1 citations · 1 across the 3 of their papers we have counts for
4 papers
Tensor Reed-Muller Codes: Achieving Capacity with Quasilinear Decoding Time
Emmanuel Abbe, Colin Sandon, Oscar Sprumont
Define the codewords of the Tensor Reed-Muller code to be the evaluation vectors of all multivariate polynomials in the variables $\le…
Reed-Muller Codes for Quantum Pauli and Multiple Access Channels
Dina Abdelhadi, Colin Sandon, Emmanuel Abbe +1
Reed-Muller (RM) codes have undergone significant analytical advancements over the past decade, particularly for binary memoryless symmetric (BMS) channels. We extend the scope of…
Polynomial Freiman-Ruzsa, Reed-Muller codes and Shannon capacity
Emmanuel Abbe, Colin Sandon, Vladyslav Shashkov +1
In 1948, Shannon used a probabilistic argument to show the existence of codes achieving a maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple…
Reed-Muller codes have vanishing bit-error probability below capacity: a simple tighter proof via camellia boosting
Emmanuel Abbe, Colin Sandon
This paper shows that a class of codes such as Reed-Muller (RM) codes have vanishing bit-error probability below capacity on symmetric channels. The proof relies on the notion of `…