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Electronic Colloquium on Computational Complexity

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All reports by Author Klim Efremenko:

TR18-054 | 24th March 2018
Klim Efremenko, Elad Haramaty, Yael Kalai

Interactive Coding with Constant Round and Communication Blowup

Revisions: 1

The problem of constructing error-resilient interactive protocols was introduced in the seminal works of Schulman (FOCS 1992, STOC 1993). These works show how to convert any two-party interactive protocol into one that is resilient to constant-fraction of error, while blowing up the communication by only a constant factor. Since ... more >>>

TR17-162 | 26th October 2017
Klim Efremenko, Ankit Garg, Rafael Mendes de Oliveira, Avi Wigderson

Barriers for Rank Methods in Arithmetic Complexity

Arithmetic complexity, the study of the cost of computing polynomials via additions and multiplications, is considered (for many good reasons) simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic complexity than ... more >>>

TR17-093 | 22nd May 2017
Klim Efremenko, Gillat Kol, Raghuvansh Saxena

Interactive Coding Over the Noisy Broadcast Channel

A set of $n$ players, each holding a private input bit, communicate over a noisy broadcast channel. Their mutual goal is for all players to learn all inputs. At each round one of the players broadcasts a bit to all the other players, and the bit received by each player ... more >>>

TR16-086 | 29th May 2016
Noga Alon, Klim Efremenko, Benny Sudakov

Testing Equality in Communication Graphs

Revisions: 1

Let $G=(V,E)$ be a connected undirected graph with $k$ vertices. Suppose
that on each vertex of the graph there is a player having an $n$-bit
string. Each player is allowed to communicate with its neighbors according
to an agreed communication protocol, and the players must decide,
deterministically, if their inputs ... more >>>

TR15-197 | 7th December 2015
Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler

Constant-rate coding for multiparty interactive communication is impossible

We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability $\epsilon$. We analyze the minimal overhead that must be added by the coding scheme in order to succeed in performing the computation despite the noise.

Our ... more >>>

TR15-014 | 18th January 2015
Noga Alon, Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler

Reliable Communication over Highly Connected Noisy Networks

We consider the task of multiparty computation performed over networks in
the presence of random noise. Given an $n$-party protocol that takes $R$
rounds assuming noiseless communication, the goal is to find a coding
scheme that takes $R'$ rounds and computes the same function with high
probability even when the ... more >>>

TR14-007 | 17th January 2014
Mark Braverman, Klim Efremenko

List and Unique Coding for Interactive Communication in the Presence of Adversarial Noise

In this paper we extend the notion of list decoding to the setting of interactive communication and study its limits. In particular, we show that any protocol can be encoded, with a constant rate, into a list-decodable protocol which is resilient
to a noise rate of up to $1/2-\varepsilon$, ... more >>>

TR11-154 | 17th November 2011
Klim Efremenko

From Irreducible Representations to Locally Decodable Codes

Locally Decodable Code (LDC) is a code that encodes a message in a way that one can decode any particular symbol of the message by reading only a constant number of locations, even if a constant fraction of the encoded message is adversarially

In this paper we ... more >>>

TR10-134 | 23rd August 2010
Avraham Ben-Aroya, Klim Efremenko, Amnon Ta-Shma

A Note on Amplifying the Error-Tolerance of Locally Decodable Codes

Revisions: 2

We show a generic, simple way to amplify the error-tolerance of locally decodable codes.
Specifically, we show how to transform a locally decodable code that can tolerate a constant fraction of errors
to a locally decodable code that can recover from a much higher error-rate. We also show how to ... more >>>

TR10-047 | 23rd March 2010
Avraham Ben-Aroya, Klim Efremenko, Amnon Ta-Shma

Local list decoding with a constant number of queries

Revisions: 1

Recently Efremenko showed locally-decodable codes of sub-exponential
length. That result showed that these codes can handle up to
$\frac{1}{3} $ fraction of errors. In this paper we show that the
same codes can be locally unique-decoded from error rate
$\half-\alpha$ for any $\alpha>0$ and locally list-decoded from
error rate $1-\alpha$ ... more >>>

TR08-069 | 5th August 2008
Klim Efremenko

3-Query Locally Decodable Codes of Subexponential Length

Locally Decodable Codes (LDC) allow one to decode any particular
symbol of the input message by making a constant number of queries
to a codeword, even if a constant fraction of the codeword is
damaged. In recent work ~\cite{Yekhanin08} Yekhanin constructs a
$3$-query LDC with sub-exponential length of size
$\exp(\exp(O(\frac{\log ... more >>>

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