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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > AMEYA VELINGKER:
All reports by Author Ameya Velingker:

TR16-090 | 27th May 2016
Bernhard Haeupler, Ameya Velingker

Bridging the Capacity Gap Between Interactive and One-Way Communication

We study the communication rate of coding schemes for interactive communication that transform any two-party interactive protocol into a protocol that is robust to noise.

Recently, Haeupler (FOCS '14) showed that if an $\epsilon > 0$ fraction of transmissions are corrupted, adversarially or randomly, then it is possible to ... more >>>


TR14-165 | 3rd December 2014
Venkatesan Guruswami, Ameya Velingker

An Entropy Sumset Inequality and Polynomially Fast Convergence to Shannon Capacity Over All Alphabets

We prove a lower estimate on the increase in entropy when two copies of a conditional random variable $X | Y$, with $X$ supported on $\mathbb{Z}_q=\{0,1,\dots,q-1\}$ for prime $q$, are summed modulo $q$. Specifically, given two i.i.d. copies $(X_1,Y_1)$ and $(X_2,Y_2)$ of a pair of random variables $(X,Y)$, with $X$ ... more >>>


TR14-067 | 4th May 2014
Venkatesan Guruswami, Madhu Sudan, Ameya Velingker, Carol Wang

Limitations on Testable Affine-Invariant Codes in the High-Rate Regime

Locally testable codes (LTCs) of constant distance that allow the tester to make a linear number of queries have become the focus of attention recently, due to their elegant connections to hardness of approximation. In particular, the binary Reed-Muller code of block length $N$ and distance $d$ is known to ... more >>>


TR12-082 | 28th June 2012
Mahdi Cheraghchi, Venkatesan Guruswami, Ameya Velingker

Restricted Isometry of Fourier Matrices and List Decodability of Random Linear Codes

We prove that a random linear code over $\mathbb{F}_q$, with probability arbitrarily close to $1$, is list decodable at radius $1-1/q-\epsilon$ with list size $L=O(1/\epsilon^2)$ and rate $R=\Omega_q(\epsilon^2/(\log^3(1/\epsilon)))$. Up to the polylogarithmic factor in $1/\epsilon$ and constant factors depending on $q$, this matches the lower bound $L=\Omega_q(1/\epsilon^2)$ for the list ... more >>>




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