# 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…

## 7 Citations

Reed–Muller Codes Achieve Capacity on Erasure Channels

- Computer ScienceIEEE Transactions on Information Theory
- 2017

This work shows that symmetry alone implies near-optimal performance in 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.

On locality of Generalized Reed-Muller codes over the broadcast erasure channel

- Computer Science2016 IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB)
- 2016

The purpose is to investigate the use of Generalized Reed Muller codes and the value of their locality property in their progressive decoding for Broadcast/Multicast communication schemes with real time video delivery.

Polar Subcodes

- Computer ScienceIEEE Journal on Selected Areas in Communications
- 2016

An extension of polar codes is proposed, which allows some of the frozen symbols, called dynamic frozen symbol, to be data-dependent, and is shown to outperform LDPC and turbo codes, as well as polar codes with CRC.

Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel

- Computer ScienceIEEE Transactions on Information Theory
- 2019

This paper shows that the result of Delfosse et al is tight: one can construct capacity approaching codes with weight almost almost as much as the capacity itself.

Evolution of the McEliece Public Key Encryption Scheme

- Computer Science, MathematicsSECITC
- 2017

This article analyzes the evolution of the main encryption variants coming from the Rank based cryptography and stresses out the main security issues and point out some new ideas coming from this field.

On codes decoding a constant fraction of errors on the BSC

- Computer ScienceSTOC
- 2021

It is shown that a linear code that is successful on the BEC can also decode over a range of binary memoryless symmetric (BMS) channels and it is proved that a Reed–Muller code of positive rate R decodes errors on the p with high probability if p < 1/2 − √2−R(1−2− R).

Towards a Proof of the Fourier-Entropy Conjecture?

- MathematicsGeometric and Functional Analysis
- 2020

A new concentration result on the Fourier spectrum of Boolean functions with small total influence implies that the class of functions whose total influence is at most $K$ is agnostically learnable in time $2^{O(K\log K)}$, using membership queries.

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