Swastik Kopparty

Learn More
The fairness and throughput of TCP suffer when it is used in mobile ad hoc networks. This is a direct consequence of TCP wrongly attributing packet losses due to link failures (a consequence of mobility) to congestion. While this problem causes an overall degradation of throughput, it especially affects connections with a large number of hops, where link(More)
Locally decodable codes are error-correcting codes that admit efficient decoding algorithms; any bit of the original message can be recovered by looking at only a small number of locations of a corrupted codeword. The tradeoff between the rate of a code and the locality/efficiency of its decoding algorithms has been well studied, and it has widely been(More)
We consider the problem of testing if a given function $f : \F_2^n \right arrow \F_2$ is close to any degree $d$ polynomial in $n$ variables, also known as the Reed-Muller testing problem. %The Gowers norm is based on a natural $2^{d+1}$-query test for this property. Alon et al.~\cite{AKKLR} proposed and analyzed a natural $2^{d+1}$-query test for(More)
An affine disperser over F<sub>2</sub><sup>n</sup> for sources of dimension d is a function f: F<sub>2</sub><sup>n</sup> &#8594; F<sub>2</sub> such that for any affine space S &#8838; F<sub>2</sub><sup>n</sup> of dimension at least d, we have {f(s) : s in S} = F<sub>2</sub>. Affine dispersers have been considered in the context of deterministic extraction(More)
The Internet’s current interdomain routing protocol, BGP (Border Gateway Protocol), has two modes of operation: eBGP (external BGP), used to exchange routing information between autonomous systems, and iBGP (internal BGP), used to propagate that information within an autonomous system (AS). In a “full mesh” iBGP configuration, every router has a BGP session(More)
In this paper, we give surprisingly efficient algorithms for list-decoding and testing <i>random</i> linear codes. Our main result is that random sparse linear codes are locally list-decodable and locally testable in the <i>high-error</i> regime with only a <i>constant</i> number of queries. More precisely, we show that for all constants c&gt; 0 and &#947;(More)
We extend the "method of multiplicities" to get the following results, of interest in combinatorics and randomness extraction. (A) We show that every Kakeya set (a set of points that contains a line in every direction) in $\F_q^n$ must be of size at least $q^n/2^n$. This bound is tight to within a $2 + o(1)$ factor for every $n$ as $q \to \infty$, compared(More)
We study the list-decodability of multiplicity codes. These codes, which are based on evaluations of high-degree polynomials and their derivatives, have rate approaching 1 while simultaneously allowing for sublinear-time error-correction. In this paper, we show that multiplicity codes also admit powerful list-decoding and local list-decoding algorithms(More)