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Electronic Colloquium on Computational Complexity

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Reports tagged with List Recovery:
TR07-109 | 7th October 2007
Venkatesan Guruswami, Atri Rudra

Better Binary List-Decodable Codes via Multilevel Concatenation

We give a polynomial time construction of binary codes with the best
currently known trade-off between rate and error-correction
radius. Specifically, we obtain linear codes over fixed alphabets
that can be list decoded in polynomial time up to the so called
Blokh-Zyablov bound. Our work ... more >>>

TR08-054 | 13th May 2008
Venkatesan Guruswami, Atri Rudra

Concatenated codes can achieve list-decoding capacity

We prove that binary linear concatenated codes with an outer algebraic code (specifically, a folded Reed-Solomon code) and independently and randomly chosen linear inner codes achieve the list-decoding capacity with high probability. In particular, for any $0 < \rho < 1/2$ and $\epsilon > 0$, there exist concatenated codes of ... more >>>

TR19-080 | 1st June 2019
Swastik Kopparty, Nicolas Resch, Noga Ron-Zewi, Shubhangi Saraf, Shashwat Silas

On List Recovery of High-Rate Tensor Codes

We continue the study of list recovery properties of high-rate tensor codes, initiated by Hemenway, Ron-Zewi, and Wootters (FOCS'17). In that work it was shown that the tensor product of an efficient (poly-time) high-rate globally list recoverable code is {\em approximately} locally list recoverable, as well as globally list recoverable ... more >>>

TR19-099 | 29th July 2019
Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman

Nearly Optimal Pseudorandomness From Hardness

Revisions: 3

Existing proofs that deduce $\mathbf{BPP}=\mathbf{P}$ from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with little slowdown. Specifically, assuming exponential lower bounds against nondeterministic circuits, we convert any randomized algorithm over inputs of length $n$ running in ... more >>>

TR20-070 | 4th May 2020
Ben Lund, Aditya Potukuchi

On the list recoverability of randomly punctured codes

Revisions: 1

We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound.
In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound.
It was previously known that there are Reed-Solomon codes that do not have this ... more >>>

TR20-162 | 7th November 2020
Dean Doron, Mary Wootters

High-Probability List-Recovery, and Applications to Heavy Hitters

Revisions: 2

An error correcting code $\mathcal{C} \colon \Sigma^k \to \Sigma^n$ is list-recoverable from input list size $\ell$ if for any sets $\mathcal{L}_1, \ldots, \mathcal{L}_n \subseteq \Sigma$ of size at most $\ell$, one can efficiently recover the list $\mathcal{L} = \{ x \in \Sigma^k : \forall j \in [n], \mathcal{C}(x)_j \in \mathcal{L}_j ... more >>>

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