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Electronic Colloquium on Computational Complexity

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Reports tagged with erasure codes:
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 >>>

TR18-065 | 8th April 2018
Avraham Ben-Aroya, Dean Doron, Amnon Ta-Shma

Near-Optimal Strong Dispersers, Erasure List-Decodable Codes and Friends

Revisions: 1

A code $\mathcal{C}$ is $(1-\tau,L)$ erasure list-decodable if for every codeword $w$, after erasing any $1-\tau$ fraction of the symbols of $w$,
the remaining $\tau$-fraction of its symbols have at most $L$ possible completions into codewords of $\mathcal{C}$.
Non-explicitly, there exist binary $(1-\tau,L)$ erasure list-decodable codes having rate $O(\tau)$ and ... more >>>

TR19-005 | 16th January 2019
Omar Alrabiah, Venkatesan Guruswami

An Exponential Lower Bound on the Sub-Packetization of MSR Codes

An $(n,k,\ell)$-vector MDS code is a $\mathbb{F}$-linear subspace of $(\mathbb{F}^\ell)^n$ (for some field $\mathbb{F}$) of dimension $k\ell$, such that any $k$ (vector) symbols of the codeword suffice to determine the remaining $r=n-k$ (vector) symbols. The length $\ell$ of each codeword symbol is called the sub-packetization of the code. Such a ... more >>>

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