Entropic Bounds on the Average Length of Codes with a Space

TL;DR

This paper introduces a linear-time algorithm for constructing nearly optimal prefix-free codes that include a space symbol only at the end of codewords, with bounds related to source entropy.

Contribution

It presents a novel algorithm for space-constrained prefix-free codes and establishes bounds linking code length to source entropy.

Findings

Constructed codes differ from optimal by at most one in average length.

Established bounds on average code length based on source entropy.

Linked space-constrained codes to one-to-one codes.

Abstract

We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that their average length differs from the minimum possible by at most one. We obtain our results by uncovering a relation between our class of codes and the class of one-to-one codes. Additionally, we derive upper and lower bounds to the average length of optimal prefix-free codes with a space in terms of the source entropy.