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Electronic Colloquium on Computational Complexity

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Reports tagged with capacity-achieving codes:
TR19-154 | 6th November 2019
Venkatesan Guruswami, Andrii Riazanov, Min Ye

Ar?kan meets Shannon: Polar codes with near-optimal convergence to channel capacity

Revisions: 3

Let $W$ be a binary-input memoryless symmetric (BMS) channel with Shannon capacity $I(W)$ and fix any $\alpha > 0$. We construct, for any sufficiently small $\delta > 0$, binary linear codes of block length $O(1/\delta^{2+\alpha})$ and rate $I(W)-\delta$ that enable reliable communication on $W$ with quasi-linear time encoding and decoding. ... more >>>

TR22-075 | 21st May 2022
Siddharth Bhandari, Prahladh Harsha, Ramprasad Saptharishi, Srikanth Srinivasan

Vanishing Spaces of Random Sets and Applications to Reed-Muller Codes

Revisions: 1

We study the following natural question on random sets of points in $\mathbb{F}_2^m$:

Given a random set of $k$ points $Z=\{z_1, z_2, \dots, z_k\} \subseteq \mathbb{F}_2^m$, what is the dimension of the space of degree at most $r$ multilinear polynomials that vanish on all points in $Z$?

We ... more >>>

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