On decoding hyperbolic codes
Eduardo Camps-Moreno, Ignacio Garc\'ia-Marco, Hiram H. L\'opez, and Irene M\'arquez-Corbella, Edgar Mart\'inez-Moro, Eliseo Sarmiento
TL;DR
This paper explores decoding algorithms for hyperbolic codes, utilizing Reed-Muller codes and cube codes, and adapts list decoding techniques to improve decoding performance.
Contribution
It introduces new decoding algorithms for hyperbolic codes based on Reed-Muller and Cube codes, and extends Sudan's list decoding to hyperbolic codes.
Findings
Decoding hyperbolic codes via Reed-Muller codes is effective.
Comparison shows hyperbolic codes have advantages over Cube codes.
Adapted list decoding improves error correction capabilities.
Abstract
This work studies several decoding algorithms for hyperbolic codes. We use some previous ideas to describe how to decode a hyperbolic code using the largest Reed-Muller code contained in it or using the smallest Reed-Muller code that contains it. A combination of these two algorithms is proposed when hyperbolic codes are defined by polynomials in two variables. Then, we compare hyperbolic codes and Cube codes (tensor product of Reed-Solomon codes) and propose decoding algorithms of hyperbolic codes based on their closest Cube codes. Finally, we adapt to hyperbolic codes the Geil and Matsumoto's generalization of Sudan's list decoding algorithm.
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · graph theory and CDMA systems