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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > LOCAL DECODING:
Reports tagged with Local Decoding:
TR08-034 | 19th January 2008
Dan Gutfreund, Guy Rothblum

The Complexity of Local List Decoding

Revisions: 1

We study the complexity of locally list-decoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that computing majority over $\Theta(1/\eps)$ bits is essentially equivalent to locally list-decoding binary codes from relative distance $1/2-\eps$ with list size $\poly(1/\eps)$. That is, a local-decoder ... more >>>


TR10-067 | 14th April 2010
Sourav Chakraborty, Eldar Fischer, Arie Matsliah

Query Complexity Lower Bounds for Reconstruction of Codes

We investigate the problem of {\em local reconstruction}, as defined by Saks and Seshadhri (2008), in the context of error correcting codes.

The first problem we address is that of {\em message reconstruction}, where given oracle access to a corrupted encoding $w \in \zo^n$ of some message $x \in \zo^k$ ... more >>>


TR17-138 | 17th September 2017
Srikanth Srinivasan, Madhu Sudan

Local decoding and testing of polynomials over grids

Revisions: 1

The well-known DeMillo-Lipton-Schwartz-Zippel lemma says that $n$-variate
polynomials of total degree at most $d$ over
grids, i.e. sets of the form $A_1 \times A_2 \times \cdots \times A_n$, form
error-correcting codes (of distance at least $2^{-d}$ provided $\min_i\{|A_i|\}\geq 2$).
In this work we explore their local
decodability and local testability. ... more >>>


TR17-183 | 28th November 2017
Sivakanth Gopi, Venkatesan Guruswami, Sergey Yekhanin

On Maximally Recoverable Local Reconstruction Codes

In recent years the explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these applications. An $(n,r,h,a,q)$-LRC is a $q$-ary code, where encoding is as a ... more >>>


TR18-195 | 18th November 2018
Sofya Raskhodnikova, Noga Ron-Zewi, Nithin Varma

Erasures versus Errors in Local Decoding and Property Testing

We initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure-resilient and tolerant property testing. Local decoding in the presence of errors has been extensively studied, but has not been considered explicitly in the presence of erasures.

Motivated by ... more >>>




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