13 July, 22:20 - 22:40 |
| Abstract |
This paper proposes algebraic soft decoding (ASD) for one-point elliptic codes, where the interpolation is realized through the perspective of obtaining a Gröbner basis. The desired interpolation polynomial $Q(x, y, z)$ is the minimum candidate in the Gröbner basis. This work shows how to obtain such a Gröbner basis. Based on an interpolation multiplicity matrix $M$, an interpolation ideal $I_M$ can be defined. With a predefined decoding output list size (OLS) $l$ $(l ≥ \deg_z{Q})$, an equivalent interpolation module $I_M$, $l$ can be led to. By further defining the Lagrange interpolation functions, a basis of the interpolation module can be constructed. The desired Gröbner basis can be obtained by reducing the module basis. Finally, the decoding complexity is also analyzed.
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