Improved Construction of Robust Gray Codes
2024 IEEE International Symposium on Information Theory (ISIT)(2024)
摘要
A robust Gray code, formally introduced by (Lolck and Pagh, SODA 2024), is a Gray code that additionally has the property that, given a noisy version of the encoding of an integer
$j$
, it is possible to reconstruct
$\hat{j}$
so that
$\vert j-\hat{j}\vert$
is small with high probability. That work presented a transformation that transforms a binary code
$\mathcal{C}$
of rate
$R$
to a robust Gray code with rate
$\Omega(R)$
, where the constant in the
$\Omega(\cdot)$
can be at most 1/4. We improve upon their construction by presenting a transformation from a (linear) binary code
$\mathcal{C}$
to a robust Gray code with similar robustness guarantees, but with rate that can approach
$R/2$
. A full version of this paper can be found in [1].
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关键词
Gray Code,High Probability,Binary Code,Can Approach,Running Time,Noise Vector,Codeword,Substring,String Length,Decoding Algorithm
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