Low-Memory Adaptive Prefix Coding

TL;DR

This paper introduces an online adaptive prefix coding algorithm that efficiently encodes large alphabet strings using minimal memory and fast encoding time, improving scalability for large data sets.

Contribution

It presents a novel online prefix coding algorithm that operates with sublinear space relative to alphabet size and guarantees worst-case encoding time per symbol.

Findings

Uses $O(\sigma^{1 / \lambda + \epsilon})$ bits of space

Encodes in $O(\log \log \sigma)$ time per symbol

Achieves near-optimal encoding length with bounded redundancy

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.