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Low-Complexity Chase Decoding of Elliptic Codes
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DOI：10.1109/TCOMM.2025.3566988.png)
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Abstract
En 中文
This paper proposes two low-complexity Chase (LCC) decoding algorithms for elliptic codes, which are realized by Kötter’s interpolation and the basis reduction (BR) interpolation, respectively. They are both developed from the perspective of computing the Gröbner bases of the interpolation modules. By identifying $\eta $ unreliable symbols, $2^{\eta } $ decoding test-vectors are formulated and the corresponding interpolation modules can be defined. The re-encoding transform (ReT) is further introduced to facilitate the interpolation. The LCC-Kötter decoding performs interpolation for the common elements, producing an intermediate outcome shared by all test-vectors. The desired Gröbner basis w.r.t. each test-vector can be obtained in a binary tree growing fashion. The new interpolation process can start from intermediate nodes of the previously interpolated paths, resulting in a low complexity. But the decoding latency cannot be contained. In contrast, the LCC-BR decoding performs the common computation in basis construction, which partly substantiates the bases for all interpolation modules. The subsequent basis construction and reduction can be performed in parallel. Besides a low complexity, it offers a latency advantage over the LCC-Kötter decoding. The decoding complexity and latency are analyzed and verified numerically. The LCC decoding performance are also presented, demonstrating their advantage over both the Guruswami-Sudan decoding and the algebraic soft decoding. Moreover, the performance advantage of elliptic codes over the Reed-Solomon (RS) codes is demonstrated.
Keywords:
Algebraic-geometric codes
chase decoding
elliptic codes
interpolation
list decoding
Journal
IF:
8.3
Papers:
1.2W
Citations:
3.6W