Error-Correction Capability of Reed-Muller codes
St\'ephanie Dib (I2M), Fran\c{c}ois Rodier (I2M)
TL;DR
This paper establishes a theoretical asymptotic boundary distinguishing correctable from uncorrectable errors in Reed-Muller codes, independent of decoding algorithms, providing fundamental insights into their error-correction limits.
Contribution
It introduces a theoretical asymptotic limit for error correction in Reed-Muller codes that applies universally, regardless of decoding method.
Findings
Defines an asymptotic error correction boundary for Reed-Muller codes
Independent of decoding algorithms, providing fundamental limits
Enhances understanding of Reed-Muller codes' error-correcting capabilities
Abstract
We present an asymptotic limit between correctable and uncor-rectable errors on the Reed-Muller codes of any order. This limit is theoretical and does not depend of any decoding algorithm.
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Taxonomy
TopicsCoding theory and cryptography · Error Correcting Code Techniques · Advanced Wireless Communication Techniques