Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

Reports tagged with Combinatorial list decoding:
TR09-013 | 4th February 2009
Atri Rudra

Limits to List Decoding Random Codes

It has been known since [Zyablov and Pinsker 1982] that a random $q$-ary code of rate $1-H_q(\rho)-\eps$ (where $0<\rho<1-1/q$, $\eps>0$ and $H_q(\cdot)$ is the $q$-ary entropy function) with high probability is a $(\rho,1/\eps)$-list decodable code. (That is, every Hamming ball of radius at most $\rho n$ has at most $1/\eps$ ... more >>>

TR12-082 | 28th June 2012
Mahdi Cheraghchi, Venkatesan Guruswami, Ameya Velingker

Restricted Isometry of Fourier Matrices and List Decodability of Random Linear Codes

We prove that a random linear code over $\mathbb{F}_q$, with probability arbitrarily close to $1$, is list decodable at radius $1-1/q-\epsilon$ with list size $L=O(1/\epsilon^2)$ and rate $R=\Omega_q(\epsilon^2/(\log^3(1/\epsilon)))$. Up to the polylogarithmic factor in $1/\epsilon$ and constant factors depending on $q$, this matches the lower bound $L=\Omega_q(1/\epsilon^2)$ for the list ... more >>>

ISSN 1433-8092 | Imprint