Multichannel Optimal Tree-Decodable Codes are Not Always Optimal Prefix Codes
Abstract
The theory of multichannel prefix codes aims to generalize the classical theory of prefix codes. Although single- and two-channel prefix codes always have decoding trees, the same cannot be said when there are more than two channels. One question is of theoretical interest: Do there exist optimal tree-decodable codes that are not optimal prefix codes? Existing literature, which focused on generalizing single-channel results, covered little about non-tree-decodable prefix codes since they have no single-channel counterparts. In this work, we study the fundamental reason behind the non-tree-decodability of prefix codes. By investigating the simplest non-tree-decodable structure, we obtain a general sufficient condition on the channel alphabets for the existence of optimal tree-decodable codes that are not optimal prefix codes.
Keywords
Cite
@article{arxiv.2205.05122,
title = {Multichannel Optimal Tree-Decodable Codes are Not Always Optimal Prefix Codes},
author = {Hoover H. F. Yin and Harry W. H. Wong and Mehrdad Tahernia and Russell W. F. Lai},
journal= {arXiv preprint arXiv:2205.05122},
year = {2022}
}
Comments
Full version of the conference version in ISIT'22