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Recursive Decoding and Its Performance for Low-Rate Reed-Muller Codes (1703.05306v1)
Published 14 Mar 2017 in cs.IT and math.IT
Abstract: Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to $n(1/2-\varepsilon)$ given that $\varepsilon$ exceeds $n{-1/2{r}}.$ This improves the asymptotic bounds known for decoding RM codes with nonexponential complexity.