Low-Memory Adaptive Prefix Coding

T. Gagie, Marek Karpinski, Yakov Nekrich
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引用次数: 2

Abstract

In this paper we study the adaptive prefix coding problem in  cases where the size of the input alphabet is large.  We present an online prefix coding algorithm that uses  $O(\sigma^{1 / \lambda + \epsilon}) $ bits of space for any constants $\eps≫0$, $\lambda≫1$, and encodes the string of symbols in  $O(\log \log \sigma)$ time per symbol  \emph{in the worst case}, where $\sigma$ is  the size of the alphabet.  The upper bound on the encoding length is  $\lambda n H (s) +(\lambda / \ln 2 + 2 + \epsilon) n +  O (\sigma^{1 / \lambda} \log^2 \sigma)$ bits.
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低内存自适应前缀编码
本文研究了输入字母较大情况下的自适应前缀编码问题。我们提出了一种在线前缀编码算法,该算法对任何常量$\eps≫0$、$\lambda≫1$使用$O(\sigma^{1 / \lambda + \epsilon}) $位空间,并且在\emph{最坏的情况下},以$O(\log \log \sigma)$时间对每个符号进行编码,其中$\sigma$是字母表的大小。编码长度的上限是$\lambda n H (s) +(\lambda / \ln 2 + 2 + \epsilon) n +  O (\sigma^{1 / \lambda} \log^2 \sigma)$位。
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