Reed-Muller Codes Achieve Capacity on Erasure Channels

@article{Kudekar2017ReedMullerCA,
  title={Reed-Muller Codes Achieve Capacity on Erasure Channels},
  author={Shrinivas Kudekar and Santhosh Kumar and Marco Mondelli and Henry D. Pfister and Eren Sasoglu and R{\"u}diger L. Urbanke},
  journal={IEEE Trans. Inf. Theory},
  year={2017},
  volume={63},
  pages={4298-4316}
}
We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, our method exploits code symmetry. In particular, the technique applies to any sequence of linear codes where the blocklengths are strictly increasing, the code rates converge, and the permutation group of each code is doubly transitive. In other words, we show that symmetry… 

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